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Transcript of Cellular Presentation [EDocFind.com][1]
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8/6/2019 Cellular Presentation [EDocFind.com][1]
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1
Vision based Motion Planning using Cellular
Neural Network
Iraji & Bagheri
Supervisor: Dr. Bagheri
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8/6/2019 Cellular Presentation [EDocFind.com][1]
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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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 3
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 4
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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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 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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 6
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 7
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 8
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 9
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 10
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 11
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 12
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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8/6/2019 Cellular Presentation [EDocFind.com][1]
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Sharif University of Techology 13
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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Sharif University of Techology 14
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)