Path Planning for Mobile Robot using 4EGSOR via Nine- Point Laplacian (4EGSOR9L) Iterative Method

paper presents an attempt to solve path planning problem for a mobile robot operating in indoor environment model using iterative numerical technique. It is based on the use of Laplace's Equation to compute the potential functions in the environment grid model of the robot. The proposed block iterative method, better known as Four Point-Explicit Group via Nine-Point Laplacian (4EGSOR9L), employs a finite- difference scheme to compute the potential functions to be used in generating smooth path between start and goal points. The simulation results demonstrate that the proposed 4EGSOR9L method performs faster than the previous methods in computing the potential functions of the environment model. Keywordspath planning; Four-Point Explicit Group SOR via Nine-Point Laplacian (4EG9LSOR); Laplace's equation.

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

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

[3]  Jumat Sulaiman,et al.  Numerical Solution of Second Kind Linear Fredholm Integral Equations Using QSGS Iterative Method with High-Order Newton-Cotes Quadrature Schemes , 2011 .

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

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

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

[7]  Dolores Blanco,et al.  Robotic Motion Using Harmonic Functions and Finite Elements , 2010, J. Intell. Robotic Syst..

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

[9]  J. Sulaiman,et al.  Robot path planning based on four Point-EGSOR iterative method , 2010, 2010 IEEE Conference on Robotics, Automation and Mechatronics.

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

[11]  D. Young,et al.  Analysis of the SOR iteration for the 9-point Laplacian , 1988 .

[12]  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.

[13]  Pradeep K. Khosla,et al.  Real-time obstacle avoidance using harmonic potential functions , 1991, IEEE Trans. Robotics Autom..

[14]  Jumat Sulaiman,et al.  Numerical technique for robot path planning using four Point-EG iterative method , 2010, 2010 International Symposium on Information Technology.

[15]  David M. Young,et al.  Second-degree iterative methods for the solution of large linear systems , 1972 .

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

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

[18]  Richard M. Murray,et al.  Vehicle motion planning using stream functions , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[19]  Marco Furini,et al.  International Journal of Computer and Applications , 2010 .

[20]  M. Muthuvalu,et al.  Numerical solutions of first kind Linear Fredholm Integral Equations using quarter-sweep successive over-relaxation (QSSOR) Iterative Method , 2011 .

[21]  J. Sulaiman,et al.  Robot Path Planning via EGSOR Iterative Method Using Nine-Point Laplacian , 2012, 2012 Third International Conference on Intelligent Systems Modelling and Simulation.