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Using Neural Networks for Motion Planning
Iraji & Bagheri
Supervisor: Dr. Bagheri
Outline
 Basic concepts
 NN for Motion Planning
 NN Models
 DWENN
 Comparative Simulation
 Conclusions
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Basic Concepts
 Robot navigation is one of the key issue in mobile
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
robotics.
 The simplest problem is to find a continuous path from a
starting location to a target location.
 The path of a robot should be:
– Safe (collision-free)
– Optimal or close to optimal
– Natural: In a complex situation the robot does not get lost and
goes far away from its destination.
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Basic Concepts (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Global Approaches
Decomposition
Road-Map
Retraction Methods
Require a preprocessing stage (a graph structure
of the connectivity of the robot’s free space)
 Local Approaches: Need heuristics, e. g. the
estimation of local gradients in a potential field
 Randomized Approaches
 Genetic Algorithms
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NN for Motion Planning
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Neural networks are used for path generation in non-
stationary environments for real-time planning.
 The neurons of the network are arranged in a regularly
discretized lattice.
 A scalar potential field is formed by repetitively
generated waves of neural activity, which originate form
the target location.
 Classification of the models:
– Environment type:
• Stationary
• Dynamic
– Environment representation:
• Algebraic
• Grid-based
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NN for Motion Planning
(cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Configuration space (C): Discretized hypercube in RN
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where N is number of degrees-Of-Freedom (DOF).
Each discrete position in C is associated with a formal
neuron.
Each neuron i is connected to its neighbors within a
certain radius, which comprise its neighborhood Si.
Dynamics of networks perform an averaging of the
potentials of the local neighboring neurons.
The initial activity potential associated with the target
location is distributed through the network field.
Neurons associated with obstacle locations receive a
negative value on their external inputs.
Each path step is done in the direction of the neighbor
with the maximal value.
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NN Models
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Resistive Grid:
– Each neuron is connected to its 2N closest neighbors,
where N is dimensionality of the state space.
– Evolution of the ith node:
1
xi (t  1)  I i 
2N
 x (t )
jSi
j
– It is based on a numerical approximation of a
solution  ( x, y ) of the Laplace equation (in 2D):
 2  2
 2 0
2
x
y
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NN Models (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Glasius et al:
– Discrete-time Hopfield-type NN, whose dynamics is described
by:
 i  j

, if i  j  r
e
xi (t  1)  g ( wij x j (t )  I i ) wij  
if i  j  r

jSi
 0,
2

– Ii encodes the information about the target and obstacle position:
i is the t arg et
 v,

I i   v, i is an obstacle
 0,
else

0,

g ( x )    x,
 1,

x0
x  [0,1]
x 1
– where v  , v  1 and 0    1 .
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NN Models (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Yang et al:
– Continuous-time dynamics, which is derived from the
Grossberg’s shunting model:
 

dxi

  Axi  ( B  xi ) [ I i ]   wij [ x j ]   ( D  xi )[ I i ]
dt
jSi




– where xi  [ D, B], [a]  max{ a,0} and [a]  max{ a,0} .
 
, if 0  i  j  r

wij   i  j
0,
if i  j  r

– Some additional efforts for tuning and selection of proper
network parameters are required.
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NN Models (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Chen et al:
– Decay rate A>0 may be chosen arbitrarily:
dxi
  Axi  Di m  wij x j  I i
dt
jSi
– where Di=0 for the obstacles, and Di=1, otherwise.
– The external input Ii is positive for the target neuron,
and is zero, otherwise.
– The connection weights wij=1 if network
2 1
neighborhoods are 4-connected, while wij  8m A  1
if the latter are 8-connected.
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Dynamic Wave Expansion
Neural Network (DWENN)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 DWENN algorithm idea: Organize wave
propagation similar to waves in water
spreading.
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DWENN (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 A neuron inherits the activity from a neighbor, which is:
– Closer to the target neuron
– Is not an obstacle neuron
and which belongs to:
– Active (i.e. this neighbor has a positive activity value)
– Actual (i.e. this neighbor has changed its activity level at the
previous time step)
wave front.
 The activities of all neurons constitute a scalar potential
field, in which the minimal positive value is always at
the target location.
 The robot is globally ‘attracted’ by the target, and starts
to move as soon as the first wave front reaches its initial
position.
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DWENN (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Initially, the activity values of all neurons and all
connection weights are zero.
 Three classes of neurons are distinguished with
dynamics given by:
– For the target (i=i*(t)): xi(t+1)=1
– For its direct neighbors ( i  Si (t )):
*
 x (t )  1, if i* (t  1)  i* (t )
xi (t  1)   i
otherwise
2,
– For all other neurons:
xi (t  1)   wij (t )( x j (t )  2)
jSi
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Network Dynamics
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 Connection weights are determined in
accordance with
 jk , if k  Si is the first neuron

wij (t  1)  
for which (a)  (d ) hold
 0,
otherwise
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 Selective flow of neural activity:
– (a) k is not an obstacle.
– (b) xk(t)>0.
– (c) xk (t )  xk (t  1)
– (d) if (xi(t)+xi(t-1))>0, then xk(t)<xi(t) must hold.
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Example
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Target
Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
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Example (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
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Example (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
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Example (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
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Example (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
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Network Dynamics (cont’d)
 Property 1: If in a stationary environment the first wave front
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
reaches neuron i at the time step ta, then this neuron becomes active
with value xi(ta)=(2ta-1).
 Property 2: If there exists a positive weight wij for neuron i, then
this weight indicates the gradient direction in the potential field:
wij  0  xi  x j
 Property 3: The activity level of neuron i is bounded by the
doubled number of network iterations n: xi (t )  n
 Property 4: If an active neuron i has become inactive, then it will
stay inactive at the following time step. Indeed, if xi(t-1)>0 and
xi(t)=0, then xk(t)<xi(t) is always false, therefore, the condition (d) is
also false, and j  Si : wij  0, and, hence, xi(t+1)=0. (propagation
of inhibitory wave)
Property 5: If an active neuron remains active, then its activity
level is increased by one at each time step: xi (t )  0  xi (t  c)  xi (t )  c
 Property 6: If neuron i became active at time ti and neuron j at time
tj>ti, then xj(t)>xi(t) for all t  t j  ti.
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Obstacle Avoidance in Dynamic
Environments
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 An inactive neuron may initiate the propagation
of an inhibitory wave.
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Comparative Simulation
 Closing Gate:
Chen
DWENN
Resistive Grid
Glasius
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Yang
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Comparative Simulation (cont’d)
 Freezing up obstacles:
Chen
DWENN
Resistive Grid
Glasius
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Yang
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Comparative Simulation (cont’d)
 In all simulations the network consists of 3600 (60×60) neurons
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
representing a 2D workspace.
 The statistical evaluations were based on 500 runs per model.
 Dynamics of other models are not fast enough to provide rapid
adaptation to the sudden stopping of the obstacles
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Comparative Simulation
 Moving Target Pursuit:
Chen
DWENN
Resistive Grid
Glasius
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Yang
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Conclusions
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 The resistive grid model has the slowest dynamics.
Usually, several local maxima appear when the
environment is changing rapidly.
 The model by Glasius et al. in complex dynamic scenes
is not fast enough to adapt to the changes. Some efforts
are also needed to find an appropriate set of the model
parameters.
 The model by Yang et al. requires a larger number of
iterations to converge to a solution.
 In the model by Chen et al. the network dynamics and
the quality of a generated path, significantly depend on
the choice of parameters. The most important model
parameters are A (the passive decay rate) and  , which
defines ‘how much’ activity is transferred between a
neuron and its neighbors.
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Conclusions (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 DWENN model is parameter-free.
 In the worst case 2N×5 simple binary operations are
needed.
 To prevent local minima, the propagation of inhibitory
waves is triggered.
 In a stationary environment the complexity of the
DWENN model does not depend on the dimensionality
of C.
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Conclusions (cont’d)
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Basic concepts
NN for Motion
Planning
NN Models
DWENN
Comparative
Simulation
Conclusions
 But, by examining experimental results, it is easy to
see that the robot does not select optimal path in
DWENN.
 It seems that it is because of non-inhibitory behavior of
stationary obstacles.
Non-optimal path
 Proposed solution: Emanating some inhibitory wave of
from obstacles with respect to target.
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Any Question?
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