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Vision-Based Motion Planning Using Cellular Neural Networks

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This paper explores vision-based motion planning through Cellular Neural Networks (CNNs), emphasizing their application in robotic and biological vision systems. Introduced in 1988, CNNs are effective for image and video signal processing, offering both versatility and simplicity in implementation. The paper delves into network topology, the r-neighborhood structure, and key components such as the basic cell and state equations. By evaluating distances and utilizing the successive comparisons method, we demonstrate how CNNs can facilitate sophisticated path planning in dynamic environments.

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Vision-Based Motion Planning Using Cellular Neural Networks

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  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

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