Path planning simulation using harmonic potential fields through four point-EDGSOR method via 9-point laplacian

Abstract

This paper presents our study on a simulation of path planning for indoor robot that relies on the use of Laplace’s equation to constrain the generation of Harmonic Potential Fields (HPF). The computation of HPF requires immense amount of computing resources, particularly when the size of environment is large. In the past, fast iterative methods that apply the use of half-sweep iteration and block technique are suggested. In this study, faster iterative method known as Four Point-Explicit Decoupled Group Successive Over relaxation via 9-Point Laplacian (4-EDGSOR-9L) is introduced. Essentially, the 4-EDGSOR-9L is actually a variant of block SOR iterative method based on four points that employs half-sweep iteration and utilizes 9-Point Laplacian discretization scheme. Once the HPF is obtained, the standard Gradient Descent Search (GDS) technique is performed for path tracing to the goal point.