Laplacian Behaviour-Based Control (LBBC) for Robot Path Planning using Explicit Group Successive Over-Relaxation via Nine-Point Laplacian (EGSOR9L) Iterative Method

In this paper, we proposed a searching algorithm for generating path of a mobile robot. The method is inspired by the behaviour-based paradigm approach to robotics architecture, in which the searching algorithm employs Laplacian Behaviour-Based Control (LBBC) during space exploration of the environment. The LBBC make use of the potential function in the configuration space to guide its exploration. Laplace’s equation was used to represent the potential function in the configuration space of the robot. Consequently, the gradient of the potential function would be used by the searching algorithm to generate path from starting to goal location. In complex environment, however, it suffers from the occurrence of flat region with no appreciable gradient, which result in the difficulty for the searching algorithm to generate path. The LBBC would enable the searching algorithm to generate path successfully even with the occurrence of this flat region. In this paper, the solution to Laplace’s equation is calculated with block iteration via Explicit Group Successive Over-Relaxation via Nine-Point Laplacian (EGSOR9L) iterative method for rapid computation compared to the traditional Gauss-Seidel iteration and standard SOR