Intelligent Systems Lectures 17 Control systems of robots based on Neural Networks

Intelligent Systems

Lectures 17

Control systems of robots based on Neural Networks

15.11.2005 2

Neuron of MacCallock&PittsThreshold Logical Unit (TLU)

15.11.2005 3

Geometry of TLU

15.11.2005 4

R-category linear classifier based on TLU

15.11.2005 5

Geometric Interpretation of action of linear classifier

15.11.2005 6

2-layer network

Three Planes Implemented by the Hidden Units

15.11.2005 7

Multi Layer Perceptron (MLP) (Feed-forward network)

15.11.2005 8

Kinds of sigmoid used in perceptrons

Exponential

Rational

Hyperbolic tangent

15.11.2005 9

15.11.2005 10

Formulas for error back propagation algorithm

Modification of weights of synapsesof jth neuron connected with ith ones,xj – state of jth neuron (output)

For output layer

For hidden layersk – number of neuron in next layerconnected with jth neuron

(1)

(2)

(3)

15.11.2005 11

Hopfield network

X1 X2

X'1 X'2

XN-1 XN

X'N-1 X'N

Y1Y2

YN-1 YN

Features of structure:•Every neuron is connected with all others•Connections are symmetric, i.e. for all i and j wij – wji

•Every neuron may be Input and output neuron•Presentation of input is set of state of input neurons

15.11.2005 12

Hopfield network (2)

• Learning– Hebbian rule is used: Weight of link increases for neurons

which fire together (with same states) and decreases if otherwise

• Working (recalling) - iteration process of calculation of states of neurons until convergence will be achieved– Each neuron receives a weighted sum of the inputs from other

neurons:

– If the input hj is positive the state of the neuron will be 1, otherwise -1:

0 if 1

0 if 1

j

j

j h

hu

ij

N

jii

ij wuh ,1

.

15.11.2005 13

Elman Network (SRN). The number of context units is the same as the number of hidden units

15.11.2005 14

Robot-manipulator

15.11.2005 15

Tasks for robot manipulator control system• Forward kinematics Kinematics is the science of

motion which treats motion without regard to the forces which cause it Within this science one studies the position velocity acceleration and all higher order derivatives of the position variables A very basic problem in the study of mechanical manipulation is that of forward kinematics This is the static geometrical problem of computing the position and orientation of the endeector hand of the manipulator

• Inverse kinematics This problem is posed as follows given the position and orientation of the endeector of the manipulator calculate all possible sets of joint angles which could be used to attain this given position and orientation This is a fundamental problem in the practical use of manipulators

15.11.2005 16

Tasks for robot manipulator control system (2)• Dynamics. Dynamics is a field of study devoted to

studying the forces required to cause motion In order to accelerate a manipulator from rest glide at a constant end-effector velocity and finally decelerate to a stop a complex set of torque functions must be applied by the joint actuators In dynamics not only the geometrical properties kinematics are used but also the physical properties of the robot are taken into account. Take for instance the weight inertia of the robotarm which determines the force required to change the motion of the arm. The dynamics introduces two extra problems to the kinematic problems:– The robot arm has a memory. Its responds to a control signal

depends also on its history (e.g. previous positions speed acceleration)

– If a robot grabs an object then the dynamics change but the kinematics don’t. This is because the weight of the object has to be added to the weight of the arm (that’s why robot arms are so heavy making the relative weight change very small)

15.11.2005 17

Tasks for robot manipulator control system (3)

• Trajectory generation. To move a manipulator from here to there in a smooth controlled fashion each joint must be moved via a smooth function of time. Exactly how to compute these motion functions is the problem of trajectory generation

15.11.2005 18

Camera-robot coordination is function approximation

• The system we focus on in this section is a work floor observed by a fixed cameras and a robot arm. The visual system must identify the target as well as determine the visual position of the end-effector.

15.11.2005 19

Camera-robot coordination is function approximation (2)

15.11.2005 20

Camera-robot coordination is function approximation (3).

Two approach to use neural networks:

• Usage of feed-forward networks– Indirect learning– General learning– Specialized learning

• Usage of topology conserving maps

15.11.2005 21

Camera-robot coordination is function approximation (4). feed-forward networks

Indirect learning system for robotics.In each cycle the network is used in two different places: first in the forward step then for feeding back the error

15.11.2005 22

Camera-robot coordination is function approximation (5). feed-forward networks (2)

15.11.2005 23

Camera-robot coordination is function approximation (6). feed-forward networks (3)

or

15.11.2005 24

Camera-robot coordination is function approximation (7). feed-forward networks (4)

The learning rule applied here regards the plant as an additional and unmodiable layer in the neural network

The Jacobian matrix can be used to calculate the change in the function when its parameters change

where i iterates over the outputs of the plant

15.11.2005 25

Camera-robot coordination is function approximation (8). Topology conserving maps

15.11.2005 26

Camera-robot coordination is function approximation (9). Topology conserving maps (2)

15.11.2005 27

Robot arm dynamics (Kawato et al, 1987)

15.11.2005 28

Robot arm dynamics (2)

15.11.2005 29

Nonlinear transformations used in the Kawato model

15.11.2005 30

Robot arms dynamics (4)

15.11.2005 31

Mobile robots

Schematic representation of the stored rooms and the partial information which is available from a single sonar scan

15.11.2005 32

Mobile robots (2)Two problems.The first called local planning relies on information available from the current viewpoint of the robot. This planning is important since it is able to deal with fast changes in the environment.

The second situation is called global path planning in which case the system uses global knowledge from a topographic map previously stored into memory Although global planning permits optimal paths to be generated it has its weakness Missing knowledge or incorrectly selected maps can invalidate a global path to an extent that it becomes useless A possible third anticipatory planning combined both strategiesthe local information is constantly used to give a best guess what the global environment may contain

15.11.2005 33

Mobile robots (3)

15.11.2005 34

Sensor based control

15.11.2005 35

The structure of the network for the autonomous land vehicle

15.11.2005 36

Experiments

The network was trained by presenting it samples with as inputs a wide variety of road images taken under different viewing angles and lighting conditions. 1200 Images were presented, 40 times each while the weights were adjusted using the backpropagation principle The authors claim that once the network is trained the vehicle can accurately drive at about km/hour along ‘… a path though a wooded area adjoining the Carnegie Mellon campus under a variety of weather and lighting conditions.’ The speed is nearly twice as high as a non-neural algorithm running on the same vehicle.

15.11.2005 37

Drama

15.11.2005 38

DRAMA (2)

15.11.2005 39

DRAMA (3). Associative module

15.11.2005 40

DRAMA (4)

15.11.2005 41

DRAMA (5)

15.11.2005 42

DRAMA (6)

Learning