Evolution of Automatons
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Transcript of Evolution of Automatons
22-12-2015
1
Evolution of Automatons
S. Mukherjee
Dept. of Mechanical Engineering
IIT Delhi
Bird Organs 1770
• Clockwork mechanism
Swiss Clockwork Singing
Bird.mp4
• Made in significant numbers
• There is one at the SalarJung
Museum
• One of the first successful
imitation of lifelike motion.
• Implemented using
mechanisms and cams that
is taught in 2nd year of engg.
Vaucanson’s Flute Player
• Paris 1738
• Three dimension cam
implementation
• Remember that in
those days, even the
lathe machine was not
around.
The writer
• Jaquet Droz The Writer
Automaton From 1774 In
Action - Inspired Hugo Movie-
ux2KW20nqHU.mp4
• Automaton built in the
1770s by Swiss
watchmaker, Pierre
Jaquet-Droz (1721-1790).
• Nearly 6000 parts, a self-
operating, programmable
machine, capable of
writing letters and words
with a quill pen.
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Millardet’s Automaton• London, 1805
• Could write poetry
and sketch ships
sailing in the seas• Henri Maillardets Automaton at
The Franklin Institute
Scien.mp4
• Lost, and finally
reassembled in
Philadelphia in 1920’s
• Progress after that ?
Long standing problem
“[A rational approach to synthesis is needed] to obtain, by direct and certain methods, all the forms and arrangements that are applicable to the desired purpose. At present, questions of this kind can only be solved by that species of intuition that which long familiarity with the subject usually confers upon experienced persons, but which they are totally unable to communicate to others. When the mind of a mechanician is occupied with the contrivance of a machine, he must wait until, in the midst of his meditations, some happy combination presents itself to his mind which may answer his purpose.”
Robert Willis, The Principles of Mechanism, 1841
One of the first synthesis challenges to be posed:
The robot generation
• 1921 RUR by Karel Capek
• 1950 ‘I robot’ by Issac Asimov
• 1952 NC Machine built at MIT
• 1956 Unimation, the first robotics company
founded by J. Engelberger
• What is often ignored is that distinctions in
development, Sensorimotor stage, Preoperational
stage, Concrete operational stage, Formal
operational stage were not proposed by Piaget till
1920’s.
First Working Manipulator
• 1962
• The first modern day manipulator was
installed in a working plant in GM.
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Cognition
• Human systems can process information at the rate of 250
– 1000 words per minute.
• GHz data rates in electronic data bus!
• Humans recognise / discriminate 7 – 8 incoming stimuli.
• This is a small “channel capacity“ compared to modern
computer system when arriving at a decision.
• A familiar task like welding is modelled by physicists
using 70+ parameters!
• Reduce robot programming complexity and increased
sensor integration are competing and contradictory goals.
• Sensor integration for task domains, not task instances
AI Paradigms
• How do we get machines to do what humans now
do better?
• How to handle unpredictable events in an
unstructured environment ?
• Learning
• Planning and problem solving
• Inference : answers in the absence of complete
information
• Search
• Vision : “All that you see is a perception” M. Aurilius
• 1969 Shakey at Stanford
Univ.
– First robot with ‘intelligence’
– Could stack blocks placed in the
room
• 1970 Lunokhod 1
– The West found out that the
Soviet Republic had sent an
autonomous vehicle to space
several years later.
Odex 1970
• Built to service
nuclear reactors
• Legs could be
straightened to make
the profile small
• The legs can also be
used to press buttons
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OSU Hexapod
• 1970
• Full digital control
• First autonomous
vehicle
• First vehicle to use
computation of
dynamics
One legged hopping machine
• 1975
• Raibert at CMU
• Hydraulic actuator
• Onboard Gyro
• Anticipatory control
through dynamics
• Inverted pendulum
• Robots from MITs Leg
Lab.mp4
Adaptive Suspension Vehicle
• Ohio State, 1986
• Completely self
contained
• Pantograph Legs
• Force control at foot
• Seven CPU’s
• More code than in the
space shuttle !
Humanoid Robots
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Looking up to animals
• Animals are
remarkably well-
adapted to the
environments in which
they must survive.
• Efficiency and
flexibility of operation
• Robustness to
contingency and
damage
Robot III
• Robot III modeled on a
Blaberus cockroach.
• 24 degrees of freedom
• Actuated by off-the-shelf
pneumatic cylinders.
• Power, pressurized air,
and control are all off-
board.
Clockwork Universe
• Mechanists were philosophers inspired by the
scientific revolution of the 17th century.
• All phenomenon explained in terms of
"mechanical laws“
• Natural laws for motion and collision of matter
imply determinism.
• Like the gears of a clock ensure strike at 2:00, an
hour after striking 1:00
• All phenomena must be completely determined,
past, present or future.
Automata
• Self operating machine following predetermined
sequence or instructions.
• Can we work with systems that are not
predetermined?
• View dynamics as systems with memory.
• Gauss and the method of least squares
• Kalman filter.
• Measurements evolving over time represents what
the system is likely to do.
• Do we need a model at all?
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Ceres
• On January 1, 1801, the Italian astronomer Joseph Piazzi discovered a planetoid he christened Ceres,
• Astronomers were only able to observe the planetoid for 41 days, during which its orbit swept out an angle of only 9 degrees. Ceres was then lost to sight into the rays of the sun
• Where would Ceres be when it reemerged?
• Gauss first adopted Kepler's hypothesis that the motion of a celestial object is determined solely by its TRAJECTORY.
• No information is needed about the mass, velocity, or any other details of the object itself.
Estimation Theory : Gauss 1795• 18 year old “kid”, studied the estimation of six parameters
of motion of heavenly bodies using telescopic data. He
published the prediction of the Ceres comet but the method
only in 1809.
• In 1806, Legendre independently invented and published
the method.
• Points discussed by Gauss were:
– Observability : minimum number of points needed to determine
orbit
– Redundancy : to eliminate errors in measurement that are
INEVITABLE
– Model : for the orbit and a process of linearization
– Residuals: difference between observation and estimate to be
minimized
– Probability Density and the Gaussian Distribution
The line fit
• Least Squares Line y = mx + c
• Slope m and intercept c to be estimated
• Given :
– (x1 , y1) ; (x2 , y2) ;……; (xi , yi) ; (xn-1 , yn-1) ; (xn , yn) ;
• Define the residual:
� = � �� − ��� − �
�� • Like Gauss, we minimize the residuals to obtain an
optimum fit.
• Excel does it, but some phenomenon is lost in the middle.
Let’s focus on that.
Solution is given by :
• Set the partials of the residuals with respect to m and c to
zero.
���� = � −2 �� − ��� − �� = 0
�
�� ��� = � −2 �� − ��� − = 0
�
�� • Equations are linear in m and c and hence easily solved
• These involve summation of:
� �����
�� ; � ����
�
�� ; � ��
�
�� ; � ��
�
��
• All previous data is contracted into these terms.
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Iterative formulation
• If a new pair (x, y) comes in we have to compute:– x, y, xy
• And add them to the accumulated sum. This is hence an iterative procedure and we don’t have to re-compute using all the data we have so far.
• This is a line in a plane. For Ceres, Gauss solved it for a ellipse in space in 100 hrs manually.
• In general, Gauss would calculate the orbit of a comet in a single hour, where it had taken Euler 3 days using previous methods.
• Instead of trajectories on conic sections, can this be done for trajectories that evolve over differential equations?
Linearizing a DE
• to be linearized about x = π/4
022
2
=++ xCosdt
dx
dt
xd
4/πδ += xx
( ) ( )( ) 04/
4/2
4/2
2
=+++
++
πδπδπδ
xCosdt
xd
dt
xd
The first two terms are straightforward, the third is not
Mathematician at work
• The linearized equation is not homogeneous and has a forcing function
on the RHS.
• One root of the characteristic equation will be +ve because of the –ve
sign in the LHS. Hence the solution will grow without bound. So the
system linearized about x = π/4 is not stable!
xxdx
xdx
xδ
πδ
ππδ π
−==
−
+
= 4sin
cos
4cos
4cos
4
xxx δδπππ
δ2
2
2
2
4sin
4cos
4cos −=
−
=
+
( ) ( )2
2
2
22
2
2
−=−+ xdt
xd
dt
xdδ
δδ
The class IX problem
• The problem of tracking a “natural” motion, ball falling.
• In this formulation, x1 is the position, x2 is the velocity and
a is the acceleration.����� = 0 1
0 0��� + 0
1 �� = 1 0 ��
� = ��• The only observed quantity is the position, x1.
• So, x2 which is velocity and acceleration a are unknown
and are to be estimated based on observation.
• We further impose that, a is locally constant, or changing
slowly in time.
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The estimator problem• Augmenting the states and imposing �� = 0 or equivalently,
��� = 0.
•��������
=0 1 00 0 10 0 0
�����
or equivalently, �� = ��
• And the output formulation is : � = 1 0 0�����
= �
• Convert this into a continuous time observer:
��� = ��� + �(� − ��)• Defining ! = � − �� and substituting into the observer model,
!� = � − � !
The error dynamics
!� = � − � !• A and c are defined by the system, but we can choose L so
that the error equation is stable.
• Ensures that e => 0 as t => ∞.
• Having established L, we can solve for the estimates ��1, ��2,
of ��3.
• As e tends to zero, these estimates approach the variables.
• What we have achieved, is that we have solved for velocity
and acceleration from observation of position without
doing any differentiation!
We can do a bit better
• We have a sequence of x’s coming in if we are analysing a
video.
• Makes sense to discretise the whole process and suppress
the noise in ‘a’ in the process.
� " + 1 # = $�("#)
$ =1 # #/2 0 1 #0 0 1
• Note that our system is now dependent on the time
interval, T, driven by the frame rate.
� "# = 1 0 0 � "# + &("#)• We create the observer, y, which has the noise w thrown in.
Kalman filter gives an iterative
estimator!
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ResultsData based approach
• Data is the key.
• Next to information, is the ability to predict the
performance
• Compact models to predict the performance at the next
time interval are available, oblivious of the physics of the
problem.
• This forms the basis of modern dynamic simulation
methods.
• Methods that use these techniques for classical mechanical
systems are called “mechantronic” systems.
• Allow for all components, including the processing
elements to be treated uniformly as input-output-observer
systems.
Four legged dynamic balancing
• Dog• Boston Dynamics Big Dog (new video March
2008).mp4
• Cheetah• Boston Dynamics - Cheetah Robot .mp4
Where is the art headed
• http://www.youtube.com/watch?v=t_qN3dgYGqE
• http://www.youtube.com/watch?v=geqip_0Vjec&feature=
player_embedded
• What is next?
• The first step is
mathematical modeling
of the nature of things.
• In itself, does not yield
new designs, but
suggests ways to
stabilize systems.
22-12-2015
10
Opportunities
• Indian polity has woken up to the fact that robotics
imparts a different way of handling data:
– Verifying one of two hypothesis : forehand or backhand
– What is the posterior hypothesis based on the prior data: If I continue to fly at this velocity will I go through the hoop?
– In the third form, data is a measure: how many people are in the
room?
• By definition, trans-disciplinary (transient + disciplinary)
in nature.
• Interpretation of data in context of an application (design
of products) is an appropriate procedure of generation of
useful knowledge.
• Robotics is not a way to replace manual labour
Philosophically
“It seemed to me that I must recognize two main directions in the forces at
work—two seemingly antagonistic tendencies, equally deleterious in their
action, and ultimately combining to produce their results: a striving to
achieve the greatest possible expansion of education on the one hand, and a
tendency to minimise and weaken it on the other. The first-named would,
for various reasons, spread learning among the greatest number of people;
the second would compel education to renounce its highest, noblest and
sublimest aims in order to subordinate itself to some other department of
life—such as the service of the State.”
Excerpt From: Friedrich Wilhelm Nietzsche. “On the Future of our
Educational Institutions.”