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This paper proposed fast Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L) iterative method for solving path planning problem for a mobile robot operating in indoor environment model. It is based on the use of Laplace's Equation to constraint the distribution of potential values in the environment of the robot. Fast computation with half-sweep iteration is obtained by considering only half of whole points in the configuration model. The inclusion of SOR and 9-point Laplacian into the formulation further speeds up the computation. The simulation results show that HSSOR9L performs much faster than the previous iterative methods in computing the potntial values to be used for generating smooth path from a given initial point to a specified goal position. Keywords - Robot path planning, Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L), Laplace's Equation, Harmonic functions The capability of moving quickly from a given initial point to a specified goal point is essential for truly autonomous mobile robot operating in indoor environment. While exploring the environment, the robot must avoid any obstacles and walls that obstructing its motion. Therefore, path planning problem pose as an important issue in building a robust indoor mobile robot. This study proposed a global numerical approach in solving this difficult path planning problem. It is based on the theory of a steady-state heat transfer, in which the configuration space is modeled with Laplace's equation. Consequently, the solutions of Laplace's equation also called harmonic functions that represent temperature values distribution in the configuration space will be used to simulate the generation of path for mobile robot motion. In the past, various approaches had been used to obtain harmonic functions, but the most common method is via numerical techniques due to the availability of fast processing machine and their elegant and efficiency in solving the problem. In this study, we investigate the performance of Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L) in computing the harmonic functions to generate path for a mobile robot operating in varying sizes of indoor environment model. II.

Path Planning for Indoor Mobile Robot using Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L)