Evolution of Automatons

10
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.

description

Evolution of Automatons

Transcript of Evolution of Automatons

Page 1: 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.

Page 2: Evolution of Automatons

22-12-2015

2

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.

Page 3: Evolution of Automatons

22-12-2015

3

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

Page 4: Evolution of Automatons

22-12-2015

4

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

Page 5: Evolution of Automatons

22-12-2015

5

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?

Page 6: Evolution of Automatons

22-12-2015

6

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.

Page 7: Evolution of Automatons

22-12-2015

7

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

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.

Page 8: Evolution of Automatons

22-12-2015

8

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!

Page 9: Evolution of Automatons

22-12-2015

9

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.

Page 10: Evolution of Automatons

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.”