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.

Redlich-Kister Finite Difference Solution for Solving Two-Point Boundary Value Problems by using Ksor Iteration Family

“…In addition to this point iteration family, Evans [32] introduced the Explicit Group (EG) iterative method which is faster than the Gauss-Seidel (GS) iterative method to get the numerical solution of this linear system. Despite the speed up the convergence rate for Explicit Group (EG) iteration, many researchers also developed new variants of the EG iteration family such as 9-Point EG [33], EGSOR [34], EDGSOR [35] and MEGSOR [36] in which all these block iterations have significantly reduced their convergence rate. Therefore, further discussion of this paper focuses on investigating the efficiency of the 4EGKSOR iterative method which is inspired by the paper research [37] and apply together with the newly established RKFD discretization scheme for solving the system of Redlich-Kister approximation equations.…”

Numerical Evaluation of Quarter-Sweep KSOR Method to Solve Time-Fractional Parabolic Equations

“…Apart from that, the application of quarter-sweep iteration concept in this study is inspired from the work done by [10], where they used the Modified Explicit Group (MEG) iterative method to find the numerical solution of two-dimensional Poisson equations. Originally, this work which they modified from their previous work [11], has extended the half-sweep iteration concept (see in [12]- [15]) to the quarter-sweep iteration concept in order to accelerate the iteration process by considering only one-fourth of the total node points located in the solution domain.…”