Vision based motion planning using cellular neural network
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Vision based Motion Planning using Cellular Neural Network. Iraji & Bagheri. Supervisor: Dr. Bagheri. Chua and Yang-CNN . Introduction Network Topology r-Neighborhood The Basic Cell Space Invariance State Equation Templates Block Diagram. Introduced 1988. Image Processing

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Vision based Motion Planning using Cellular Neural Network

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Vision based motion planning using cellular neural network

Vision based Motion Planning using Cellular Neural Network

Iraji & Bagheri

Supervisor: Dr. Bagheri


Chua and yang cnn

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

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

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

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

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

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

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

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

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

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

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

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

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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