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This paper presents the application of harmonic functions in solving the robot path planning problem. The harmonic function is obtained by solving the Laplace’s equation. In this study, the harmonic functions act as potential values at each point in the robot environment. These potential values are then used to find path from the starting point to the specified target point. In order to obtain these harmonic functions, the most commonly used approaches are the finite difference methods of Jacobi, Gauss-Seidel and Successive Over-relaxation (SOR). However, these standard iterative methods are too slow, especially when it involves large environments. Therefore, this study proposes faster methods that employ the combination of quarter sweep techniques with SOR iteration. The results of experiments show that these proposed methods have successfully reduced the time of computation of harmonic functions drastically. This has directly improved the overall performance of the path planning algorithm, particularly in terms of execution time. J. Sci. Math. Lett. UPSI Volume 5 (2017) 1 15 ISSN 2462-2052 2

Perancangan Laluan Robot menggunakan Fungsi Harmonik melalui Kaedah Lelaran Sapuan Suku