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Vision based Motion Planning using Cellular Neural Network

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Chua and Yang-CNN

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- 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.

Sharif University of Techology

Network Topology

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- 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)

Sharif University of Techology

r - Neighborhood

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- 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)

Sharif University of Techology

The Basic Cell

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- 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:

Sharif University of Techology

Space Invariance

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- Inner cells.
- same circuit elements and element values
- has (2r+1)^2 neighbors
- Space invariance.
- Boundary cells.

Inner Cells

Boundary Cells

Sharif University of Techology

State Equation

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- 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.

Sharif University of Techology

Templates

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- 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.

Sharif University of Techology

Block diagram of one cell

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram

- The first-order non-linear differential equation defining the dynamics of a cellular neural network

Sharif University of Techology

ROBOT PATH PLANNING USING CNN

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram
- Path Planning By 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.

Sharif University of Techology

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

Sharif University of Techology

Distance Evaluation

- Introduction
- Network Topology
- r-Neighborhood
- The Basic Cell
- Space Invariance
- State Equation
- Templates
- Block Diagram
- Path Planning By CNN
- Flowchart of Planning
- 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.

Sharif University of Techology

SUCCESSIVE COMPARISONS METHOD

- 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

- 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

Sharif University of Techology

Motion Planning Methods

Decomposition

- Basic concepts
- Proposed Model (FAPF)
- Local Minima
- Stochastic Learning Automata
- Adaptive planning system (AFAPF)
- Conclusions

- Global Approaches

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

Sharif University of Techology

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