Vision based Motion Planning using Cellular Neural Network

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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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