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INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
robot (noun) hellip
What is a robot
Jacques de VaucansonJacques de Vaucanson(1709-1782)(1709-1782)
bull Master toy maker who won the heart of Europe
bull Flair for inventing the mechanical revealed itself early in life
bull He was impressed by the uniform motion of the pendulum of the clock in his parents hall
bull Soon he was making his own clock movements
The Origins of Robots
Mechanical horse
Pre-History of Real-World Pre-History of Real-World RobotsRobots
bull The earliest remote control vehicles were built by Nikola Tesla in the 1890s
bull Tesla is best known as the inventor of AC power induction motors Tesla coils and other electrical devices
Robots Robots of the of the mediamedia
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
robot (noun) hellip
What is a robot
Jacques de VaucansonJacques de Vaucanson(1709-1782)(1709-1782)
bull Master toy maker who won the heart of Europe
bull Flair for inventing the mechanical revealed itself early in life
bull He was impressed by the uniform motion of the pendulum of the clock in his parents hall
bull Soon he was making his own clock movements
The Origins of Robots
Mechanical horse
Pre-History of Real-World Pre-History of Real-World RobotsRobots
bull The earliest remote control vehicles were built by Nikola Tesla in the 1890s
bull Tesla is best known as the inventor of AC power induction motors Tesla coils and other electrical devices
Robots Robots of the of the mediamedia
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Jacques de VaucansonJacques de Vaucanson(1709-1782)(1709-1782)
bull Master toy maker who won the heart of Europe
bull Flair for inventing the mechanical revealed itself early in life
bull He was impressed by the uniform motion of the pendulum of the clock in his parents hall
bull Soon he was making his own clock movements
The Origins of Robots
Mechanical horse
Pre-History of Real-World Pre-History of Real-World RobotsRobots
bull The earliest remote control vehicles were built by Nikola Tesla in the 1890s
bull Tesla is best known as the inventor of AC power induction motors Tesla coils and other electrical devices
Robots Robots of the of the mediamedia
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The Origins of Robots
Mechanical horse
Pre-History of Real-World Pre-History of Real-World RobotsRobots
bull The earliest remote control vehicles were built by Nikola Tesla in the 1890s
bull Tesla is best known as the inventor of AC power induction motors Tesla coils and other electrical devices
Robots Robots of the of the mediamedia
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Mechanical horse
Pre-History of Real-World Pre-History of Real-World RobotsRobots
bull The earliest remote control vehicles were built by Nikola Tesla in the 1890s
bull Tesla is best known as the inventor of AC power induction motors Tesla coils and other electrical devices
Robots Robots of the of the mediamedia
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Pre-History of Real-World Pre-History of Real-World RobotsRobots
bull The earliest remote control vehicles were built by Nikola Tesla in the 1890s
bull Tesla is best known as the inventor of AC power induction motors Tesla coils and other electrical devices
Robots Robots of the of the mediamedia
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Robots Robots of the of the mediamedia
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
History of RoboticsHistory of Robotics
RUR Metropolis(1927) Forbidden planet(1956) 2001 A Space Odyssey(1968) Logans Run(1976) Aliens(1986)
Popular culture influenced by these ideas
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The US military contracted the walking truck to be built by the
General Electric Company for the US
Army in 1969
Walking robotsWalking robots
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Unmanned Ground Vehiclesbull Three categories
ndash Mobilendash Humanoidanimalndash Motes
bull Famous examplesndash DARPA Grand Challengendash NASA MERndash Roombandash Honda P3 Sony Asimondash Sony Aibo
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Unmanned Aerial Vehicles
bull Three categoriesndash Fixed wingndash VTOLndash Micro aerial vehicle (MAV)
which can be either fixed wing or VTOL
bull Famous examplesndash Global Hawkndash Predatorndash UCAV
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Autonomous Underwater Vehiclesbull Categories
ndash Remotely operated vehicles (ROVs) which are tethered
ndash Autonomous underwater vehicles which are free swimming
bull Examplesndash Persephonendash Jason (Titanic)ndash Hugin
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Discussion of Ethics and Philosophy in Robotics
bull Can robots become consciousbull Is there a problem with using robots in military
applicationsbull How can we ensure that robots do not harm
peoplebull Isaac Asimovrsquos Three Laws of Robotics
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Isaac Asimov and Joe Isaac Asimov and Joe EnglebergerEngleberger
bull Two fathers of robotics
bull Engleberger built first robotic arms
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Asimovrsquos Laws of RoboticsFirst law (Human safety)A robot may not injure a human being or through inaction allowa human being to come to harm
Second law (Robots are slaves)A robot must obey orders given it by human beings except wheresuch orders would conflict with the First Law
Third law (Robot survival)A robot must protect its own existence as long as such protectiondoes not conflict with the First or Second Law
These laws are simple and straightforward and they embrace the essential guiding principles of a good many of the worldrsquos ethical systems
ndash But They are extremely difficult to implement
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The Advent of Industrial Robots -
Robot ArmsRobot Arms
bull There is a lot of motivation to use robots to perform task which would otherwise be performed by humansndash Safety
ndash Efficiency
ndash Reliability
ndash Worker Redeployment
ndash Cheaper
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Industrial Robot DefinedA general-purpose programmable machine possessing
certain anthropomorphic characteristicsbull Hazardous work environmentsbull Repetitive work cyclebull Consistency and accuracybull Difficult handling task for humansbull Multishift operationsbull Reprogrammable flexiblebull Interfaced to other computer systems
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
What are robots made of
bullEffectors Manipulation
Degrees of Freedom
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Robot Anatomybull Manipulator consists of joints and links
ndash Joints provide relative motionndash Links are rigid members between jointsndash Various joint types linear and rotaryndash Each joint provides a ldquodegree-of-freedomrdquondash Most robots possess five or six degrees-of-
freedombull Robot manipulator consists of two sections
ndash Body-and-arm ndash for positioning of objects in the robots work volume
ndash Wrist assembly ndash for orientation of objects
BaseLink0
Joint1
Link2
Link3Joint3
End of Arm
Link1
Joint2
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Manipulator Joints
bull Translational motionndash Linear joint (type L)ndash Orthogonal joint (type O)
bull Rotary motionndash Rotational joint (type R) ndash Twisting joint (type T)ndash Revolving joint (type V)
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Polar Coordinate Body-and-Arm Assembly
bull Notation TRL
bull Consists of a sliding arm (L joint) actuated relative to the body which can rotate about both a vertical axis (T joint) and horizontal axis (R joint)
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Cylindrical Body-and-Arm Assembly
bull Notation TLO
bull Consists of a vertical column relative to which an arm assembly is moved up or down
bull The arm can be moved in or out relative to the column
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Cartesian Coordinate Body-and-Arm Assembly
bull Notation LOO
bull Consists of three sliding joints two of which are orthogonal
bull Other names include rectilinear robot and x-y-z robot
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Jointed-Arm Robot
bull Notation TRR
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
SCARA Robotbull Notation VRObull SCARA stands for
Selectively Compliant Assembly Robot Arm
bull Similar to jointed-arm robot except that vertical axes are used for shoulder and elbow joints to be compliant in horizontal direction for vertical insertion tasks
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Wrist Configurationsbull Wrist assembly is attached to end-of-arm
bull End effector is attached to wrist assembly
bull Function of wrist assembly is to orient end effector ndash Body-and-arm determines global position of end effector
bull Two or three degrees of freedomndash Roll
ndash Pitch
ndash Yaw
bull Notation RRT
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
An Introduction to Robot Kinematics
Renata Melamud
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Kinematics studies the motion of bodies
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
An Example - The PUMA 560
The PUMA 560 has SIX revolute jointsA revolute joint has ONE degree of freedom ( 1 DOF) that is defined by its angle
1
23
4
There are two more joints on the end effector (the gripper)
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Other basic joints
Spherical Joint3 DOF ( Variables - 1 2 3)
Revolute Joint1 DOF ( Variable - )
Prismatic Joint1 DOF (linear) (Variables - d)
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
We are interested in two kinematics topics
Forward Kinematics (angles to position)What you are given The length of each link
The angle of each joint
What you can find The position of any point (ie itrsquos (x y z) coordinates
Inverse Kinematics (position to angles)What you are given The length of each link
The position of some point on the robot
What you can find The angles of each joint needed to obtain that position
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Quick Math ReviewDot Product Geometric Representation
A
Bθ
cosθBABA
Unit VectorVector in the direction of a chosen vector but whose magnitude is 1
B
BuB
y
x
a
a
y
x
b
b
Matrix Representation
yyxxy
x
y
xbaba
b
b
a
aBA
B
Bu
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Quick Matrix Review
Matrix Multiplication
An (m x n) matrix A and an (n x p) matrix B can be multiplied since the number of columns of A is equal to the number of rows of B
Non-Commutative MultiplicationAB is NOT equal to BA
dhcfdgce
bhafbgae
hg
fe
dc
ba
Matrix Addition
hdgc
fbea
hg
fe
dc
ba
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Basic TransformationsMoving Between Coordinate Frames
Translation Along the X-Axis
N
O
X
Y
VNO
VXY
Px
VN
VO
Px = distance between the XY and NO coordinate planes
Y
XXY
V
VV
O
NNO
V
VV
0
PP x
P
(VNVO)
Notation
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
NX
VNO
VXY
PVN
VO
Y O
NO
O
NXXY VPV
VPV
Writing in terms of XYV NOV
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
X
VXY
PXY
N
VNO
VN
VO
O
Y
Translation along the X-Axis and Y-Axis
O
Y
NXNOXY
VP
VPVPV
Y
xXY
P
PP
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
oV
nV
θ)cos(90V
cosθV
sinθV
cosθV
V
VV
NO
NO
NO
NO
NO
NO
O
NNO
NOV
o
n Unit vector along the N-Axis
Unit vector along the N-Axis
Magnitude of the VNO vector
Using Basis VectorsBasis vectors are unit vectors that point along a coordinate axis
N
VNO
VN
VO
O
n
o
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Rotation (around the Z-Axis)X
Y
Z
X
Y
N
VN
VO
O
V
VX
VY
Y
XXY
V
VV
O
NNO
V
VV
= Angle of rotation between the XY and NO coordinate axis
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
X
Y
N
VN
VO
O
V
VX
VY
Unit vector along X-Axis
x
xVcosαVcosαVV NONOXYX
NOXY VV
Can be considered with respect to the XY coordinates or NO coordinates
V
x)oVn(VV ONX (Substituting for VNO using the N and O components of the vector)
)oxVnxVV ONX ()(
))
)
(sinθV(cosθV
90))(cos(θV(cosθVON
ON
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Similarlyhellip
yVα)cos(90VsinαVV NONONOY
y)oVn(VV ONY
)oy(V)ny(VV ONY
))
)
(cosθV(sinθV
(cosθVθ))(cos(90VON
ON
Sohellip
)) (cosθV(sinθVV ONY )) (sinθV(cosθVV ONX
Y
XXY
V
VV
Written in Matrix Form
O
N
Y
XXY
V
V
cosθsinθ
sinθcosθ
V
VV
Rotation Matrix about the z-axis
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
X1
Y1
N
O
VXY
X0
Y0
VNO
P
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
(VNVO)
In other words knowing the coordinates of a point (VNVO) in some coordinate frame (NO) you can find the position of that point relative to your original coordinate frame (X0Y0)
(Note Px Py are relative to the original coordinate frame Translation followed by rotation is different than rotation followed by translation)
Translation along P followed by rotation by
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
O
N
y
x
Y
XXY
V
V
cosθsinθ
sinθcosθ
P
P
V
VV
HOMOGENEOUS REPRESENTATIONPutting it all into a Matrix
1
V
V
100
0cosθsinθ
0sinθcosθ
1
P
P
1
V
VO
N
y
xY
X
1
V
V
100
Pcosθsinθ
Psinθcosθ
1
V
VO
N
y
xY
X
What we found by doing a translation and a rotation
Padding with 0rsquos and 1rsquos
Simplifying into a matrix form
100
Pcosθsinθ
Psinθcosθ
H y
x
Homogenous Matrix for a Translation in XY plane followed by a Rotation around the z-axis
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Rotation Matrices in 3D ndash OKlets return from homogenous repn
100
0cosθsinθ
0sinθcosθ
R z
cosθ0sinθ
010
sinθ0cosθ
Ry
cosθsinθ0
sinθcosθ0
001
R z
Rotation around the Z-Axis
Rotation around the Y-Axis
Rotation around the X-Axis
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
1000
0aon
0aon
0aon
Hzzz
yyy
xxx
Homogeneous Matrices in 3D
H is a 4x4 matrix that can describe a translation rotation or both in one matrix
Translation without rotation
1000
P100
P010
P001
Hz
y
x
P
Y
X
Z
Y
X
Z
O
N
A
O
N
ARotation without translation
Rotation part Could be rotation around z-axis x-axis y-axis or a combination of the three
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
1
A
O
N
XY
V
V
V
HV
1
A
O
N
zzzz
yyyy
xxxx
XY
V
V
V
1000
Paon
Paon
Paon
V
Homogeneous Continuedhellip
The (noa) position of a point relative to the current coordinate frame you are in
The rotation and translation part can be combined into a single homogeneous matrix IF and ONLY IF both are relative to the same coordinate frame
xA
xO
xN
xX PVaVoVnV
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Finding the Homogeneous MatrixEX
Y
X
Z
J
I
K
N
OA
T
P
A
O
N
W
W
W
A
O
N
W
W
W
K
J
I
W
W
W
Z
Y
X
W
W
W Point relative to theN-O-A frame
Point relative to theX-Y-Z frame
Point relative to theI-J-K frame
A
O
N
kkk
jjj
iii
k
j
i
K
J
I
W
W
W
aon
aon
aon
P
P
P
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1
W
W
W
A
O
N
kkkk
jjjj
iiii
K
J
I
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
k
J
I
zzz
yyy
xxx
z
y
x
Z
Y
X
W
W
W
kji
kji
kji
T
T
T
W
W
W
1
W
W
W
1000
Tkji
Tkji
Tkji
1
W
W
W
K
J
I
zzzz
yyyy
xxxx
Z
Y
X
Substituting for
K
J
I
W
W
W
1
W
W
W
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
1
W
W
W
A
O
N
kkkk
jjjj
iiii
zzzz
yyyy
xxxx
Z
Y
X
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
1
W
W
W
H
1
W
W
W
A
O
N
Z
Y
X
1000
Paon
Paon
Paon
1000
Tkji
Tkji
Tkji
Hkkkk
jjjj
iiii
zzzz
yyyy
xxxx
Product of the two matrices
Notice that H can also be written as
1000
0aon
0aon
0aon
1000
P100
P010
P001
1000
0kji
0kji
0kji
1000
T100
T010
T001
Hkkk
jjj
iii
k
j
i
zzz
yyy
xxx
z
y
x
H = (Translation relative to the XYZ frame) (Rotation relative to the XYZ frame) (Translation relative to the IJK frame) (Rotation relative to the IJK frame)
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The Homogeneous Matrix is a concatenation of numerous translations and rotations
Y
X
Z
J
I
K
N
OA
TP
A
O
N
W
W
W
One more variation on finding H
H = (Rotate so that the X-axis is aligned with T)
( Translate along the new t-axis by || T || (magnitude of T))
( Rotate so that the t-axis is aligned with P)
( Translate along the p-axis by || P || )
( Rotate so that the p-axis is aligned with the O-axis)
This method might seem a bit confusing but itrsquos actually an easier way to solve our problem given the information we have Here is an examplehellip
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
F o r w a r d K i n e m a t i c s
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The SituationYou have a robotic arm that
starts out aligned with the xo-axisYou tell the first link to move by 1 and the second link to move by 2
The QuestWhat is the position of the
end of the robotic arm
Solution1 Geometric Approach
This might be the easiest solution for the simple situation However notice that the angles are measured relative to the direction of the previous link (The first link is the exception The angle is measured relative to itrsquos initial position) For robots with more links and whose arm extends into 3 dimensions the geometry gets much more tedious
2 Algebraic Approach Involves coordinate transformations
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
X2
X3Y2
Y3
1
2
3
1
2 3
Example Problem You are have a three link arm that starts out aligned in the x-axis
Each link has lengths l1 l2 l3 respectively You tell the first one to move by 1
and so on as the diagram suggests Find the Homogeneous matrix to get the position of the yellow dot in the X0Y0 frame
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 )
ie Rotating by 1 will put you in the X1Y1 frame Translate in the along the X1 axis by l1 Rotating by 2 will put you in the X2Y2 frame and so on until you are in the X3Y3 frame
The position of the yellow dot relative to the X3Y3 frame is(l1 0) Multiplying H by that position vector will give you the coordinates of the yellow point relative the the X0Y0 frame
X1
Y1
X0
Y0
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Slight variation on the last solutionMake the yellow dot the origin of a new coordinate X4Y4 frame
X2
X3Y2
Y3
1
2
3
1
2 3
X1
Y1
X0
Y0
X4
Y4
H = Rz(1 ) Tx1(l1) Rz(2 ) Tx2(l2) Rz(3 ) Tx3(l3)
This takes you from the X0Y0 frame to the X4Y4 frame
The position of the yellow dot relative to the X4Y4 frame is (00)
1
0
0
0
H
1
Z
Y
X
Notice that multiplying by the (0001) vector will equal the last column of the H matrix
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
More on Forward Kinematicshellip
Denavit - Hartenberg Parameters
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Denavit-Hartenberg Notation
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i
d i
i
IDEA Each joint is assigned a coordinate frame Using the Denavit-Hartenberg notation you need 4 parameters to describe how a frame (i) relates to a previous frame ( i -1 )
THE PARAMETERSVARIABLES a d
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The Parameters
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
You can align the two axis just using the 4 parameters
1) a(i-1)
Technical Definition a(i-1) is the length of the perpendicular between the joint axes The joint axes is the axes around which revolution takes place which are the Z(i-1) and Z(i) axes These two axes can be viewed as lines in space The common perpendicular is the shortest line between the two axis-lines and is perpendicular to both axis-lines
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
a(i-1) cont
Visual Approach - ldquoA way to visualize the link parameter a(i-1) is to imagine an expanding cylinder whose axis is the Z(i-1) axis - when the cylinder just touches the joint axis i the radius of the cylinder is equal to a(i-1)rdquo (Manipulator Kinematics)
Itrsquos Usually on the Diagram Approach - If the diagram already specifies the various coordinate frames then the common perpendicular is usually the X(i-1) axis So a(i-1) is just the displacement along the X(i-1) to move from the (i-1) frame to the i frame
If the link is prismatic then a(i-1) is a variable not a parameter Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
2) (i-1)
Technical Definition Amount of rotation around the common perpendicular so that the joint axes are parallel
ie How much you have to rotate around the X(i-1) axis so that the Z(i-1) is pointing in
the same direction as the Zi axis Positive rotation follows the right hand rule
3) d(i-1)
Technical Definition The displacement along the Zi axis needed to align the a(i-1) common perpendicular to the ai common perpendicular
In other words displacement along the
Zi to align the X(i-1) and Xi axes
4) i
Amount of rotation around the Zi axis needed to align the X(i-1) axis with the Xi
axis
Z(i - 1)
X(i -1)
Y(i -1)
( i - 1)
a(i - 1 )
Z i Y i
X i a i d i
i
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The Denavit-Hartenberg Matrix
1000
cosαcosαsinαcosθsinαsinθ
sinαsinαcosαcosθcosαsinθ
0sinθcosθ
i1)(i1)(i1)(ii1)(ii
i1)(i1)(i1)(ii1)(ii
1)(iii
d
d
a
Just like the Homogeneous Matrix the Denavit-Hartenberg Matrix is a transformation matrix from one coordinate frame to the next Using a series of D-H Matrix multiplications and the D-H Parameter table the final result is a transformation matrix from some frame to your initial frame
Z(i -
1)
X(i -1)
Y(i -1)
( i -
1)
a(i -
1 )
Z i Y
i X
i
a
i
d
i
i
Put the transformation here
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
3 Revolute Joints
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
Denavit-Hartenberg Link Parameter Table
Notice that the table has two uses
1) To describe the robot with its variables and parameters
2) To describe some state of the robot by having a numerical values for the variables
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Z0
X0
Y0
Z1
X2
Y1
Z2
X1
Y2
d2
a0 a1
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
1
V
V
V
TV2
2
2
000
Z
Y
X
ZYX T)T)(T)((T 12
010
Note T is the D-H matrix with (i-1) = 0 and i = 1
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
1000
0100
00cosθsinθ
00sinθcosθ
T 00
00
0
i (i-1) a(i-1) di
i
0 0 0 0 0
1 0 a0 0 1
2 -90 a1 d2 2
This is just a rotation around the Z0 axis
1000
0000
00cosθsinθ
a0sinθcosθ
T 11
011
01
1000
00cosθsinθ
d100
a0sinθcosθ
T22
2
122
12
This is a translation by a0 followed by a rotation around the Z1 axis
This is a translation by a1 and then d2 followed by a rotation around the X2 and Z2 axis
T)T)(T)((T 12
010
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
I n v e r s e K i n e m a t i c s
From Position to Angles
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
A Simple Example
1
X
Y
S
Revolute and Prismatic Joints Combined
(x y)
Finding
)x
yarctan(θ
More Specifically
)x
y(2arctanθ arctan2() specifies that itrsquos in the
first quadrant
Finding S
)y(xS 22
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
2
1
(x y)
l2
l1
Inverse Kinematics of a Two Link Manipulator
Given l1 l2 x y
Find 1 2
RedundancyA unique solution to this problem
does not exist Notice that using the ldquogivensrdquo two solutions are possible Sometimes no solution is possible
(x y)l2
l1
l2
l1
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
The Geometric Solution
l1
l22
1
(x y) Using the Law of Cosines
21
22
21
22
21
22
21
22
212
22
122
222
2arccosθ
2)cos(θ
)cos(θ)θ180cos(
)θ180cos(2)(
cos2
ll
llyx
ll
llyx
llllyx
Cabbac
2
2
22
2
Using the Law of Cosines
x
y2arctanα
αθθ
yx
)sin(θ
yx
)θsin(180θsin
sinsin
11
22
2
22
2
2
1
l
c
C
b
B
x
y2arctan
yx
)sin(θarcsinθ
22
221
l
Redundant since 2 could be in the first or fourth quadrant
Redundancy caused since 2 has two possible values
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
21
22
21
22
2
2212
22
1
211211212
22
1
211212
212
22
12
1211212
212
22
12
1
2222
2
yxarccosθ
c2
)(sins)(cc2
)(sins2)(sins)(cc2)(cc
yx)2((1)
ll
ll
llll
llll
llllllll
The Algebraic Solution
l1
l22
1
(x y)
21
21211
21211
1221
11
θθθ(3)
sinsy(2)
ccx(1)
)θcos(θc
cosθc
ll
ll
Only Unknown
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
))(sin(cos))(sin(cos)sin(
))(sin(sin))(cos(cos)cos(
abbaba
bababa
Note
)c(s)s(c
cscss
sinsy
)()c(c
ccc
ccx
2211221
12221211
21211
2212211
21221211
21211
lll
lll
ll
slsll
sslll
ll
We know what 2 is from the previous slide We need to solve for 1 Now we have two equations and two unknowns (sin 1 and cos 1 )
2222221
1
2212
22
1122221
221122221
221
221
2211
yx
x)c(ys
)c2(sx)c(
1
)c(s)s()c(
)(xy
)c(
)(xc
slll
llllslll
lllll
sls
ll
sls
Substituting for c1 and simplifying many times
Notice this is the law of cosines and can be replaced by x2+ y2
22
222211
yx
x)c(yarcsinθ
slll
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Joint Drive Systemsbull Electric
ndash Uses electric motors to actuate individual jointsndash Preferred drive system in todays robots
bull Hydraulicndash Uses hydraulic pistons and rotary vane actuatorsndash Noted for their high power and lift capacity
bull Pneumaticndash Typically limited to smaller robots and simple material
transfer applications
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Robot Control Systemsbull Limited sequence control ndash pick-and-place
operations using mechanical stops to set positionsbull Playback with point-to-point control ndash records
work cycle as a sequence of points then plays back the sequence during program execution
bull Playback with continuous path control ndash greater memory capacity andor interpolation capability to execute paths (in addition to points)
bull Intelligent control ndash exhibits behavior that makes it seem intelligent eg responds to sensor inputs makes decisions communicates with humans
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
End Effectorsbull The special tooling for a robot that enables it to perform a
specific task
bull Two types
ndash Grippers ndash to grasp and manipulate objects (eg parts) during work cycle
ndash Tools ndash to perform a process eg spot welding spray painting
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Grippers and Tools
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Industrial Robot Applications1 Material handling applications
ndash Material transfer ndash pick-and-place palletizingndash Machine loading andor unloading
2 Processing operationsndash Weldingndash Spray coatingndash Cutting and grinding
3 Assembly and inspection
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Robotic Arc-Welding Cellbull Robot performs
flux-cored arc welding (FCAW) operation at one workstation while fitter changes parts at the other workstation
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Servo RobotsServo Robots
bull A more sophisticated level of control can be achieved by adding servomechanisms that can command the position of each joint
bull The measured positions are compared with commanded positions and any differences are corrected by signals sent to the appropriate joint actuators
bull This can be quite complicated
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Teach and Play-back RobotsTeach and Play-back Robots
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Robotic Vision system
The most powerful sensor which can equip a robot with largevariety of sensory information is ROBOTIC VISION1048708 Vision systems are among the most complex sensory system inuse1048708 Robotic vision may be defined as the process of acquiringand extracting information from images of 3-d world1048708 Robotic vision is mainly targeted at manipulation andinterpretation of image and use of this information in robotoperation control1048708 Robotic vision requires two aspects to be addressed1 Provision for visual input2 Processing required to utilize it in a computer basedsystems
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Why UVs Need AI
bull Sensor interpretationndash Bush or Big Rock Symbol-ground problem Terrain interpretation
bull Situation awareness Big Picture
bull Human-robot interaction
bull ldquoOpen worldrdquo and multiple fault diagnosis and recovery
bull Localization in sparse areas when GPS goes out
bull Handling uncertainty
bull Manipulators
bull Learning
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Artificial Intelligent RobotsAll Have 5 Common Components bull Mobility legs arms neck wrists
ndash Platform also called ldquoeffectorsrdquo
bull Perception eyes ears nose smell touchndash Sensors and sensing
bull Control central nervous systemndash Inner loop and outer loop layers of the brain
bull Power food and digestive systembull Communications voice gestures hearing
ndash How does it communicate (IO wireless expressions)ndash What does it say
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
7 Major Areas of AI1 Knowledge representation
bull how should the robot represent itself its task and the world
2 Understanding natural language
3 Learning
4 Planning and problem solvingbull Mission task path planning
5 Inferencebull Generating an answer when there isnrsquot complete information
6 Searchbull Finding answers in a knowledge base finding objects in the world
7 Vision
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
ldquoUpper brainrdquo or cortexReasoning over information about goals
ldquoMiddle brainrdquoConverting sensor data into information
Spinal Cord and ldquolower brainrdquoSkills and responses
Intelligence and the CNS
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
AI Focuses on Autonomybull Automation
ndash Execution of precise repetitious actions or sequence in controlled or well-understood environment
ndash Pre-programmed
Autonomyndash Generation and execution of actions to meet a goal or
carry out a mission execution may be confounded by the occurrence of unmodeled events or environments requiring the system to dynamically adapt and replan
ndash Adaptive
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
So How Does Autonomy Work
bull In two layersndash Reactivendash Deliberative
bull 3 paradigms which specify what goes in what layerndash Paradigms are based on 3 robot primitives
sense plan act
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
AI Primitives within an Agent
SENSE PLAN ACT
LEARN
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Reactive
ACTSENSE
ACTSENSE
ACTSENSE
PLAN
Users loved it because it worked
AI people loved it but wanted to put PLAN back in
Control people hated it because couldnrsquot rigorously prove it worked
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-
Thank you all
- INDUSTRIAL ROBOTICS AND EXPERT SYSTEMS
- robot (noun) hellip
- Jacques de Vaucanson (1709-1782)
- The Origins of Robots
- Mechanical horse
- Pre-History of Real-World Robots
- Slide 7
- History of Robotics
- The US military contracted the walking truck to be built by the General Electric Company for the US Army in 1969
- Unmanned Ground Vehicles
- Slide 11
- Unmanned Aerial Vehicles
- Autonomous Underwater Vehicles
- Slide 14
- Discussion of Ethics and Philosophy in Robotics
- Isaac Asimov and Joe Engleberger
- Asimovrsquos Laws of Robotics
- The Advent of Industrial Robots - Robot Arms
- Industrial Robot Defined
- What are robots made of
- Robot Anatomy
- Manipulator Joints
- Polar Coordinate Body-and-Arm Assembly
- Cylindrical Body-and-Arm Assembly
- Cartesian Coordinate Body-and-Arm Assembly
- Jointed-Arm Robot
- SCARA Robot
- Wrist Configurations
- An Introduction to Robot Kinematics
- Slide 30
- An Example - The PUMA 560
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Joint Drive Systems
- Robot Control Systems
- End Effectors
- Grippers and Tools
- Industrial Robot Applications
- Robotic Arc-Welding Cell
- Servo Robots
- Slide 78
- Robotic Vision system
- Slide 80
- Why UVs Need AI
- Artificial Intelligent Robots
- Slide 83
- 7 Major Areas of AI
- Intelligence and the CNS
- AI Focuses on Autonomy
- So How Does Autonomy Work
- AI Primitives within an Agent
- Reactive
- Slide 90
- Slide 91
- Slide 92
-