PATH PLANNING FOR MOBILE ROBOT WITH HALF-SWEEP SUCCESSIVE OVER- RELAXATION (HSSOR) ITERATIVE METHOD

This paper describes our work in solving path planning problem for mobile robot by using harmonic functions to generate path in the configuration space. Harmonic functions are known to have an advantage as a global potential function in the potential field based approach for robot path planning. However, an immense amount of computations are required as the size of the environment get bigger. This work attempts to speed up the computation by solving the harmonic functions with faster solver using Half-Sweep Successive Over-Relaxation (HSSOR) iterative method. The efficiency of this approach is shown by comparing its performance with the previous method.

[1]  D. Young Iterative methods for solving partial difference equations of elliptic type , 1954 .

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

[3]  O. Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[4]  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.

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

[6]  Abdul Rahman Abdullah The four point explicit decoupled group (EDG) Method: a fast poisson solver , 1991, Int. J. Comput. Math..

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

[8]  David J. Evans,et al.  Explicit De-coupled Group Iterative Methods and their Parallel Implementations , 1995, Parallel Algorithms Appl..

[9]  Azzam Ibrahim,et al.  Solving the two dimensional diffusion equation by the four point explicit decoupled group (edg) iterative method , 1995, Int. J. Comput. Math..

[10]  Man Ieee Systems,et al.  IEEE transactions on systems, man and cybernetics. Part B, Cybernetics , 1996 .

[11]  Abdul Rahman Abdullah,et al.  A Comparative Study of Parallel Strategies for the Solution of Elliptic Pde's , 1996, Parallel Algorithms Appl..

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

[13]  Mohamed Othman,et al.  The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) Method for Diffusion Equation , 2004, CIS.

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

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

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

[17]  Mohamed Othman,et al.  Nine Point-EDGSOR Iterative Method for the Finite Element Solution of 2D Poisson Equations , 2009, ICCSA.

[18]  J. Sulaiman Block Iterative Method for Robot Path Planning Azali Saudi , 2010 .