1 Vision based Motion Planning using Cellular Neural Network Iraji & Bagheri Supervisor: Dr. Bagheri

Sharif University of Techology2 Chua and Yang-CNN  Introduced  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

Sharif University of Techology3 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

Sharif University of Techology4 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 Techology5 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

Sharif University of Techology6 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

Sharif University of Techology7 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

Sharif University of Techology8 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

Sharif University of Techology9 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

Sharif University of Techology10 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 Techology11 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 Techology12 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

Sharif University of Techology13 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

Sharif University of Techology14 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)