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 finitedifference 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.
Essentially, a truly autonomous mobile robot be capable of finding its own path from start to goal location without colliding with any obstacles. This paper investigates the effectiveness of a robot path planning technique that utilizes Laplacian Behaviour-Based Control (LBBC) for robot control and uses Laplace's Equation for generating potential function in the configuration space model. The robot control namely LBBC would enable the robot to recover from getting stuck in a flat region. Furthermore, an efficient iteration technique via Half-Sweep Successive Over-Relaxation (HSSOR) would provide fast computation for solving the Laplace's equation that represents the potential values of the configuration space.
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