Lecture on Robotics

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    ROBOTICS: ADVANCED CONCEPTS

    &

    ANALYSIS

    MODULE 2 ELEMENTS OF ROBOTS: JOINTS, LINKS,

    ACTUATORS & SENSORS

    Ashitava Ghosal1

    1Department of Mechanical Engineering&

    Centre for Product Design and Manufacture

    Indian Institute of ScienceBangalore 560 012, India

    Email: [email protected]

    NPTEL, 2010

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    1 CONTENTS

    2 LECTURE 1

    Mathematical Preliminaries

    Homogeneous Transformation3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4 LECTURE 3

    Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission

    6 LECTURE 5

    Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

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    OUTLINE1 CONTENTS

    2 LECTURE 1

    Mathematical PreliminariesHomogeneous Transformation

    3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4 LECTURE 3

    Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission6 LECTURE 5

    Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

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    ORIENTATION OF A RIGID BODY

    Position of one point on the rigid body not enough todescribe it in 3D space.

    Orientation of a rigid body B with respect to {A}

    YA

    YB

    Bp

    Rigid Body B

    k

    ZA

    XB

    {B}

    {A}

    ZB

    OA,OB

    XA

    Figure 2: Orientation of a rigid body

    Attach coordinatesystem,

    {B

    }, to rigid

    body B.

    Origin of{B}coincident with origin of{A} (see Figure 2).Obtain description of{B} with respect to{A}.

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    ORIENTATION DIRECTION COSINES

    Unit vectors XB, YB, and ZB, attached to B, can bedescribed in

    {A

    }AXB = r11XA + r21YA + r31ZAAYB = r12XA + r22YA + r32ZA (2)AZB = r13XA + r23YA + r33ZA

    rij, i,j = 1,2,3 are called direction cosinesr11 =

    A XB XAMagnitude of unit vectors are 1 r11 is cosine of anglebetween AXB and XA. All rijs are cosines of angles.

    Define 3 3 rotation matrixA

    B[R] with rij, i,j = 1,2,3 asits elements. Columns of AB[R] are

    AXB,AYB, and

    AZB.AB[R] completely describes all three coordinate axis of{B}with respect to {A}.A

    B

    [R] gives orientation of rigid body B in{

    A}

    .

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    ORIENTATION PROPERTIES OF AB[R]

    The vector Bp in rigid body B can be described in {A} byA

    p =AB[R]

    B

    p (3)The columns of the rotation matrix are unit vectors,orthogonal to one another AXB A XB =A YB A YB =A ZB A ZB = 1, andAXB

    A YB =

    A YBA ZB =

    A ZBA XB = 0

    The determinant of the rotation matrix is +11.AB[R]

    TAB[R] = [U], where [U] is a 3 3 identity matrix.

    Inverse is same as transpose BA [R]= AB[R]

    1= AB[R]

    T.

    Three eigenvalues of AB[R] are +1, e, where =

    1,and = cos

    1

    (

    r11+r22+r33

    1

    2 ).The eigenvector corresponding to +1 isk = (1/2sin)[r32 r23, r13 r31, r21 r12]T, = {0,n},where n is a natural number. For = {0,2n}, there is norotation and = 2(n

    1) needs to handled specially!

    1det(AB[R]) = +1 is due to the use of a right-handed coordinate system.ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 7 / 1 38

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    ORIENTATION USING (k,)

    Rotation axis k fixed in {A} and {B}: Ak = AB[R]Bk = 1Bk.First equality is transformation of a vector from

    {B

    }to

    {A} and the second equality follows from equation (3) andthe definition of an eigenvector.Elements of AB[R] in terms of (kx,ky,kz)

    T and angle

    r11 = kx2(1

    cos) + cos

    r12 = kxky(1 cos) kzsinr13 = kzkx(1 cos) + ky sinr21 = kxky(1 cos) + kzsinr22 = ky

    2(1

    cos) + cos (4)

    r23 = kykz(1 cos) kxsinr31 = kzkx(1 cos) kysinr32 = kykz(1 cos) + kxsinr33 = kz

    2(1

    cos) + cos

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    ORIENTATION SIMPLE ROTATION

    Rotation axis k is parallel to XA and hence to XB Rotation about X axis.

    AB[R] = [R(X,)] =

    1 0 00 cos sin

    0 sin cos

    (5)

    ZA

    Bp

    Rigid Body BXA, XB

    k

    {B}

    {A}

    ZB

    OA, OB YA

    YB

    Figure 3: Rotation about X by angle

    Rotation about Xshown in Figure 3.

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    SIMPLE ROTATIONS (CONTD.)

    Rotation about Y and Z

    [R(Y,)] =

    cos 0 sin0 1 0

    sin 0 cos

    (6)

    [R(Z,)] =

    cos sin 0sin cos 0

    0 0 1

    (7)

    Rotation matrices in equations (5) through (7) calledsimple rotations.

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    SUCCESSIVE ROTATIONS

    Two successive rotations:1 Initially B is coincident with {A}.2

    First rotation relative to {A}. After first rotation{A} {B1}.3 Second rotation relative to {B1}. After second rotation

    {B1} {B}.

    {B}

    {A}

    ZB

    ZA

    YA

    YB

    Rigid Body BXA

    XB1

    XB

    YB1ZB1

    OA,OB1,OB

    Rigid Body B1

    Figure 4: Successive rotation

    Resultant rotation:AB[R] =

    AB1

    [R] B1B [R] Note orderof matrix multiplication.

    Resultant of n rotations AB[R] =

    AB1

    [R] B1B2 [R] ...Bn1B [R]

    Matrix multiplication is noncommutative in general AB1

    [R] B1B [R] =B1B [R]

    AB1

    [R] Order of rotation is important!

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    ORIENTATION THREE ANGLES

    Orientation described by 3 independent parameters Three rotations completely describe orientation of a rigidbody.

    Three successive rotations about axes fixed to moving body

    Rotations about three distinct axes: 6 combinations

    X-Y-Z, X-Z-Y, Y-Z-X, Y-X-Z, Z-X-Y & Z-Y-XRotations about two distinct axes: 6 combinations X-Y-X, X-Z-X, Y-X-Y, Y-Z-Y, Z-X-Z, & Z-Y-Z

    Rotations about axes fixed in space 12 possible

    combinations for 3 and 2 distinct axes.Minimal representation of orientation of rigid body Onlythree parameters (angles) and no constraints.

    Three angles also called Euler angles.

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    XYZEULER ANGLES

    Rotation about X AB1 [R] = [R(X,1)] =

    1 0 00 cos1 sin10 sin1 cos1

    Rotation about Y B1B2 [R] = [R(Y,2)] =

    cos2 0 sin20 1 0

    sin2 0 cos2

    XA, XB1

    YA

    YB1

    ZA

    ZB1

    XA, XB1

    YA 2

    ZA

    ZB1

    ZB2

    XA, XB1

    {B2}

    {A}, {B1}

    ZA

    YA

    YB1

    YB

    ZB, ZB2

    XB2XB2

    {B}

    OA, OB OA, OB

    3

    XB

    {B2}

    YB1 , YB2

    ZB1

    {A}{B1}

    1

    OA, OB

    {A}, {B1}

    Figure 5: XYZ Euler angles

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    XYZEULER ANGLES (CONTD.)

    Rotation about Z

    B2B [R] = [R(Z,3)] =

    cos3 sin3 0sin3 cos3 0

    0 0 1

    Resultant rotation AB

    [R] = AB1

    [R] B1B2

    [R] B2B

    [R] = c2c3 c2s3 s2s1s2c3 + s3c1 s1s2s3 + c3c1 s1c2

    c1s2c3 + s3s1 c1s2s3 + c3s1 c1c2

    Note: ci, si denote cosi and sini, respectively.

    AB[R] gives orientation of{B} given XYZ angles.AB[R] will be different if order of rotations is different.

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    XYZEULER ANGLES (CONTD.)

    Given AB[R], find XYZ Euler angles.

    Algorithm rij i for XYZ rotationsIf r13 = 1, then

    2 = atan2(r13,

    (r211 + r212))

    1 = atan2(r23/cos2, r33/cos2)3 = atan2(r12/cos2, r11/cos2)Else

    If r13 = 1, 1 = atan2(r21, r22), 2 = /2, 3 = 0If r31 = 1, 1 = atan2(r21, r22), 2 = /2, 3 = 0

    atan2(y,x): four-quadrant arc-tangent function (see

    function atan2 in MATLAB R) 1, 2, 3 [,].Two sets of values of1, 2 and 3.

    2 = /2 1, 2 not unique 1 3 can be found.Singularities in Euler angle representation.

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    ZYZEULER ANGLES

    OA, OB OA, OB

    ZA, ZB1 ZA, ZB1

    YB1, YB2

    XB1

    XB2

    XB

    {A}{B1}

    1

    ZA, ZB1

    XA

    XB1

    YA

    YB1

    OA, OB

    {B2}{A}, {B1}

    2

    XA

    XB1 XB2

    YA

    YB1, YB2

    ZB2

    3

    ZB2 , ZB

    XA

    YA

    YB

    {A}{B}

    Figure 6: ZYZ Euler angles

    A

    B[R] =

    c1 s1 0s1 c1 00 0 1

    c2 0 s20 1 0

    s2 0 c2

    c3 s3 0s3 c3 00 0 1

    =

    c1c2c3 s1s3 c1c2s3 s1c3 c1s2s1c2c3 + c1s3 s1c2s3 + c1c3 s1s2

    s2c3 s2s3 c2

    (8)

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    ZYZEULER ANGLES (CONTD.)

    Algorithm rij ZYZ Euler anglesIf r33

    =

    1, then

    2 = atan2(

    (r231 + r232), r33)

    1 = atan2(r23/sin2, r13/sin2)3 = atan2(r32/sin2,r31/sin2)

    Else

    If r33 = 1, then1 = 2 = 0, 3 = atan2(r12, r11)

    If r33 = 1, then1 = 0, 2 = , 3 = atan2(r12,r11)

    Two possible sets of ZYZ Euler angles (1,2,3) for agiven AB[R].

    r33 = 1 Singularity 1 3 can be found.For unique 1 and 3 when r33 = 1 Choose 1 = 0.

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    OTHER REPRESENTATIONS

    Euler parameters (see Kane et al., 1983, McCarthy, 1990):

    4 parameters derived from k = (kx,ky,kz)T and angle 3 parameters = k sin/2fourth parameter 4 = cos/2One constraint 1

    2 + 22 + 3

    2 + 42 = 1

    Quaternions (pp. 185 Arfken(1985), Wolfram website2): 4parameters

    Sum of a scalar q0 and a vector (q1,q2,q3)T

    Q= q0 + q1i + q2j + q3k.i, j, and k are the unit vectors in 3.Product of two quaternion also a quaternion.

    Inverse of quaternion exists.q20

    + q21

    + q22

    + q23

    = 1 Unit quaternion representorientation of a rigid body in 3.

    2

    See Known Bugs in Module 0, slide #10 for viewing links.ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 1 8 / 1 38

    http://mathworld.wolfram.com/Quaternion.html
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    ORIENTATION OF A RIGID BODY

    SUMMARY

    Orientation of a rigid body in 3 is specified by 3

    independent parameters.Various representation of orientation with their ownadvantages and disadvantages

    Rotation matrix AB[R] 9 rijs + 6 constraints Toomany variables and constraints but ideal for analysis.

    Axis (kx,ky,kz)T

    and angle 4 parameters + oneconstraint k2x + k

    2y + k

    2z = 1 Useful for insight and

    extension to screws, twists and wrenches.Euler angles: 3 parameters and zero constraints Minimalrepresentation but suffer from problem of singularitiesand

    sequence must be known.Euler parameters and quaternions: 4 parameters +1constraint Similar but not exactly same as axis-angleform, no singularities, used in motion planning.

    Can convert from one representation to any other for

    regular cases!ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 1 9 / 1 38

    C

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    COMBINED TRANSLATION AND

    ORIENTATION OF A RIGID BODY

    {A}

    OA

    OB

    ApAOB

    Bp

    Rigid Body B

    XA

    {B}

    YA

    ZA

    XB

    YB

    ZB

    Figure 7: General transformation

    {A} and {B}, OA andOB not coincident

    Orientation of{B} withrespect to {A} AB[R]Ap =A OB +

    AB[R]

    BpAOB locates OB withrespect to OA.

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    O

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    OUTLINE1 CONTENTS

    2 LECTURE 1

    Mathematical PreliminariesHomogeneous Transformation

    3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4 LECTURE 3Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission6 LECTURE 5

    Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

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    4 4 T M

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    44 TRANSFORMATION MATRIXCombined translation and orientation AP = AB[T]

    BPA

    P andB

    P are 4 1 homogeneous coordinates (seeAdditional Material) constructed by concatenating a 1 toAp and BpAP = [Ap | 1]T and BP = [Bp | 1]T4

    4 homogeneous transformation matrix AB[T] is formed as

    AB[T] =

    AB[R]

    AOB0 0 0 1

    (9)

    In computer graphics and computer vision

    Last row is

    used for perspective and scaling and not [0 0 0 1].Upper left 3 3 matrix is identity matrix Puretranslation.

    Top right 3 1 vector is zero Pure rotation.

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    4 4 TRANSFORMATION MATRIX

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    4 4 TRANSFORMATION MATRIX PROPERTIES

    Inverse of AB[T] is given by

    AB[T]

    1=

    AB[R]

    T AB[R]TAOB

    0 0 0 1

    Two successive transformations {A} {B1} {B} givesAB[T] =

    AB1

    [T] B1B [T].

    AB[T] =

    AB1

    [R]B1B [R]AB1

    [R]B1OB +AOB1

    0 0 0 1

    n successive transformationsAB[T] =

    AB1

    [T] B1B2 [T] ...Bn1B [T]

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    PROPERTIES OF A [T ] (CONTD )

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    PROPERTIES OF AB[T] (CONTD.)

    Four eigenvalues of AB[T] are +1, +1,e, same as for

    AB[R].

    Eigenvectors for +1 is k No other eigenvector!AB[T] represents the general motion of a rigid body in 3Dspace 6 parameters must be present.General motion of rigid body as a twist Rotation abouta line and translation along the line.

    Direction of the line: (kx,ky,kz)T 2 independentparameters.Rotation about the line: angle 1 independentparameter.Location of the line in 3: (k,Y k) whereY = ([U]

    AB[R]

    T

    )A

    OB

    2(1cos) 4 independent parameters in k and Y k.Translation along the line by an amount (AOB k).

    More details about twists, eigenvalues and eigenvectors

    (see Sangamesh Deepak and Ghosal, 2006).ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 2 4 / 1 38

    SUMMARY

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    SUMMARY

    A rigid body B in 3D space has 6 DOF with respect toanother rigid body A: 3 for position & 3 for orientation.

    Definition of a right-handed coordinate system {A} X,Y, Z and origin OA.Rigid body B conceptually identical to a coordinate system{B}.Position of rigid body

    Position of a point of interest on

    rigid body with respect to coordinate system {A} 3Cartesian coordinates: Ap = (px,py,pz)

    T.Orientation described in many ways: 1) by 3 3 rotationmatrix AB[R], 2) (, k) or angle-axis form, 3) 3 Eulerangles, 4) Euler parameters & quaternions.Algorithms available to convert one representation toanother.4 4 homogeneous transformation matrix, AB[T], representposition and orientation in a compact manner.

    Properties ofA

    B[T] can be related to a screw.ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 2 5 / 1 38

    OUTLINE

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    OUTLINE1 CONTENTS

    2 LECTURE 1

    Mathematical PreliminariesHomogeneous Transformation

    3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4 LECTURE 3Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission6 LECTURE 5

    Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

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    JOINTS INTRODUCTION

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    JOINTS INTRODUCTION

    A joint connects two or more links.

    A joint imposes constraints on the links it connects.2 free rigid bodies have 6 + 6 degrees of freedom.Hinge joint connecting two free rigid bodies 6 + 1degrees of freedom.Hinge joint imposes 5 constraints, i.e., hinge joint allows 1

    relative (rotary) degree of freedom.

    Degree of freedom of a joint in 3D space: 6 m where m isthe number of constraint imposed.

    Serial manipulators

    All joints actuated

    One-degree-of-freedom joints used.Parallel and hybrid manipulators Some joints passive Multi-degree-of-freedom joints can be used.

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    TYPES OF JOINTS

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    TYPES OF JOINTS

    D O F

    Figure 8: Types of joints

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    CONSTRAINTS IMPOSED BY A

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    CONSTRAINTS IMPOSED BY A

    ROTARY (R) JOINTRigid bodies, {i1} and

    {i}, connected by a rotary(R) joint (Figure 9).

    {i} can rotate about k,with respect to {i1}, byangle i0i [R] = 0i1[R] i1i [R(k,i)]Three independentequations in the matrixequation above; i is

    unknown 2 constraintsin the 3 equations.

    {0}

    {i 1}

    {i}

    Oi1

    Oi

    ip

    i1p

    0Oi1

    0Oi

    0p

    k

    Li

    iRigid Body i 1

    Rigid Body i

    Rotary Joint

    Figure 9: A rotary joint

    For a common point P on the rotation axis along line Li0p =0 Oi1 + 0i1[R]

    i1p =0 Oi + 0i [R]ip 3 constraints

    present.ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 2 9 / 1 38

    CONSTRAINTS IMPOSED BY A

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    CONSTRAINTS IMPOSED BY A

    ROTARY (R) JOINT IN A LOOP

    Rotary joint in aloop 2 ends {L}and

    {R

    }.

    k

    Li

    i

    Rotary Joint

    Rigid Body i 1

    Oi1

    Oi

    {L}

    LOi1

    i1p

    i

    p

    {R}

    Rigid Body i

    ROi

    LD

    {i 1}

    {i}

    Figure 10: A rotary joint in a loop

    Two constraints in Li [R] =Li1[R]

    i1i [R(k,i)] =

    LR[R]

    Ri [R]

    since i is an unknown variable.Three constraints inLp =L Oi

    1 +

    Li

    1[R]i1p =L D +R Oi + Ri [R]

    ip

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    CONSTRAINTS IMPOSED BY A

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    CONSTRAINTS IMPOSED BY A

    PRISMATIC (P) JOINTTwo rigid bodies,

    {i

    1}

    and{

    i}

    ,connected by asliding/prismatic (P)joint

    Orientation of

    {i

    }is

    same as {i1} 3independent constraintsin 0i [R] =

    0i1[R]

    {i} can slide by di,

    alongL

    i, with respectto {i1}

    {0}

    k

    Li

    di

    Rigid Body i 1

    Rigid Body i

    {i 1}

    {i}

    Oi1

    Oi

    0Oi1

    i1p

    ip

    0Oi Prismatic Joint0p

    Figure 11: A prismatic joint

    2 constraints in 0Oi1 + 0i1[R]i1p + dik =0 Oi + 0i [R]

    ip

    since di is an unknown variable.

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    CONSTRAINTS IMPOSED BY A

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    CONSTRAINTS IMPOSED BY A

    SPHERICAL (S) JOINT

    Spherical(S) or ball andsocket joint allows threerotations.

    S joint can berepresented as 3intersecting rotary(R)joints. {0}

    Rigid Body i 1

    Rigid Body i

    {i}

    {i 1}

    0Oi10Oi

    Spherical Joint

    i1p

    ip

    0p

    Figure 12: A spherical joint

    3 constraints: 0p =0 Oi1 + 0i1[R]i1p =0 Oi + 0i [R]

    ip

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    CONSTRAINTS IMPOSED BY A

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    CONSTRAINTS IMPOSED BY A

    HOOKE (U) JOINT

    Common in many parallel manipulators.

    Equivalent to two intersecting rotary (R) joints Twodegrees of freedom

    4 constraints.

    For a common point P at the intersection of two rotationaxes 0p =0 Oi1 + 0i1[R]

    i1p =0 Oi + 0i [R]ip 3

    constraints.0i [R] =

    0i1[R]

    i1i [R(k1,1i)][R(k2,2i)] Only 1

    constraint present as 1i and 2i are unknown rotationsabout k1 and k2

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    CONSTRAINTS IMPOSED BY A

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    CONS N S OS

    SPHERICAL-SPHERICAL (SS) JOINT

    PAIR

    The SS pair appearin many parallelmanipulators.

    Distance betweentwo spherical joint isconstant. {L}

    Rigid Body i

    Si

    {i}

    LSiLOi

    iSi

    {j}

    Sjj

    Sj

    RORSj

    lij

    Rigid Body j

    S-S Pair

    LD

    Figure 13: A SS pair in a loop

    One constraint equation(LSi (LD +R Sj)) (LSi (LD +R Sj)) = l2ij, lij is aconstant.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 3 4 / 1 38

    OUTLINE

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    1 CONTENTS

    2 LECTURE 1

    Mathematical PreliminariesHomogeneous Transformation

    3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4 LECTURE 3Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission6 LECTURE 5

    Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 3 5 / 1 38

    LINKS INTRODUCTION

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    A link A is a rigid body in 3D space Can be describedby a coordinate system {A}.A rigid body in 3 has 6 degrees of freedom 3 rotation+ 3 translation 6 parameters (see Lecture 1)For links connected by rotary (R) and prismatic (P),possible to use 4 parameters Denavit-Hartenberg(D-H)parameters (see Denavit & Hartenberg, 1955).

    4 parameters since lines related to rotary(R) and prismatic(P) joint axis are used.

    For multi-degree-of-freedom joints Use equivalentnumber of one-degree-of-freedom joints.

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    LINKS DENAVIT-HARTENBERG

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    (D-H) PARAMETERS

    A word about conventions Several ways to derive D-Hparameters!

    Convention used:

    1 Coordinate system{

    i}

    is attached to the link i.2 Origin of{i} lies on the joint axis i Link i is after joint

    i.3 after for serial manipulators Numbers increasing from

    fixed {0} Link 1 {1} . . . Free end {n}.4 after for parallel manipulators Not so straight-forward

    due to one or more loops.

    Convention same as in Craig (1986) or Ghosal(2006).

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    ASSIGNMENT OF COORDINATE AXES

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    Three intermediate links {i 1}, {i} and {i+ 1}.Rotary joint axis Labeled Zi1, Zi and Zi+1 .

    {0}

    X0

    Y0

    Z0

    Zi+1

    Oi1

    Oi{i 1}

    {i}

    Xi1

    Link i 2

    Link i 1

    Link i

    Link i + 1

    Li1

    Li

    Li+1

    ZiZi1

    ai1

    di

    i

    i1

    Figure 14: Intermediate links and D-H parameters

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    D-H PARAMETERS ASSIGNMENT

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    OF COORDINATE AXIS (CONTD.)

    For coordinate system {i 1}Zi1 is along joint axis i 1.Xi1 is chosen along the common perpendicular betweenlines Li1 and Li.

    Yi1 = Zi1 Xi1 Right-handed coordinate system.The origin Oi1 is the point of intersection of the mutualperpendicular line and the line Li1.

    For coordinate system {i}: Zi is along the joint axis i, Xiis along the common perpendicular between Zi and Zi+1,

    and the origin of{i}, Oi, is the point of intersection of theline along Xi and line along Zi (see Figure 14).

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    D-H PARAMETERS FOR LINK i

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    Twist anglei1 Twist angle for link i has subscripti 1!

    Angle between joints axis i

    1 and i & measured aboutXi1 using right-hand rule (see Figure 14).Signed quantity between 0 and radians.

    Link length ai1 Link length for link i is ai1!Distance between joints axis i 1 and i & measured alongXi

    1 (see Figure 14).

    Always a positive quantity.Link offset di

    Measured along Zi from Xi1 to Xi Can be < 0.Joint i rotary di constant.Joint i prismatic

    di is joint variable (see Figure 14).

    Rotation angleiAngle between Xi1 and Xi measured about Zi usingright-hand rule Between 0 and radians.Joint i is prismatic i is constant.Joint i rotary

    i is joint variable (see Figure 14).

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    D-H PARAMETERS SPECIAL CASES

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    Consecutive joints axis parallel commonperpendiculars

    i1 = 0,, ai

    1 along any common perpendicular.

    Joint i is rotary (R) di is taken as zero.Joint i is prismatic (P) i is taken as zero.Consecutive P joints parallel ds not independent!

    Consecutive joints axis intersecting ai1 = 0 and Xnormal to plane.

    First link {1}: choice of Z0 and thereby X1 is arbitrary.R joint Choose {0} and {1} coincident &i1 = ai1 = 0, di = 0.P joint Choose {0} and {1} parallel &i

    1 = ai

    1 = i = 0.

    Last link {n}: Zn+1 not definedR joint Origins of{n} and {n + 1} are chosencoincident & dn = 0 and n = 0 when Xn1 aligns with Xn.P joint Xn is chosen such that n = 0 & origin On ischosen at the intersection of Xn

    1 and Zn when dn = 0.

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    LINK TRANSFORMATION MATRICES

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    Four D-H parameters describe link i with respect to linki 1

    Orientation of of{

    i}

    with respect to{

    i

    1}

    is given byi1i [R] = [R(X,i1)][R(Z,i)]Location of origin of{i} with respect to {i 1} is given byi1Oi = ai1 i1Xi1 + di i1Zi

    Recall i1Xi1 = (1,0,0)T. The vector i1Zi is the last

    column ofi

    1

    i [R] and is (0,si1 ,ci1)T3

    .The 4 4 transformation matrix relating {i} with respectto {i1} is

    i1i [T] =

    ci si 0 ai1

    sici1 cici1 si1 si1disisi1 cisi1 ci1 ci1di

    0 0 0 1

    (10)3The symbols si1 , ci1 denote sin(i1) and cos(i1),

    respectively. Please seeNotations

    in Module 0.ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 4 2 / 1 38

    LINK TRANSFORMATION MATRICES

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    i

    1

    i [T

    ] is a functiononly

    one joint variable d

    i or

    i.i1Oi locates a point on the joint axis i at the beginning oflink i.

    Position and orientation of link i determined by i1 andai

    1. Note: subscript i

    1 in the twist angle and length!

    The mix of subscripts are a consequences of the D-Hconvention used!

    Link i with respect to {0} 0i [T] = 01[T] 12[T] ... i1i [T]The positioin and orientation of any link can be obtained

    with respect any other link by suitable use of 44 linktransformation matrices.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 4 3 / 1 38

    SUMMARY

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    Two elements of robots Links and joints.Joints allow relative motion between connected links Joints impose constraints.

    Serial robots mainly use one-degree-of-freedom rotary (R)and prismatic (P) actuated joints.Parallel and hybrid robots use passivemulti-degree-of-freedom joints and actuatedone-degree-of-freedom joints.

    One degree-o-freedom R and P joints represented by linesalong joint axis Z is along joint axis.

    Formulation of constraints imposed by various kinds ofjoints.

    Link is a rigid body in 3D space Represented by 4Denavit-Hartenberg (D-H) parameters.Convention to derive D-H parameters and for special cases.

    4 4 link transformation matrix in terms of D-Hparameters.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 4 4 / 1 38

    OUTLINEC

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    1 CONTENTS

    2 LECTURE 1

    Mathematical PreliminariesHomogeneous Transformation

    3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4 LECTURE 3Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission

    6 LECTURE 5

    Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

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    SERIAL MANIPULATORS

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    Steps to obtain D-H parameters for a n link serialmanipulator (see Lecture 2 for details)

    1 Label joint axis from 1 (fixed) to n free end.2 Assign Zi to joint axis i, i = 1,2,...,n.3 Obtain mutual perpendiculars between lines along Zi1

    and Zi Xi1.4 Origin Oi

    1 on joint axis i

    1.

    5 Handle special cases a) consecutive joint axes paralleland perpendicular, b) first and last link

    6 Obtain 4 D-H parameters for link i, i1, ai1, di and i.

    For each link i obtain i1i [T] using equation (10).

    Obtain link transform for link i with respect to fixedcoordinate system {0}, 0i [T], by matrix multiplication.Obtain, if required, ij[T] by appropriate matrix operations.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 4 6 / 1 38

    PLANAR 3R MANIPULATOR

    A

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    ASSIGNMENT OF COORDINATE

    SYSTEMS

    All 3 rotary joint axisZi parallel and pointingout.

    {0} Z0 is pointingout, X0 and Y0pointing to the rightand top, respectively.

    Origin O0 is coincidentwith O1 shown infigure.

    {2}

    {3}

    YTool

    X0

    Y0

    Link 1

    {0}

    {1}

    Y1

    O2

    l1

    O1

    2l2

    l3

    Link 3

    O3

    X2

    Link 2

    X3, XTool

    {Tool}3

    Y3

    Y2 X1

    1

    Figure 15: The planar 3R manipulator

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    PLANAR 3R MANIPULATOR

    A

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    ASSIGNMENT OF COORDINATE

    SYSTEMS

    For {1} origin O1 and Z1 are coincident with O0 and Z0.X1 and Y1 are coincident with X0 and Y0 when 1 is zero.

    X1 is along the mutual perpendicular between Z1 and Z2.

    X2 is along the mutual perpendicular between Z2 and Z3.

    For {3}, X3 is aligned to X2 when 3 = 0.O2 is located at the intersection of the mutualperpendicular along X2 and Z2.

    O3 is chosen such that d3 is zero.

    The origins and the axes of {1}, {2}, and {3} are shown inFigure 15.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 4 8 / 1 38

    PLANAR 3R MANIPULATOR D - H

    TABLE

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    TABLE

    From the assigned axes and origins, the D-H parameters are as

    follows:i i1 ai1 di i1 0 0 0 12 0 l1 0 23 0 l2 0 3

    l1 and l2 are the link lengths and i, i = 1,2,3 are rotaryjoint variables (see Figure 15).

    Length of the end-effector l3 does not appear in the table Recall: D-H parameters are till the origin which is at the

    beginning of a link!For end-effector frame, {Tool}:

    Axis of{Tool} parallel to {3} 3Tool[R] is identity matrix.Origin of{Tool} at the mid-point of the parallel jawgripper, at a distance of l3 from O3 along X3.

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    PLANAR 3R MANIPULATOR LINK

    TRANSFORMS

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    TRANSFORMS

    Substitute elements of first row of D-H table in

    equation (10) to get 01[T] =

    c1 s1 0 0s1 c1 0 00 0 1 00 0 0 1

    The second row of the D-H table gives

    12[T] =

    c2 s2 0 l1s2 c2 0 00 0 1 00 0 0 1

    Finally, third row of D-H table gives

    23[T] =

    c3 s3 0 l2s3 c3 0 00 0 1 00 0 0 1

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    PLANAR 3R MANIPULATOR: LINK

    TRANSFORMS (CONTD )

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    TRANSFORMS (CONTD.)

    The 3Tool[T] is obtained as 3Tool[T] =

    1 0 0 l3

    0 1 0 00 0 1 00 0 0 1

    To obtain 03[T] multiply

    01[T]

    12[T]

    23[T] and get

    4

    03[T] =

    c123

    s123 0 l1c1 + l2c12

    s123 c123 0 l1s1 + l2s120 0 1 00 0 0 1

    To obtain 0Tool[T], multiply

    03[T]

    3Tool[T]

    0Tool[T] =

    c123

    s123 0 l1c1 + l2c12 + l3c123

    s123 c123 0 l1s1 + l2s12 + l3s1230 0 1 00 0 0 1

    4The symbols s12, c123 denote sin(1 +2) and cos(1 +2 +3),

    respectively. Please see Notations in Module 0.ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 5 1 / 1 38

    PUMA 560 MANIPULATOR

    The PUMA 560 is a six degree of freedom manipulator with all

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    The PUMA 560 is a six-degree-of-freedom manipulator with allrotary joints Figure 16 shows assigned coordinate systems.

    X1

    Y1

    {1}

    Z1X2

    Z2

    Y2

    {2}

    O1, O2

    X3

    Y3

    Z3

    {3}O3

    X4Y4

    Z4{4}

    O4

    a2

    d3

    (a) The PUMA 560 manipulator

    d4

    a3

    Y3

    X3 Z4

    X4

    Z6

    X6

    Y5

    X5O3

    {3}

    {4}

    {5}{6}

    O4, O5, O6

    (b) PUMA 560 - forearm and wrist

    Figure 16: The PUMA 560 manipulator

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    PUMA 560 MANIPULATOR D - H

    PARAMETERS

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    PARAMETERS

    The D-H parameters for the PUMA 560 manipulator (seeFigure 16) are

    i i1 ai1 di i

    1 0 0 0 12 /2 0 0 23 0 a2 d3 34 /2 a3 d4 45 /2 0 0 56 /2 0 0 6

    Note: i, i = 1,2,...,6 are the six joint variables.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 5 3 / 1 38

    PUMA 560 MANIPULATOR LINK

    TRANSFORMS

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    TRANSFORMS

    Substituting elements of row #1 of D-H table and using

    equation (10), we get 01[T] =

    c1 s1 0 0s1 c1 0 00 0 1 00 0 0 1

    From row # 2, we get 12[T] =

    c2 s2 0 00 0 1 0

    s2 c2 0 00 0 0 1

    From row # 3, we get 23[T] =

    c3 s3 0 a2s3 c3 0 0

    0 0 1 d30 0 0 1

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    PUMA 560 MANIPULATOR: LINK

    TRANSFORMS (CONTD )

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    TRANSFORMS (CONTD.)

    From row # 4 , we get 34[T] =

    c4 s4 0 a30 0 1 d4

    s4 c4 0 00 0 0 1

    From row # 5 , we get 45[T] =

    c5

    s5 0 0

    0 0 1 0s5 c5 0 00 0 0 1

    From row # 6 , we get 56[T] =

    c6

    s6 0 0

    0 0 1 0s6 c6 0 00 0 0 1

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 5 5 / 1 38

    PUMA 560 MANIPULATOR: LINK

    TRANSFORMS (CONTD )

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    TRANSFORMS (CONTD.)

    {3}

    with respect to{

    0}

    is given by03[T] =

    01[T]

    12[T]

    23[T] =

    c1c23 c1s23 s1 a2c1c2 d3s1s1c23 s1s23 c1 a2s1c2 + d3c1s23 c23 0 a2s2

    0 0 0 1

    {6} with respect to {3} is given by36[T] =

    34[T]

    45[T]

    56[T] =

    c4c5c6 s4s6 c4c5s6 s4c6 c4s5 a3

    s5c6

    s5s6 c5 d4

    s4c5c6 c4s6 s4c5s6 c4c6 s4s5 00 0 0 1

    Can obtain any required link transformation matrix onceD-H is table known!

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    SCARA MANIPULATOR

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    O0, O1 O2

    1

    2

    d3

    { 1}

    { 2}

    O3, O4

    { 3}

    { 4}

    Z 1

    X 1

    Z 2

    X 2

    X

    Z 3

    4

    Figure 17: A SCARA manipulator

    SCARA Selective

    Compliance AssemblyRobot Arm

    Very popular for roboticassembly

    Capability of desiredcompliance and rigidityin selected directions.

    Three rotary(R) jointand one prismatic (P)joint.

    A 4 DOF manipulator.

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    SCARA MANIPULATOR: D-H

    PARAMETERS

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    PARAMETERS

    {0} and {1} have same origin & origins of {3} and {4}chosen at the base of the parallel jaw gripper.

    Directions of Z3 chosen pointing upward (see Figure 17).

    Note: Actual SCARA manipulator has ball-screw at the

    third joint We assume P joint.D-H Table for SCARA robot

    i i1 ai1 di i1 0 0 0 12 0 a

    10

    23 0 a2 d3 04 0 0 0 4

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    SCARA MANIPULATOR LINK

    TRANSFORMS

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    TRANSFORMS

    Using equation (10) and the D-H table, link transforms can be

    obtained as

    01[T] =

    c1 s1 0 0s1 c1 0 00 0 1 00 0 0 1

    , 12[T] =

    c2 s2 0 a1s2 c2 0 00 0 1 00 0 0 1

    23[T] =

    1 0 0 a20 1 0 00 0 1 d30 0 0 1

    , 34[T] =

    c4 s4 0 0s4 c4 0 00 0 1 00 0 0 1

    The transformation matrix 04[T] is

    04[T] =

    01[T]

    12[T]

    23[T]

    34[T] =

    c124 s124 0 a1c1 + a2c12s124 c124 0 a1s1 + a2s12

    0 0 1 d30 0 0 1

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 5 9 / 1 38

    PARALLEL MANIPULATORS

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    Extend idea of D-H parameters to a closed-loopmechanism/parallel manipulator.

    Key idea Break a parallel manipulator into serialmanipulators.

    Obtain D-H parameters for serial manipulators.Several ways to breakChoose one that leads to simple serial manipulators

    During analysis Combine serial manipulators using

    constraints

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    PARALLEL MANIPULATORS: 4-BA R

    MECHANISM

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    l0

    {L}

    2

    1

    YL

    XL

    YR

    XR

    {R}

    OL

    OR

    Link 1l1

    l3

    Link 2

    Link 3

    l2

    1

    Figure 18: A planar four-bar mechanism

    Rotary joints 1 and4 fixed to ground attwo places.

    Break4-barmechanism into two

    serial manipulators.

    Break at joint 3 A 2R planar

    manipulator + a 1Rmanipulator

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    4-BA R MECHANISM D-H

    PARAMETERS

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    For 2R planar manipulator D-H parameter with respectto {L}

    i i1 ai1 di i1 0 0 0 1

    2 0 l1 0 2

    For 1R planar manipulator D-H parameters with respectto {R}

    i i1 ai1 di i

    1 0 0 0 1The constant transform LR[T] is known.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 6 2 / 1 38

    PARALLEL MANIPULATORS: THREE

    DOF EXAMPLES i l 3 DOF ll l

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    X

    Y

    ZMoving Platform

    l3

    l2

    1

    l1

    2

    3

    p(x,y,z)

    S1

    S2S3

    Axis ofR1

    Base Platform

    Axis ofR3

    O

    {Base}

    Axis ofR2

    Figure 19: A three DOF parallel

    manipulator

    Spatial 3- DOF parallelmanipulator.

    Top (moving) platform &(fixed) bottom platformare equilateral triangles.

    Figure 19 shows the home

    position andZ need notpass through top platform

    centre always.

    Three legs Each leg isof R-P-S configuration.

    Three P joints actuated.

    First proposed by Lee andShah (1988) as a parallelwrist.

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    THREE DOF EXAMPLE: D-H

    PARAMETERS

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    D-H parameter for first leg with respect to {L1}i i1 ai1 di i1 0 0 0 12 /2 0 l1 0

    D-H parameter for all R-P-S leg same except the referencecoordinate system.

    {L1}, {L2}, and {L3} are at the three rotary joints R1, R2,and R3, respectively.

    {Base

    }is located at the centre of the base platform &

    BaseLi

    [T], i = 1,2,3, are constant and known.

    Note: The angle 1 shown in figure is same as /21.

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    THREE DOF EXAMPLE: LINK

    TRANSF ORMATION MATRICES

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    L11

    [T] =

    c1

    s1 0 0

    s1 c1 0 00 0 1 00 0 0 1

    , 12[T] = 1 0 0 0

    0 0 1 l10 1 0 00 0 0 1

    2S1

    [T] is an identity matrix {S1} is located at the centreof the spherical joint and parallel to

    {2

    }.

    BaseS1

    [T] = BaseL1 [T]L11 [T]

    12[T]2S1 [T]

    Location of spherical joint S1 with respect to {Base} fromBaseS1

    [T] BaseS1 = (b l1 cos1,0, l1 sin1)T, b is thedistance of R1 from the origin of{Base} (see figure 19).Location of S2 and S3BaseS2 = (b2 + 12 l2 cos2,

    3b2

    3l22 cos2, l2 sin2)

    T

    BaseS3 = (b2 + 12 l3 cos3,

    3b2 +

    3l32 cos3, l3 sin3)

    T

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    PARALLEL MANIPULATORS: SIX

    DOF EXAMPLE

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    l13

    l12

    l11

    Z

    ll l

    l

    ll

    2122 23

    31

    32

    33

    1

    1

    1

    2

    2

    2

    3

    3

    b

    b

    b

    1

    2

    3

    pp

    p

    1

    2

    3

    s

    s

    s

    d

    d

    h

    3

    X

    Y

    Figure 20: A six DOF parallel (hybrid)manipulator

    Moving platformconnected to fixed baseby three chains.

    Each chain is R-R-R &S joint at top.

    Model of a

    three-fingered hand(Salisbury, 1982)gripping an object withpoint contact andno-slip.

    Each finger modeledwith R-R-R joints andpoint of contactmodeled as S joint.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 6 6 / 1 38

    SIX DOF EXAMPLE: D-H

    PARAMETERS AND LINK TRANS-

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    FORMS

    D-H parameters for R-R-R chain.

    i i1 ai1 di i1 0 0 0 1

    2 /2 l11 0 13 0 l12 0 1

    D-H parameter does not contain last link length l13.

    D-H parameters for three fingers with respect to

    {F

    i}, i = 1,2,3 identical.

    Can obtain transformation matrix Fipi [T] by matrixmultiplication.

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    SIX DOF EXAMPLE: LINK

    TRANSFORMS (CONTD.)

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    Position vector of spherical joint i

    Fipi =

    cosi(li1 + li2 cosi + li3 cos(i +i))sini(li1 + li2 cosi + li3 cos(i +i))

    li2 sini + li3 sin(i +i)

    With respect to {Base}, the locations of{Fi}, i = 1,2,3,are known and constant (see Figure (20))Baseb1 = (0,d,h)T Baseb2 = (0,d,h)T Baseb3 = (0,0,0)TOrientation of{Fi}, i = 1,2,3, with respect to {Base} arealso known - {F1} and {F2} are parallel to {Base} and

    {F3

    }is rotated by about the Y (not shown in figure!).

    The transformation matrices Basepi [T] isBaseF1

    [T]01[T]12[T]

    23[T]

    3p1 [T] Last transformation includes

    l13.

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    SIX DOF EXAMPLE: LINK

    TRANSFORMS (CONTD.)

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    Extract the position vector Basep1

    from the last column ofBaseF1

    [T] Basep1 =Base b1 +

    F1 p1 =

    cos1(l11 + l12 cos1 + l13 cos(1 +1))

    d+ sin1(l11 + l12 cos1 + l13 cos(1 +1))h + l12 sin1 + l13 sin(1 +1)

    Similarly for second leg

    Basep2 =

    cos2(l21 + l22 cos2 + l23 cos(2 +2))d+ sin2(l21 + l22 cos2 + l23 cos(2 +2))

    h + l22 sin2 + l23 sin(2 +2)

    For third leg

    Base

    p3 =

    [R(Y,)]

    cos3(l31 + l32 cos3 + l33 cos(3 +3))sin3(l31 + l32 cos3 + l33 cos(3 +3))

    l32 sin3 + l33 sin(3 +3)

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 6 9 / 1 38

    SUMMARY

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    D-H parameters obtained for serial manipulators Planar3R, PUMA 560, SCARA

    To obtain D-H parameters for parallel manipulators

    Break parallel manipulator into serial manipulators.Obtain D-H parameters for each serial chain.

    Examples of 4-bar mechanism, 3-degree-of-freedom and6-degree-of-freedom parallel manipulators.

    Can extract position vectors of point of interest &orientation of links from link transforms.

    Kinematic analysis, using the concepts presented here,discussed in Module 3 and Module 4.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 7 0 / 1 38

    OUTLINE1 CONTENTS

    2 LECTURE 1

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    2 LECTURE 1

    Mathematical Preliminaries

    Homogeneous Transformation3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4

    LECTURE 3Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission

    6 LECTURE 5Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 7 1 / 1 38

    ACTUATORS FOR ROBOTS

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    Actuators are required to move joints, provide power anddo work.

    Serial robot actuators must be of low weight Actuators ofdistal links need to be moved by actuators near the base.

    Parallel robots Often actuators are at the base.

    Actuators drive a joint through a transmission device

    Three commonly used types of actuators:

    HydraulicPneumatic

    Electric motors

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    ACTUATORS FOR ROBOTS

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    Source: http://www.hocdelam.org/vn/category/ho-tro/robotandcontrol/

    Figure 21: Examples of actuators used in robots

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    ACTUATORS FOR ROBOTS

    HYDRAULIC

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    Early industrial robots were driven by hydraulic actuators.

    Pump supplies high-pressure fluid (typically oil) to a linearcylinders, rotary vane actuator or a hydraulic motor at thejoint!

    Large force capabilities.

    Large power-weight ratio The pump, electric motordriving the pump, accumulator etc. stationary and notconsidered in the weight calculation!

    Control is by means of on/off solenoid valves or

    servo-valves controlled electronically.The entire system consisting of Electric motor, pump,accumulator, cylinders etc. is bulky and often expensive Limited to big robots.

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    ACTUATORS FOR ROBOTS

    PNEUMATIC

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    Similar to hydraulic actuators but working fluid is air.Similar to hydraulic actuators, air is supplied from acompressor to cylinders and flow of air is controlled bysolenoid or servo controlled valves.

    Less force and power capabilities.Less expensive than hydraulic drives.

    Chosen where electric drives are discouraged or for safetyor environmental reasons such as in pharmaceutical andfood packaging industries.

    Closed-loop servo-controlled manipulators have beendeveloped for many applications.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 7 5 / 1 38

    COMPARISON OF PNEUMATIC &

    HYDRAULIC ACTUATORS

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    Air used in pneumatic actuators is clean and safe.Oil in hydraulic actuator can be a health and fire hazardespecially if there is a leakage.

    Pneumatic actuators are typically light-weight, portable

    and faster.Air is compressible (oil is incompressible) and hencepneumatic actuators are harder to control.

    Hydraulic actuators have the largest force/power densitycompared to any actuator.

    With compressors, accumulators and other components,the space requirement is larger than electric actuators.

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    ACTUATORS FOR ROBOTS

    ELECTRIC MOTORS

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    Electric or electromagnetic actuators are widely used inrobots.

    Readily available in wide variety of shape, sizes, power andtorque range.

    Very easily mounted and/or connected with transmissionelements such as gears, belts and timing chains.

    Amenable to modern day digital control.

    Main types of electric actuators:

    Stepper motorsPermanent magnet DC servo-motorBrushless motors

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 7 7 / 1 38

    ELECTRIC ACTUATORS STEPPER

    MOTORS

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    Used in small robots with small payload and low speeds.

    Stepper motors are of permanent magnet, hybrid orvariable reluctance type.

    Actuated by a sequence of pulses For a single pulse,rotor rotates by a known step such that poles on stator and

    rotor are aligned.Typical step size is 1.8 or 0.9.Speed and direction can be controlled by frequency ofpulses.

    Can be used in open-loop as cumulative error andmaximum error is one step!

    Micro-stepping possible with closed-loop feedback control.

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    STEPPER MOTORS

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    Parts of a Stepper Motor

    http://www.engineersgarage.com/articles/stepper-motors

    http://www.societyofrobots.com/member_tutorials/node/28

    Variable Reluctance (VR) Stepper MotorsNumber of teeth in the inner rotor (permanent magnet) isdifferent than the number of teeth in stator.

    1) Electro-magnet 1 is activated Rotor rotates up such that nearest teeth line up.2) Electro-magnet 1 is deactivated and 2 is turned on Rotor rotates such that nearest teeth line up

    rotation is by astep (designed amount) of typically 1.8 or 0.9 degrees.

    3) Electro-magnet 2 is deactivated and 3 is turned on Rotor rotates by another step.4) Electro-magnet 3 is deactivated and 4 is turned on and cycle repeated.Permanent Magnet (PM) Stepper Motors Similar to VR but rotor is radially magnetized.

    Hybrid Stepper Motors Combines best features of VR and PM stepper motors.

    Figure 22: Stepper motor components and working principle

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 7 9 / 1 38

    STEPPER MOTORS

    Typically stepper motors have two phases.

    Four stepping modes

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    Four stepping modes

    Wave drive Only one phase/winding is on/energized

    Torque output is smaller.Full step drive Both phases are on at the same time Rated performance.Half step drive Combine wave and full-step drive Angular movement half of first two.

    Micro-stepping Current is varying continuously Smaller than 1.8 or 0.9 degree step size, lower torque.

    Choice of a stepper motor based on:Load, friction and inertia Higher load can cause slipping!Torque-speed curve and quantities such as holding torque,

    pull-in and pull-out curve.Torque-speed characteristic determined by the drive Bipolar chopper drives for best performance.Maximum slew-rate: maximum operating frequency withno load (related to maximum speed).

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 8 0 / 1 38

    ELECTRIC ACTUATORS DC/AC

    SERVO-MOTORS

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    Rotor is a permanent magnet and stator is a coil.

    Permanent magnets with rare earth materials(Samarium-Cobalt, Neodymium) can provide largemagnetic fields and hence high torques.

    Commutation done using brushes or in brushless motor

    using Hall-effect sensors and electronics.

    Widely available in large range of shape, sizes, power andtorque range and low cost.

    Easy to control with optical encoder/tacho-generators

    mounted in-line with rotor.Brushless AC and DC servo-motors have low friction, lowmaintenance, low cost and are robust.

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    DC SERVO MOTORS

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    http://www.brushlessdcmotorparts.info http://www.rc-book.com/wiki Small RC Servo motors

    /brushless-electric-motor http://www.drivecontrol-details.info

    /rc-servo-motor.html

    Slotted-brushless DC Servo motors Direct drive motor, Applimotion, Inc Brushless Hub motor for E-bike

    http://www.motioncontroltips.com/ http://news.thomasnet.com/ http://visforvoltage.org/

    company_detail.html?cid=20082162 system-voltage/49-60-volts

    Figure 23: Examples of DC servo motors

    See also Wikipedia entry on electric motors.ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 8 2 / 1 38

    MODEL OF A DC PERMANENT

    MAGNET MOTOR

    LR

    Rotor is apermanent magnet.

    http://en.wikipedia.org/wiki/Electric_motor
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    ia

    m

    LaRa

    Va

    Motor

    Figure 24: Model of a permanent magnet DCservo-motor

    p g

    Stator Armaturecoil with resistanceRa and inductanceLa.

    Applied voltage Va,

    ia current in coil.Rotation speed ofmotor m Mechanical part.

    Torque developed Tm = Kt ia Kt is constant.

    Back-emf V = Kg m Kg is constant.Motor dynamics can be modeled as first-order ODE

    La ia + Raia + Kg m = Va

    Mechatronic model Mechanical + Electrical/ElectronicsASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL, 2 01 0 8 3 / 1 38

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    TRANSMISSIONS USED IN ROBOTS

    Purpose of transmission is to transfer power from source to

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    Purpose of transmission is to transfer power from source toload.

    The purpose of a transmission is also to transfer power atappropriate speed.

    Typical rated speed of a DC motor is between 1800 & 3600rpm.3000 rpm = 60 rps

    360 radians/sec.

    For a (typical) 1 m link Tip speed is 36 m/sec Greater than speed of sound!Need for large reduction in speed.

    Transmissions can (if needed) also convert rotary to linear

    motion and vice-versa.Transmissions also transfer motion to different joints andto different directions.

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    TRANSMISSIONS USED IN ROBOTS

    Transmissions in robots are decided based on motion, loadand power requirements and by the placement of actuator

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    and power requirements, and by the placement of actuatorrelative to the joint.

    Transmissions for robots must be (a)stiff, (b) low weight,(c) backlash free, and (d) efficient.

    Direct drives with motor directly connected to joint. It hasadvantages of low friction and low backlash but are

    expensive.Typical transmissions

    Gear boxes of various kinds Spur, worm and worm wheel,planetary etc..Belts and chain drives.

    Harmonic drive for large reduction.Ball screws and rack-pinion drives To transform rotary tolinear motions.Kinematic linkages 4-bar linkage.

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    TRANSMISSIONS USED IN ROBOTS

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    Figure 26: Examples of transmissions used in robots

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    OUTLINE1 CONTENTS

    2 LECTURE 1

    M h i l P li i i

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    Mathematical Preliminaries

    Homogeneous Transformation3 LECTURE 2

    Elements of a robot JointsElements of a robot Links

    4 LECTURE 3

    Examples of D-H Parameters & Link TransformationMatrices

    5 LECTURE 4

    Elements of a robot Actuators & Transmission

    6 LECTURE 5Elements of a robot Sensors

    7 ADDITIONAL MATERIAL

    Problems, References, and Suggested Reading

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL 2 01 0 8 8 / 1 38

    INTRODUCTION

    A robot without sensors is like a human being without eyes,ears, sense of touch, etc.

    S l b t i tl /ti i

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    Sensor-less robots require costly/time consuming

    programming.Can perform only in playback mode.No change in their environment, tooling and work piececan be accounted for.

    Sensors constitute the perceptual system of a robot,designed:

    To make inferences about the physical environment,To navigate and localise itself,To respond more flexibly to the events occurring in itsenvironment, andTo enable learning, thereby endowing robots with

    intelligence.

    Sensors allow less accurate modeling and control.

    Sensors enable robots to perform complex and increasedvariety of tasks reliably thereby reducing cost.

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    INTRODUCTION (CONTD.)

    Dynamical system

    h h d b d ff l

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    Changes with time Governed by differential equations.

    For a given input there is a well defined output.Linear dynamical system Modeled by linear ordinarydifferential equations Can be analysed using Laplacetransforms and transfer function5.

    Control system is used to

    Obtain desired response from dynamical system.Stabilize an unstable dynamical system.Improve performance.

    Two kinds of system Open-loop and closed-loop orfeedback control systems.

    Importance of sensors in modeling and control shown innext few slides.

    5Other methods such as frequency domain analysis can also be used.

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    OPEN-LOOP CONTROL SYSTEM

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    Figure 27: An open-loop control system

    Time domain linear function f(t) converted to s

    domain

    using Laplace transforms:F(s)

    = L{f(t)} = 0 f(t)est dt

    Time derivatives become polynomials in s.

    Transfer function Ratio of output to input in sdomain.Open-loop system No feedback: Input R(s) SystemG(s) Output Y(s) (see Figure above)For error G(s) in the modeling of the plant Y(S)Y(s) =

    G(s)G(s)

    x% error in G(s) results in x% error in Y(s)ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL 2 01 0 9 1 / 1 38

    CLOSED-LOOP CONTROL SYSTEM

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    Figure 28: A closed-loop control system

    Y(s) =D(s)G(s)

    1 + D(s)G(s)R(s); Chosen D(s)G(s) >> 1

    For error G(s) in the modeling of the plant

    Y(S)

    Y(s)=

    G(s)

    G(s)

    1

    1 + D(s)G(s)

    Since 1 + D(s)G(s) >> 1

    x% error in G(s) results in

    much smaller error of(

    11+D(s)G(s))

    x% in Y(s).

    With sensors and feedback, less complex and expensivecontrollers and/or models of system can be used for morerobust performance.

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    CLOSED-LOOP CONTROL SYSTEM

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    Figure 29: Closed-loop control with sensors

    Sensors must have low noise and be good for effectiveness.

    Consider a noisy sensor (see Figure above).

    Output of system

    Y(s) = D(s)G(s)1 + D(s)G(s) (R(s)N(s)); ChosenD(s)G(s)>> 1

    Note that output is proportional to corrupted(R(s)N(s))input, hence output error can never be reduced!

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL 2 01 0 9 3 / 1 38

    SENSORS IN ROBOTS

    Sensor is a device to make a measurement of a physicali bl f i t t d t it i t l t i l i l

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    variable of interest and convert it into electrical signal.

    Desirable features in sensors areHigh accuracy.High precision.Linear response.Large operating range.

    Low response time.Easy to calibrate.Reliable and rugged.Low costEase of operation

    Broad classification of sensors in robotsInternal state sensors.External state sensors.

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    SENSORS IN ROBOTS INTERNAL

    Internal sensors measure variables for controlJoint position.Joint velocity

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    Joint velocity.

    Joint torque/force.Joint position sensors (angular or linear)

    Incremental & absolute encoders Optical, magnetic orcapacitive.Potentiometers.

    Linear analog resistive or digital encoders.Joint velocity sensors

    DC tacho-generator & resolver.sOptical encoders.

    Force/torque sensors.At joint actuators for control.At wrist to measure components of force/moment beingapplied on environment.At end-effector to measure applied force on gripped object.

    ASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL 2 01 0 9 5 / 1 38

    SENSORS IN ROBOTS EXTERNAL

    Detection of environment variables for robot guidance,object identification and material handling.

    T i t C t ti d t ti

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    Two main types Contacting and non-contacting sensors.

    Contacting sensors: Respond to a physical contactTouch: switches, Photo-diode/LED combination.Slip.Tactile: resistive/capacitive arrays.

    Non-contacting sensors: Detect variations in optical,

    acoustic or electromagnetic radiations or change inposition/orientation.

    Proximity: Inductive, Capacitive, Optical and Ultrasoni.cRange: Capacitive and Magnetic, Camera, Sonar, Laserrange finder, Structured light.

    Colour sensors.Speed/Motion: Doppler radar/sound, Camera,Accelerometer, Gyroscope.Identification: Camera, RFID, Laser ranging, Ultrasound.Localisation: Compass, Odometer, GPS.

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    SENSORS IN ROBOTS

    How to compute resolution of a sensor?Example: Optical encoder to measure joint rotation

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    Figure 30: Resolution and required accuracy

    Optical encoders and resolvers Desired accuracy e One must be able to measure a minimum angle e/L.Number of bits/revolution required: Compute 2/( eL ),express as a binary number and round-off to the next

    higher power of 2.Example: L = 1m, e 0.5mm = eL = 5x104,2/( eL ) 10000 2

    13 = 8192,214 = 16384 14 bitencoder needed.

    IfL

    i ll 12 bi ll hASHITAVA GHOSAL (IISC) ROBOTICS: ADVANCED CONCEPTS & ANALYSIS N PTEL 2 01 0 9 7 / 1 38

    OPTICAL ENCODER

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    Figure 31: Optical encoder

    One of the most important and widely used internal sensor.Consists of an etched encoding disk with photo-diodes andLEDS. Disk made from

    Glass, for high-resolution applications (11 to >16 bits).

    Plastic (Mylar) or metal, for applications requiring morerugged construction (resolution of 8 to 10 bits).

    As disk rotates, light is alternately allowed to reachphoto-diode, resulting in digital output similar to a squarewave.

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    OPTICAL ENCODER

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    Figure 32: Optical encoder outputs

    Typically 3 signals available Channel A, B and I; A and Bare phase shifted by 90 degrees and I is called as the indexpulse obtained every full rotation of disk.

    Signals read by a microprocessor/counter.

    Output of counter includes rotation and direction.

    Output can be absolute or relative joint rotation.

    Can be used for estimating velocity.

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    SENSORS FOR JOINT ROTATION

    Potentiometers Voltage resistance and resistance rotation at joint

    N b

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    Not very accurate but very inexpensive.

    More suitable for slow rotations.Adds to joint friction.

    Resolvers Rotary electrical transformer to measure jointrotation

    Analog output, need ADC for digital control.Electromagnetic device Stator + Rotor (connected tomotor shaft).Voltage (at stator) sin(), = rotor angle.

    Tachometers measures joint velocity

    Similar to resolver.Voltage (at stator) , = angular velocity of the rotor.Analog output ADC required for digital control.

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    FORCE/TORQUE SENSOR (CONTD.)

    Performance specifications to ensure that the wrist motions

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    Performance specifications to ensure that the wrist motions

    generated by the force/torque sensors do not affect theposition accuracy of the manipulator:

    High stiffness to ensure quick dampening of the disturbingforces which permits accurate readings during short timeintervals.

    Compact design to ensure easy movement of themanipulator.Need to be placed close to end-effector/tool.Linear relation between applied force/torque and straingauge readings.

    Made from single block of metal No hysteresis.

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    FORCE/TORQUE WRIST SENSORF= [RF]W

    wherea

    RF =

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    Figure 33: Six axisforce/torque sensors at wrist

    RF =

    0 0 r13 0 0 0 r17 0r12 0 0 0 r25 0 0 00 r32 0 r34 0 r36 0 r380 0 0 r44 0 0 0 r480 r52 0 0 0 r56 0 0

    r61 0 r63 0 r65 0 r67 0

    F= (Fx,Fy,Fz,Mx,My,Mz)T.

    W = (w1,w2,w3,w4,w5,w6,w7,w8).wi are the 8 strain gauge readings.

    aThe formula can be derived from statics,please see Module 0, Lecture 5.

    Rij are found during calibration process using least-squaretechniques.

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    EXTERNAL SENSORS TOUCH

    Allows a robot or manipulator to interact with itsenvironment to touch and feel, see and locate.

    Two classes of external sensors Contact and non contact

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    Two classes of external sensors Contact and non-contact

    Figure 34: Touch sensor

    Simple LED-Photo-diode

    pair used to detectpresence/absence of objectto be grasped

    Micro-switch to detecttouch.

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    EXTERNAL SENSORS SLIP

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    Figure 35: Slip sensor

    Slip sensor to detect if grasped object is slipping.

    Free moving dimpled ball Deflects a thin rod on the axisof a conductive disk

    Evenly spaced electrical contacts placed under diskObject slips past the ball, moving rod and disk Electricalsignal from contact to detect slip.

    Direction of slip determined from sequence of contacts.

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    EXTERNAL SENSORS TACTILE

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    Figure 36: Robot hand with tactilearray

    Skin like membrane tofeel the shape of thegrasped object

    Also used to measureforce/torque required to

    grasp object

    Change inresistance/capacitance dueto local deformation from

    applied force

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    EXTERNAL SENSORS PROXIMITY

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    Detect presence of an object near a robot or manipulatorWorks at very short ranges (

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    Figure 38: A magnetic proximity sensor

    Electronic proximity sensor based on change of inductance.

    Detects metallic objects without touching them.

    Consists of a wound coil, located next to a permanentmagnet, packaged in a simple housing.

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    INDUCTIVE PROXIMITY SENSOR MAGNETIC

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    Figure 39: Flux lines in a magnetic sensor

    Ferromagnetic material enters or leaves the magnetic field

    Flux lines of the permanent magnet change theirposition.

    Change in flux Induces a current pulse with amplitudeand shape proportional to rate of change in flux.

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    INDUCTIVE PROXIMITY SENSOR MAGNETIC

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    Figure 40: Schematic of flux response in magnetic proximity sensor

    Coils output voltage waveform For proximity sensing.Useful where access is a challenge.Applications Metal detectors, Traffic light changing,Automated industrial processes.

    Limited to ferromagnetic materials.

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    INDUCTIVE HALL EFFECTPROXIMITY SENSOR

    Hall effect relates the voltage between two points in a

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    conducting or semiconducting material subjected to astrong magnetic field across the material.

    When a semi-conductor magnet device is brought in closeproximity of a ferromagnetic material

    the magnetic field at the sensor weakens due to bending ofthe field lines through the material,the Lorentz forces are reduced, andthe voltage across the semiconductor is reduced.

    The drop in the voltage is used to sense the proximity.

    Applications: Ignition timings in IC engines, tachometersand anti-lock braking systems, and brushless DC electricmotors.

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    CAPACITIVE PROXIMITY SENSORS

    Objects entry in electrostatic field of electrodes changes

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    capacitance.Oscillations start once capacitance exceeds a predefinedthreshold.

    Triggers output circuit to change between on and off.

    When object moves away, oscillators amplitude decreases,changing output back to original state.

    Larger size and dielectric constant of target, means largercapacitance and easier detection.

    Useful in level detection through a barrier.

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    ULTRASONIC PROXIMITY SENSORS

    Electro-acoustic transducer to send and receive highfrequency sound waves.

    Emitted sonic waves are reflected by an object back to the

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    transducer which switches to receiver mode.Same transducer is used for both receiving and emittingthe signals Fast damping of acoustic energy is essentialto detect close proximity objects.

    Achieved by using acoustic absorbers and by decoupling thetransducer from its housing.

    Typically of low resolution.

    Important specifications 1) Maximum operating distance,2) Repeatability, 3) Sonic cone angle, 4) Impulse frequency,

    and 5) Transmitter frequency.Some well-known applications 1) Useful in difficultenvironments, 2) Liquid level detection and 3) Car parkingsensors.

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    OPTICAL PROXIMITY SENSORS

    Also known as light beam sensors Solid state LED actingas a transmitter by generating a light beam.

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    A solid-state photo-diode acts as a receiver.

    Field of operation of the sensor Long pencil like volume,formed due to intersection of cones of light from sourceand detector.

    Any reflective surface that intersects the volume getsilluminated by the source and is seen by the receiver.

    Generally a binary signal is generated when the receivedlight intensity exceeds a threshold value.

    Applications: 1) Fluid level control, 2) Breakage and jamdetection, 3) Stack height control, box counting etc.

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    RANGE SENSORS TRIANGULATIONA narrow beam of lightsweeps the plane definedby the detector, the objectand the source,

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    Figure 43: Triangulation

    illuminating the target.

    Detector output is peakwhen illuminated patch isin front.

    With B and known Obtain D = Btan.

    Changing B and , onecan get D for all visibleportions of object.

    Very little computation required.

    Very slow as one point is done at a time.

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    RANGE SENSORS STRUCTUREDLIGHTING

    A sheet of light

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    Figure 44: Structured lighting

    generated through acylindrical lens or narrowslit is projected on a target.

    Intersection of the sheet

    with target yields a lightstripe.

    A camera offset slightlyfrom the projector, viewsand analyze the shape ofthe line.

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    RANGE SENSORS STRUCTUREDLIGHTING

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    Distortion of the line is related to distance and can becalculated.

    Horizontal displacement (in image) proportional to depthgradient.

    Integration gives absolute range.

    Calibration is required.

    Advantages:

    Fast, very little computation is required.Can scan multiple points or entire view at once.

    Structured lighting should be permitted.

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    RANGE SENSORS TIME-OF-FLIGHT

    Utilizes pulsed lasers and ultrasonics to measure time takenby the pulse to coaxially return from a surface.

    If D is the targets distance, c is the speed of radiation,

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    and t is elapsed time taken for the pulse to return

    D =ct

    2

    Light or electromagnetic radiation more useful for large

    (kilometers) distances.Light not very suitable in robotic applications as c is large.

    To measure range with 0.25 inch accuracy, one needs tomeasure very small time intervals 50 ps.

    Suitable for acoustic (ultrasonic) radiation, since c

    330m/s.

    Can only detect distance of one point in its view Scanrequired for object.

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    RANGE SENSORS TIME-OF-FLIGHT

    Phase shift and continuous laser light for measuring distance

    Laser beam ofwavelength split

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    Figure 45: Range measurement using phaseshift

    Two beams travel todetector through twodifferent paths.

    Phase delay between

    two beams is measured.Distance traveled byfirst beam L.

    Total distance traveledby the second beamD = L + 2D D = L + 360, is thephase shift.

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    RANGE SENSORS ULTRASONIC

    Similar to the pulsed laser technique.

    An ultrasonic chirp is transmitted over a short time period.

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    From the time difference between the transmitted andreflected wave, D can be obtained.

    Generally used for navigation and obstacle avoidance inrobots.

    Much cheaper than laser range finder.

    Shorter range as waves disperse.

    Wavelength of ultrasonic radiation much larger Notreflected very well from small objects and corners.

    Ultrasonic waves not reflected very well from plastics andsome other materials.

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    VISION SENSORS

    Most powerful and complex form of sensing, analogous tohuman eyes.

    C i i f id i h i d

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    Comprising of one or more video cameras with integratedsignal processing and imaging electronics.

    Includes interfaces for programming and data output, and avariety of measurement and inspection functions.

    Also referred to as machine or computer vision.Computations required are very large compared to anyother form of sensing.

    Computer vision can be sub-divided into six main areas: 1)

    Sensing, 2) Pre-processing, 3) Segmentation, 4)Description, 5) Recognition and 6) Interpretation.

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    VISION SENSORS

    Three levels of processing.

    Low level vision

    P i i i i i i lli h f

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    Primitive in nature, requires no intelligence on the part ofthe vision functions.Sensing and pre-processing can be considered as low levelvision functions.

    Medium level vision

    Processes that extract, characterize and label componentsin an image resulting from a low level vision.Segmentation, description and recognition of the individualobjects refer to the medium level function.

    High level vision: Processes that attempt to emulatecognition.

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    VISION SENSORS

    Smaller number of robotic applications Primarily due tocomputational complexity and low speed.

    Vision system can

    D t i di t f bj t

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    Determine distances of objects.Determine geometrical shape and size of objects.Determine optical (color, brightness) properties of objectsin an environment.Can be used for navigation (map making), obstacle

    avoidance, Cartesian position and velocity feedback,locating parts, and many other uses.Can learn about environment.Acquire knowledge and intelligence.

    Vision systems extensively used in autonomous navigation

    in mobile robots (Mars rovers).

    Use of vision systems increasing rapidly as technologyimproves!

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    NEW DEVELOPEMENTS IN SENSORTECHNOLOGY MEMS SENSORS

    Consist of very small electrical, electronics and mechanical

    t i t t d i l hi

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    components integrated on a single chip.Provide an interface to sense, process and/or control thesurrounding environment.

    Generally silicon based, allowing integration with

    microelectronics.Sensing mechanisms employed are a) Capacitive, b)Piezoelectric, c) Piezoresistive, d) Ferroelectric, e)Electromagnetic and f) Optical.

    Capacitive sensing most successful due to a) Norequirement of exotic materials, b) Low power consumptionand c) Stability over temperature ranges.

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    SMART SENSORS

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    Figure 47: Components of a smart sensor

    Smart Sensor A single device combining data collectionand information output.

    As per IEEE 1451.2, a smart sensor is:a transducer that provides functions beyond thosenecessary for generating a correct representation of a

    sensed or control quantity.Integration of transducer + applications + networking.

    Evolving concept Often sensors not complying with IEEEdefinition are also called smart sensors!

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    INTELLIGENT SENSORS

    For advanced robotic devices, large amount of sensory

    information slows down the controllerll k l d ff h ll b

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    information slows down the controller.Intelligent sensors take some load off the controller by

    Taking some predefined action based on the input received.Efficiently and precisely measuring the parameters,enhancing or interrupting them.

    Intelligent sensors: An adaptation of smart sensors withembedded algorithms for detection of noise,instrumentation anomalies and sensor anomalies.

    Enabling technology for ISHM (Integrated Systems Health

    Management) used in spaceships by NASA.

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    SENSOR-BASED ROBOTICS ASMIOASIMO: Advanced Step in InnovativeMObility.

    A humanoid robot developed byHONDA car company of Japan.

    Sensors for vision speed balance

    http://world.honda.com/ASIMO/history/
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    Sensors for vision, speed, balance,force, angle, and foot area.34 degrees of freedom controlled byservo motors.

    Capable of advanced movement

    Walking and running.Maintaining posture and balance.Climbing stairs & avoiding obstacle.

    Intelligence

    Charting a shortest route.Recognizing moving objects.Distinguish sounds and recognizefaces and gestures.

    Figure 48: ASIMOclimbing stairs

    Figure 49: ASIMOplaying soccer

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    SENSORS IN ROBOTS SUMMARY

    Sensors enhance performance of robots/manipulators, andmake them more flexible. for different application.

    Two main types of sensors

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    Two main types of sensorsInternal sensors for measuring variables such as jointrotation, velocity, force, and torque.External sensors for measuring variables such as proximity,touch, range, and geometry.

    Large varieties of sensors exist for large variety ofmeasurement tasks.

    More than one sensor is typically used in a robot.

    Vision system is the most powerful and complex sensor.

    New and modern sensor technologies are becoming matureand are finding their way into robots.

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