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Vision based Motion Planning using Cellular

Neural Network

Iraji & Bagheri

Supervisor: Dr. Bagheri

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Sharif University of Techology 2

Chua and Yang-CNN

Introduced 1988.

Image Processing

Multi-disciplinary:

Robotic Biological vision

Image and video signal processing

Generation of static and dynamic patterns:

Chua & Yang-CNN is widely used due to Versatility versus simplicity. Easiness of implementation.

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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Network Topology

Regular grid , i.e. matrix, ofcells.

In the 2-dimensional case: Each cell corresponds to a pixel in the

image.

A Cell is identified by its position inthe grid.

Local connectivity. Direct interaction among adjacent

cells.

Propagation effect -> Globalinteraction.

C(I , J)

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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r - Neighborhood

The set of cells within a certain distance r to

cell C(i,j). where r >=0.

Denoted Nr(i,j).

Neighborhood size is (2r+1)x(2r+1)

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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The Basic Cell

Cell C(i,j) is a dynamical system The state evolves according to prescribed state equation.

Standard Isolated Cell: contribution of state and inputvariables is given by using weighting coefficients:

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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Space Invariance

Inner cells.

same circuit elements and element values

has (2r+1)^2 neighbors

Space invariance.

Boundary cells.

Boundary Cells Inner Cells

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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State Equation

xijis the state of cell

Cij.

Iis an independent bias constant.

yij(t) =f(xij(t)), wherefcan be any

convenient non-linear function.

The matricesA(.) andB(.) are known ascloning templates.

constant external input uij.

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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Templates

The functionality of the CNN array can be

controlled by the cloning templateA, B,I

WhereAandBare (2r+1) x (2r+1) real

matrices

Iis a scalar number in two dimensional cellular

neural networks.

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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Block diagram of one cell

The first-order non-linear differential equation

defining the dynamics of a cellular neural network

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

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ROBOT PATH PLANNING USING

CNN Environment with obstacles must be divided into

discrete images.

Representing the workspace in the form of an MN

cells. Having the value of the pixel in the interval [-1,1].

Binary image, that represent obstacle and target and

start positions.

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

Path Planning

By CNN

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Flowchart of Motion Planning

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

Path Planning

By CNN

Flowchart ofPlanning

CNN Computing

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Distance Evaluation

Distance evaluation between free points from the

workspace and the target point.

Using the template explore.tem

ais a nonlinear function, and depends on thedifference yij-ykl.

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

Path Planning

By CNN

Flowchart ofPlanning

Distance

Evaluation

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SUCCESSIVE COMPARISONS METHOD

Path planning methodthrough successivecomparisons.

Smallest neighbor cellfrom eight possibledirections N, S, E, V,SE, NE, NV, SV, is

chosen. Template from the

shift.tem family

Introduction

Network

Topology

r-Neighborhood

The Basic Cell

SpaceInvariance

State Equation

Templates

Block Diagram

Path Planning

By CNN

Flowchart ofPlanning

Distance

Evaluation

Successive

Comparison

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Motion Planning Methods

Global Approaches Basic concepts Proposed

Model (FAPF)

Local Minima

Stochastic

LearningAutomata

Adaptive

planning system

(AFAPF)

Conclusions

Randomized Approaches

Genetic Algorithms

Local Approaches:Need heuristics, e. g. theestimation of local gradients in a potential field

Decomposition

Road-Map

Retraction Methods

Require a preprocessing stage (a graph structure

of the connectivity of the robots free space)