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Vision based Motion Planning using Cellular Neural Network

Iraji & Bagheri

Supervisor: Dr. Bagheri

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 Space

Invariance State Equation Templates Block Diagram

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Network Topology

Regular grid , i.e. matrix, of cells.

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

image.– A Cell is identified by its position in

the grid.

Local connectivity.– Direct interaction among adjacent

cells.– Propagation effect -> Global

interaction. C(I , J)

Introduction Network

Topology r-Neighborhood The Basic Cell Space

Invariance 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 Space

Invariance State Equation Templates Block Diagram

Sharif University of Techology 5

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 input variables is given by using weighting coefficients:

Introduction Network

Topology r-Neighborhood The Basic Cell Space

Invariance 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 Space

Invariance State Equation Templates Block Diagram

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State Equation

xij is the state of cell Cij. I is an independent bias constant. yij(t) = f(xij(t)), where f can be any convenient

non-linear function. The matrices A(.) and B(.) are known as cloning

templates. constant external input uij.

Introduction Network

Topology r-Neighborhood The Basic Cell Space

Invariance State Equation Templates Block Diagram

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Templates The functionality of the CNN array can be

controlled by the cloning template A, B, I Where A and B are (2r+1) x (2r+1) real

matrices I is a scalar number in two dimensional cellular

neural networks.

Introduction Network

Topology r-Neighborhood The Basic Cell Space

Invariance 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 Space

Invariance 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 M×N

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 Space

Invariance State Equation Templates Block Diagram Path Planning

By CNN

Sharif University of Techology 11

Flowchart of Motion Planning Introduction Network

Topology r-Neighborhood The Basic Cell Space

Invariance State Equation Templates Block Diagram Path Planning

By CNN Flowchart of

Planning

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

– a is a nonlinear function, and depends on the difference yij-ykl.

Introduction Network

Topology r-Neighborhood The Basic Cell Space

Invariance State Equation Templates Block Diagram Path Planning

By CNN Flowchart of

Planning Distance

Evaluation

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SUCCESSIVE COMPARISONS METHOD

Path planning method through successive comparisons.

Smallest neighbor cell from eight possible directions N, S, E, V, SE, NE, NV, SV, is chosen.

Template from the shift.tem family

Introduction Network

Topology r-Neighborhood The Basic Cell Space

Invariance State Equation Templates Block Diagram Path Planning

By CNN Flowchart of

Planning Distance

Evaluation Successive

Comparison

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Motion Planning Methods Global Approaches Basic concepts

Proposed Model (FAPF)

Local Minima Stochastic

Learning Automata

Adaptive planning system (AFAPF)

Conclusions

Randomized Approaches Genetic Algorithms

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

Decomposition

Road-Map

Retraction Methods

Require a preprocessing stage (a graph structure of the connectivity of the robot’s free space)