Intelligent Systems

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Intelligent Systems

• Lectures 17
• Control systems of robots based on Neural
  Networks

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Neuron of MacCallockPittsThreshold Logical Unit
(TLU)
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Geometry of TLU
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R-category linear classifier based on TLU
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Geometric Interpretation of action of linear
classifier
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2-layer network
Three Planes Implemented by the Hidden Units
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Multi Layer Perceptron (MLP) (Feed-forward
network)
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Kinds of sigmoid used in perceptrons
Exponential Rational Hyperbolic tangent
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Formulas for error back propagation algorithm
(1)
Modification of weights of synapses of jth neuron
connected with ith ones, xj state of jth neuron
(output)
(2)
For output layer
(3)
For hidden layers k number of neuron in next
layer connected with jth neuron
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Hopfield network

• 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

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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

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

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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 dont. This is because
  the weight of the object has to be added to the
  weight of the arm (thats why robot arms are so
  heavy making the relative weight change very
  small)

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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

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.

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Camera-robot coordination is function
approximation (2)
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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

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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
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Camera-robot coordination is function
approximation (5). feed-forward networks (2)
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Camera-robot coordination is function
approximation (6). feed-forward networks (3)
or
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Camera-robot coordination is function
approximation (7). feed-forward networks (4)
The Jacobian matrix can be used to calculate the
change in the function when its parameters change
The learning rule applied here regards the plant
as an additional and unmodiable layer in the
neural network
where i iterates over the outputs of the plant
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Camera-robot coordination is function
approximation (8). Topology conserving maps
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Camera-robot coordination is function
approximation (9). Topology conserving maps (2)
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Robot arm dynamics (Kawato et al, 1987)
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Robot arm dynamics (2)
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Nonlinear transformations used in the Kawato model
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Robot arms dynamics (4)
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Mobile robots
Schematic representation of the stored rooms and
the partial information which is available from a
single sonar scan
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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
strategies the local information is constantly
used to give a best guess what the global
environment may contain
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Mobile robots (3)
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Sensor based control
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The structure of the network for the autonomous
land vehicle
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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.
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Drama
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DRAMA (2)
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DRAMA (3). Associative module
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DRAMA (4)
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DRAMA (5)
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DRAMA (6)
Learning