Robot Path Planning via EGSOR Iterative Method Using Nine-Point Laplacian

Path planning is an important issue as it allows a robot to get from start point to goal point. In this study, we attempts to solve path planning problem for mobile robot based on potential field method that relies on the use of Laplace's Equation to constrain the generation of a potential function over regions of the configuration space of a mobile robot. An experiment based on finite-difference techniques shows a local minima-free motion with smooth path between the start and goal points. This paper proposed a weighted block iterative method also known as EGSOR via 9-Point Laplacian (EGSOR-9) for solving robot path planning problem. The simulation result shows that this new method provides faster solution and smoother path compared to the previous work.

[1]  D.M. Bevly,et al.  Harmonic potential field path planning for high speed vehicles , 2008, 2008 American Control Conference.

[2]  Daniel E. Koditschek,et al.  Exact robot navigation by means of potential functions: Some topological considerations , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[3]  Marina L. Gavrilova,et al.  Roadmap-Based Path Planning - Using the Voronoi Diagram for a Clearance-Based Shortest Path , 2008, IEEE Robotics & Automation Magazine.

[4]  Roderic A. Grupen,et al.  The applications of harmonic functions to robotics , 1993, J. Field Robotics.

[5]  D. J. Evans,et al.  Group explicit iterative methods for solving large linear systems , 1985 .

[6]  I. Parberry,et al.  Optimal Path Planning for Mobile Robot Navigation , 2008, IEEE/ASME Transactions on Mechatronics.

[7]  Mohamed Othman,et al.  Red-Black EDG SOR Iterative Method Using Triangle Element Approximation for 2D Poisson Equations , 2007, ICCSA.

[8]  J. Brian Burns,et al.  Path planning using Laplace's equation , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[9]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[10]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Autonomous Robot Vehicles.

[11]  S. Sasaki.  A practical computational technique for mobile robot navigation , 1998, Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104).

[12]  Simon X. Yang,et al.  Real-Time Robot Path Planning via a Distance-Propagating Dynamic System with Obstacle Clearance , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Explicit group iterative methods for solving elliptic partial differential equations in 3-space dimensions , 1986 .