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1 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 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 2 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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 Motion Planning Methods Basic concepts Proposed Model (FAPF) Local Minima Stochastic Learning Automata Adaptive planning system (AFAPF) Conclusions Global Approaches Decomposition 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 14
