Date post: | 21-Dec-2015 |
Category: |
Documents |
View: | 245 times |
Download: | 0 times |
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