References

Akishita, S., S. Kawamura and K. Hayashi, 1990. New navigation function utilizing hydrodynamic potential for mobile robot. Proceedings of the IEEE International Workshop on Intelligent Motion Control, Volume 2, August 20-22, 1990, Istanbul, Turkey, pp: 413-417.

Arkin, R.C., 2001. Combining deliberation, reactivity and motivation in the context of a behavior-based robot architecture. Proceedings of the IEEE International Symposium on Computational Intelligence in Robotics and Automation, July 29-August 1, 2001, Banff, Aberta, Canada, pp: 290-295.

Brooks, R.A., 1985. A robust layered control system for a mobile robot. IEEE J. Robot. Automat., 2: 14-23.
CrossRef  |  

Connolly, C.I. and R.A. Grupen, 1993. The applications of harmonic functions to robotics. J. Robotic Syst., 10: 931-946.
CrossRef  |  

Connolly, C.I., J.B. Burns and R. Weiss, 1990. Path planning using Laplace's equation. Proceedings of the IEEE International Conference on Robotics and Automation, Volume 3, May 13-18, 1990, Cincinnati, OH., pp: 2102-2106.

Daily, R. and D.M. Bevly, 2008. Harmonic potential field path planning for high speed vehicles. Proceeding of American Control Conference, June 11-13, 2008, Seattle, WA., pp: 4609-4614.

Evans, D.J. and W.S. Yousif, 1986. Explicit group iterative methods for solving elliptic partial differential equations in 3-space dimensions. Int. J. Comput. Math., 18: 323-340.
CrossRef  |  

Evans, D.J., 1985. Group explicit iterative methods for solving large linear systems. Int. J. Comput. Math., 17: 81-108.
CrossRef  |  

Fauzi, N.I.M. and J. Sulaiman, 2012. Quarter-sweep modified SOR iterative algorithm and cubic spline basis for the solution of second order two-point boundary value problems. J. Applied Sci., 12: 1817-1824.
CrossRef  |  

Garrido, S., L. Moreno, D. Blanco and F.M. Monar, 2010. Robotic motion using harmonic functions and finite elements. J. Intell. Robotic Syst., 59: 57-73.
CrossRef  |  

Hasan, M.K., J. Sulaiman, S.A.A. Karim and M. Othman, 2011. Development of some numerical methods applying complexity reduction approach for solving scientific problem. J. Applied Sci., 11: 1255-1260.
CrossRef  |  Direct Link  |  

Ibrahim, A. and A.R. Abdullah, 1995. Solving The two dimensional diffusion equation by the four point Explicit Decoupled Group (EDG) iterative method. Int. J. Comput. Math., 58: 253-256.
CrossRef  |  Direct Link  |  

Kazemi, M. and M. Mehrandezh, 2004. Robotic navigation using harmonic function-based probabilistic roadmaps. Proceedings of the IEEE International Conference on Robotics and Automation, Volume 5, April 26-May 1, 2004, New Orleans, LA, USA., pp: 4765-4770.

Khatib, O., 1985. Real time obstacle avoidance for manipulators and mobile robots. Proceedings of the IEEE International Conference on Robotics and Automation, Volume 2, March 25-28, 1985, Philadelphia, pp: 500-505.

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, Volume 4, March 1987, Raleigh, NC., pp: 1-6.

Muthuvalu, M.S. and J. Sulaiman, 2011. Numerical solution of second kind linear fredholm integral equations using QSGS iterative method with high-order newton-cotes quadrature schemes. Malaysian J. Math. Sci., 5: 85-100.
Direct Link  |  

Muthuvalu, M.S. and J. Sulaiman, 2011. Numerical solutions of first kind linear fredholm integral equations by using quarter-sweep SOR with piecewise linear collocation method QSSOR with piecewise linear collocation method for fredholm equations. Aust. J. Basic Applied Sci., 5: 18-24.
Direct Link  |  

Rosell, J. and P. Iniguez, 2005. Path planning using harmonic functions and probabilistic cell decomposition. Proceedings of the IEEE International Conference on Robotics and Automation, April 18-22, 2005, Barcelona, Spain, pp: 1803-1808.

Sasaki, S., 1998. A practical computational technique for mobile robot navigation. Proceedings of the IEEE International Conference on Control Applications, Volume 2, September 1-4, 1998, Trieste, pp: 1323-1327.

Saudi, A. and B. Hallam, 2004. A tale of two behaviour-based robots mindstorms vs technic. Proceedings of the IEEE Region 10 Conference, Volume 4, November 21-24, 2004, Chiang Mai, Thailand, pp: 479-482.

Saudi, A. and J. Sulaiman, 2010. Block iterative method using nine-point laplacian for robot path planning. Eur. J. Scient. Res., 43: 204-211.
Direct Link  |  

Saudi, A. and J. Sulaiman, 2010. Numerical technique for robot path planning using four point-eg iterative method. Proceedings of the 2010 International Symposium on Information Technology, June 15-17, 2010, Kuala Lumpur, Malaysia, pp: 831-836.

Saudi, A. and J. Sulaiman, 2010. Robot path planning based on four point-EGSOR iterative method. Proceedings of the IEEE Conference on Robotics Automation and Mechatronics, June 28-30, 2010, Singapore, pp: 476-481.

Saudi, A. and J. Sulaiman, 2012. Laplacian Behaviour-Based Control (LBBC) for the path planning of mobile robot via four point-EGSOR. Int. J. Comput. Inform. Technol., 1: 81-87.
Direct Link  |  

Saudi, A. and J. Sulaiman, 2012. Laplacian behaviour-based control for robot path planning using Full-Sweep Successive Over-Relaxation via nine-point laplacian (FSSOR9L). Int. J. Applied Sci. Technol., 2: 255-261.
Direct Link  |  

Saudi, A. and J. Sulaiman, 2012. Robot path planning using four point-explicit group via nine-point laplacian (4EG9L) iterative method. J. Procedia Eng., 41: 182-188.
CrossRef  |  

Saudi, A. and J. Sulaiman, 2012. Robot path planning via EGSOR iterative method using nine-point laplacian. Proceedings of the 3rd International Conference on Intelligent Systems, Modelling and Simulation, February 8-10, 2012, Kota Kinabalu, Malaysia, pp: 61-66.

Saudi, A. and J. Sulaiman, 2013. Indoor path planning for mobile robot using LBBC-EG. Int. J. Imaging Robotics, 11: 37-45.

Saudi, A. and J. Sulaiman, 2014. Hybrid path planning for indoor robot with laplacian Behaviour-based control via four Point-explicit group. Int. J. Imaging Robotics, 12: 12-21.
Direct Link  |  

Silva Jr. E.P., P.M. Engel, M. Trevisan and M.A.P. Idiart, 2002. Exploration method using harmonic functions. Robotics Autonomous Syst., 40: 25-42.
CrossRef  |  

Sulaiman, J., M. Othman and M.K. Hasan, 2007. Red-black EDGSOR iterative method using triangle element approximation for 2D poisson equations. Proceedings of the International Conference on Computational Science and Its Applications, August 26-29, 2007, Kuala Lumpur, Malaysia, pp: 298-308.

Szulczynski, P., D. Pazderski and K. Kozłowski, 2011. Real-time obstacle avoidance using harmonic potential functions. J. Autom. Mobile Robotics Intell. Syst., 5: 59-66.
Direct Link  |  

Young, D.M., 1972. Second-degree iterative methods for the solution of large linear systems. J. Approximation Theory, 5: 137-148.