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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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)

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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

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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.

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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

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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

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