We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 November 2024
Call for Paper
December Edition
IJCA solicits high quality original research papers for the upcoming December edition of the journal. The last date of research paper submission is 20 November 2024

Submit your paper
Know more
The week's pick
Responsive image
An Efficient Restoration Method for the Faint Dot Matrix Images

Ao Zhu Peng Cao
Random Articles
Reseach Article

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

by Azali Saudi, Jumat Sulaiman
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 53 - Number 16
Year of Publication: 2012
Authors: Azali Saudi, Jumat Sulaiman
10.5120/8509-2568

Azali Saudi, Jumat Sulaiman . Path Planning for Mobile Robot using 4EGSOR via Nine-Point Laplacian (4EGSOR9L) Iterative Method. International Journal of Computer Applications. 53, 16 ( September 2012), 38-42. DOI=10.5120/8509-2568

@article{ 10.5120/8509-2568,
author = { Azali Saudi, Jumat Sulaiman },
title = { Path Planning for Mobile Robot using 4EGSOR via Nine-Point Laplacian (4EGSOR9L) Iterative Method },
journal = { International Journal of Computer Applications },
issue_date = { September 2012 },
volume = { 53 },
number = { 16 },
month = { September },
year = { 2012 },
issn = { 0975-8887 },
pages = { 38-42 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume53/number16/8509-2568/ },
doi = { 10.5120/8509-2568 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:54:29.445142+05:30
%A Azali Saudi
%A Jumat Sulaiman
%T Path Planning for Mobile Robot using 4EGSOR via Nine-Point Laplacian (4EGSOR9L) Iterative Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 53
%N 16
%P 38-42
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This 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.

References
  1. Khatib, O. 1985. Real time obstacle avoidance for manipulators and mobile robots. IEEE Transactions on Robotics and Automation 1:500–505.
  2. Koditschek, D. E. 1987. Exact robot navigation by means of potential functions: Some topological considerations. Proceedings of the IEEE International Conference on Robotics and Automation: 1-6.
  3. Connolly, C. I. , Burns, J. B. , & Weiss, R. 1990. Path planning using Laplace's equation. Proceedings of the IEEE International Conference on Robotics and Automation: 2102–2106.
  4. Akishita, S. , Kawamura, S. , & Hayashi, K. 1990. Laplace potential for moving obstacle avoidance and approach of a mobile robot. Japan-USA Symposium on flexible automation, A Pacific rim conference: 139–142.
  5. Connolly, C. I. , & Gruppen, R. 1993. On the applications of harmonic functions to robotics. Journal of Robotic Systems, 10(7): 931–946.
  6. Sasaki, S. 1998. A Practical Computational Technique for Mobile Robot Navigation. Proceedings of the IEEE International Conference on Control Applications: 1323-1327.
  7. Waydo, S. & Murray, R. M. 2003. Vehicle motion planning using stream functions. In Proc. of the Int. Conf. on Robotics and Automation (ICRA), 2003, pp. 2484-2491.
  8. Daily, R. , & Bevly, D. M. 2008. Harmonic Potential Field Path Planning for High Speed Vehicles. In the proceeding of American Control Conference, Seattle, June 11-13, 4609-4614.
  9. Garrido, S. , Moreno, L. , Blanco, D. & Monar, F. M. 2010. Robotic Motion Using Harmonic Functions and Finite Elements. Journal of Intelligent and Robotic Systems archive. Volume 59, Issue 1, July 2010. Pages 57 – 73.
  10. Szulczy?ski, P. , Pazderski, D. & Koz?owski, K. 2011. Real-Time Obstacle Avoidance Using Harmonic Potential Functions. Journal of Automation, Mobile Robotics & Intelligent Systems. Volume 5, No 3, 2011.
  11. Evans, D. J. 1985. Group Explicit Iterative methods for solving large linear systems. Int. J. Comp. Maths. , 17: 81-108.
  12. Evans, D. J & Yousif, W. S. 1986. Explicit Group Iterative Methods for solving elliptic partial differential equations in 3-space dimensions. Int. J. Computer Maths, 18:323-340.
  13. Ibrahim, A. 1993. The Study of the Iterative Solution of Boundary Value Problem by the Finite Difference Methods. PhD Thesis. Universiti Kebangsaan Malaysia.
  14. Sulaiman, J. , Hasan, M. K. & Othman, M. 2007. Red-Black EDGSOR Iterative Method Using Triangle Element Approximation for 2D Poisson Equations. In. O. Gervasi & M. Gavrilova (Eds). Computational Science and Its Application 2007. Lecture Notes in Computer Science (LNCS 4707): 298-308. Berlin: Springer-Verlag.
  15. Adams, L. M. , Leveque, R. J. & Young, D. M. 1988. Analysis of the SOR Iteration for the 9-Point Laplacian. SIAM Journal of Numerical Analysis 25 (5): 1156-1180.
  16. Saudi, A. and Sulaiman, J. 2010. Numerical technique for robot path planning using four Point-EG iterative method. In proc. of the 2010 Int. Symposium on Information Technology (ITSim), Page(s): 831 – 836. ISBN: 978-1-4244-6715-0.
  17. Saudi, A. and Sulaiman, J. 2010. Robot path planning based on four Point-EGSOR iterative method. In proc. of the 2010 IEEE Conference on Robotics Automation and Mechatronics (RAM), Page(s): 476 – 481. ISBN: 978-1-4244-6503-3.
  18. Saudi, A. and Sulaiman, J. 2010. Block Iterative Method using Nine-Point Laplacian for Robot Path Planning. European Journal of Scientific Research. ISSN 1450-216X Vol. 43 No. 2 (2010), pp. 204-211.
  19. Saudi, A. and Sulaiman, J. 2012. Robot Path Planning via EGSOR Iterative Method Using Nine-Point Laplacian. In proc. of the 2012 3rd Int. Conf. on Intelligent Systems, Modelling and Simulation (ISMS), Page(s): 61 – 66. ISBN: 978-1-4673-0886-1.
  20. Young, D. M. 1971. Iterative solution of large linear systems. London: Academic Press.
  21. Young, D. M. 1972. Second-degree iterative methods for the solution of large linear systems. Journal of Approximation Theory. 5:37-148.
  22. Young, D. M. 1976. Iterative solution of linear systems arising from finite element techniques. In: Whiteman, J. R. (Eds. ). The Mathematics of Finite Elements and Applications II: 439-464. London: Academic Press.
  23. Akhir, M. K. M, Othman, M. , Sulaiman, J. , Majid, Z. A. & Suleiman, M. 2012. Half-Sweep Iteration for Solving Two-Dimensional Helmholtz Equations. International Journal of Applied Mathematics and Statistics, Vol. 29(5):101-109. ISSN: 0973-7545.
  24. Muthuvalu, M. S. & Sulaiman, J. 2011. Numerical Solution of Second Kind Linear Fredholm Integral Equations Using QSGS Iterative Method with High-Order Newton-Cotes Quadrature Schemes. Malaysian Journal of Mathematical Sciences. Vol. 5(1): 85-100.
  25. Muthuvalu, M. S. & Sulaiman, J. 2011. Numerical Solutions of First Kind Linear Fredholm Integral Equations Using Quarter-Sweep Successive Over-Relaxation (QSSOR) Iterative Method. International Journal of Open Problems in Computer Science and Mathematics. Vol. 4. No. 1, March 2011:184-196.
Index Terms

Computer Science
Information Sciences

Keywords

Robot path planning Four-Point Explicit Group SOR via Nine-Point Laplacian (4EG9LSOR) Laplace's equation

Powered by PhDFocusTM