Guided Autowave Pulse Coupled Neural Network (GAPCNN) based real time path planning and an obstacle...

Problem Statement Background Research MPCNN Model GAPCNN Model MPCNN vs GAPCNN Performance Comparison Results

Guided Autowave Pulse Coupled NeuralNetwork (GAPCNN) based real time path

planning and an obstacle avoidance schemefor mobile robots

Probabilistic Robotics and Intelligent Systems in Motion(PRISM) Lab

Mechatronics EngineeringNational University of Sciences and Technology

17 May, 2014

Usman Ahmed Syed, Usman Malik, Faraz Kunwar, Mazhar Iqbal GAPCNN based real time path planning and obstacle avoidance


Outline

1 Problem Statement

2 Background Research

3 MPCNN Model

4 GAPCNN Model

5 MPCNN vs GAPCNN

6 Performance Comparison

7 Results



Section 1

Problem Statement



Problem Statement

1 Path planning corresponds to two problems:- Determine a feasible path if it exists- Optimality of the path (time, distance, . . . )

2 This paper presents a varient of MPCNN to compute theshortest path in a 2D space for mobile robots.

3 This work presents:- Shortcomings of the MPCNN model proposed recently for

mobile robots.- Directional constraints on the autowave of MPCNN for

informed search of the configuration space.- Dynamic thresholding of the underlaying neural network to

increase time efficiency.- Simulation and experimental results of GAPCNN path planner.



Section 2

Background Research



Background Research

1 Problem of path planning is long addresses by roboticscommunity:- Probabilistic Methods

Fast but lack optimality of paths- Potential Fields

Degrades in the presence of local minima- Visibility Graphs and Voronoi Diagrams

Computationally inefficient- Machine Learning

In most of the cases path ends up to be Non-optimal



Section 3

MPCNN Model



Standard Neuron Model

Single neuron model Feedforward network

1 In general an input-output pair is given through whichweights are learned by repeated measurement of neuronprediction error.

2 Similarly such neurons can be stacked together to getvarious network architectures such as Feedforward andRecurrent Neural nets.



MPCNN: Connectivity Model

w=1 w=1

w=1 w=1

w=1 w=1

w=1

w=1

w=1

w=1

w=1

w=1

w=2

w=2

w=2

w=2

w=1 w=1

w=1

w=1 w=1

w=

1w

=1

w=2

w=2

w=2

w=2

without obstacle neuron with obstacle neuron

1 Assume that the 2D configuration is represented by a 2Dlattice of neurons.

2 Each neuron is connected to its neighbours throughweights given by:

wij =

{1 if j Ns | a-type neurons

2 if j Nd | b-type neurons



MPCNN: Neuron Output

1 Similar to a simple neuron, MPCNN neuron also fires whenits internal energy exceeds a threshold level.

2 A neuron i fires only if some neuron j in its neighborhoodNi fires and this sets neuron i as child neuron to fire atsome later time. The neuron j is said to be the parent NPiand its firing time is denoted as tN

Pi .

3 Each neuron fires only once in its life time.

Yi(t) =

0 for T t < T1 for t = T0 for T < t T +

where could be any amount of time and T = t ifire is the time atwhich neuron i fires.



MPCNN: Internal Energy Model

Activity of each neuron is controlled by its internal energy givenby {

dUi (t)dt = Fi +CLi for t > t

NPi

Ui(t) = 0 for t tNPiWhere C is a constant Fi(t) and Li(t) are the linking andfeeding fields given by:

Li(t) = f (YN1 , . . . ,YNk , t) =

{0 if t < tN

Pi

1 otherwise

Linking input is the actual input from the environment mapwhereas the feeding field is due to the connections with theneighboring neurons.



MPCNN: Internal Energy Model

Fi(t) =g(wir1 , . . . ,wirk , t)Ui(t)Here g is a function of time t and connection weights amongthe k neighbors and is given by:

g(wir1 , . . . ,wirk , t) =

{0 if t < tN

Pi

(wij) if t > tNPi

where (wij) is given by:

(wij) =Bwij

=

{B if j NsB2

if j Nd

Here B is a positive constant.



MPCNN: Threshold/Activation function

When a neuron is activated by a neighboring parent neuron itsinternal energy builds upon. Its energy level is continuouslycompared with the threshold level. The threshold for i th neuroncan be written as:

i(t) =

init for t < tN

Pi

ij for tNPi t < t ifire

f for t > t ifire

where init and f are constants. f is set to a very large valueto ensure that the neuron may not fire again and ij is given as:

ij =

{s if j Nsd if j Nd



MPCNN: Single Neuron Model

Output of a MPCNN neuron is given by the following relation:

Yi(t) = Step(Ui(t)i(t)) ={

1 if Ui(t) i0 otherwise



MPCNN Working

1 Consider that the in 2D configuration space eachconfiguration is represented by a neuron.

2 Initially the goal neuron is intentionaly activated whichenables its neighbors to fire at a later time thus becomingtheir parent.

3 The search proceeds in the form of a pulse through whichneighboring neurons are coupled.

4 Firing pattern propagates outwards in the form of a waveuntil the robot neuron is reached.

5 Parent-child relationship is back traced to find the path.



Section 4

GAPCNN Model



Issues with MPCNN

Analysis of the MPCNN algorithm reveals that it suffers in twoimportant aspects.

1 To find the shortest path it undegoes an uninformed searchby propagating a wave in all directions, not using any of theavailable information to perform an intelligent search.Solution: Perform an informed search.

2 MPCNN assigns the same threshold level to all theneurons in the search space leading to time inefficiency.Solution: Dynamic thresholding to reduce computationaltime.



Dynamic Thresholding

1 Dynamic thresholding is used which accelerates firingneurons that are tentatively along the path while retardingneuron firing in the oppisite direction.

2 The threshold for i th neuron can be written as:

i(t , ) =

init for t < tN

Pi

ij i for tNPi t < t ifiref for t > t ifire

i is the normalized distance of the i th neuron from thetarget neuron given by:

i = A(

1 DtargetDmax

)Here Dtarget is the Euclidean distance from the targetneuron, Dmax and A are scaling constants.



Informed Search BehaviorDirectional constraints on the au-towave are applied by employing anangle modification in the original dif-ferential equation of the internal activ-ity of the neuron.The directional con-straint i is given by:

i = K (i)

g(wiN1 , . . . ,wiNk ,, t) =

{0 if t < tN

Pi

(wij)+i if t > tNPi

Fi(t) =g(wiN1 , . . . ,wiNk ,, t)Ui(t)Usman Ahmed Syed, Usman Malik, Faraz Kunwar, Mazhar Iqbal GAPCNN based real time path planning and obstacle avoidance


GAPCNN Model

1NY C i

f iL

kNY + i

iiNw dt

dU i i iY

g iF Output

riNw )(tU i

Recep!ve Field Modula!on Field Pulse Generator

1

0

f

ij



Section 5

MPCNN vs GAPCNN



Wave propagation control

The MPCNN wave propagatesequally in all directions regard-less of the location of the robotwhile the GAPCNN wavefrontonly propagates in a small re-gion around the target reducingthe number of neurons that havefired.

(a) MPCNN (b) GAPCNN

Robot

Target

Robot

Target

Robot

Target Target

Robot

(a) K = 0.2 (b) K = 0.75 (c) K = 1 (d) K = 5



Dynamic threshold controll

In GAPCNN each neuron of the grid possesses a uniquethreshold in accordance to its location whereas in MPCNNeach neuron was associated with the same threshold level.




Section 6

Performance Comparison



Comparison with MPCNN

Under identical conditions GAPCNN is compared with MPCNN.The mean execution time of MPCNN comes out to be 11.82 mswhereas that of GAPCNN is 3.57 ms. The mean timeimprovement is 8.25 ms which corresponds to a 70 percenttime improvement.



Local Minima Problem

GAPCNN successfully evades with lower computational timeand reduced search space than MPCNN.




Comparison with A*

1 A* works in as similar manner as that of GAPCNN i.e. firstexploration is carried out based upon a cost function andthen shortest path is extracted through parent-childrelations.

2 In all the cases cumulative cost of the resulting paths wasequal but GAPCNN took much lesser time than A*.



Section 7

Results



Simulation Results

B

A

R

B

AR

B

A

R B

A

R

B A

R

B

A

T

R

T B

ARR

T

A

B

T

R

B

A

TR

BA



Simulation Results

B

A R

B

A

R

B

A

RB

A

R B

A

R

R

B

A

T

R

A

B

T

R

T

B

A

BR

T

A A

BR

T

Pursuer

Target

Target

Pursuer

Target

Pursuer

TargetPursuer

TargetPursuer



Experimental Results: Static Environment

T

R

T

R

T

R

T

R

T

R

T

R

(a) (b) (c) (d) (e) (f)

Target

Start



Experimental Results: Dynamic Environment

T

D

R

T

D

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T

DR

T

D

R

T

D

R

TD

R

Start

Target

Dynamic

Obstacle

Target

Start

Dynamic

Obstacle

Start

Target

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Obstacle

Target

Start Dynamic

Obstacle



Experimental Results: Dynamic Environment

T

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T

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T

DR

T

D

R

T

D

R

TD

R

Start

TargetDynamic

ObstacleTarget

Start

Dynamic

Obstacle


Problem StatementBackground ResearchMPCNN ModelGAPCNN ModelMPCNN vs GAPCNNPerformance ComparisonResults

Guided Autowave Pulse Coupled Neural Network (GAPCNN) based real time path planning and an obstacle...

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