Path planning for indoor mobile robot using half-sweep SOR via nine-point Laplacian (HSSOR9L)

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

Half-sweep quadrature-difference schemes with iterative method in solving linear Fredholm integro-differential equations

In this paper, half-sweep iteration concept applied on quadrature-difference schemes with Gauss-Seidel (GS) iterative method in solving linear Fredholm integro-differential equations. The combinations of discretization schemes of repeated trapezoidal and Simpson's 1/3 with central difference schemes are analyzed. The formulation and the implementation of the proposed methods are explained in detail. In addition, several numerical experiments and computational complexity analysis were also carried out to validate the presentation of the schemes and methods. The findings show that, the HSGS iteration method is superior to the standard GS method. As well the high order quadrature scheme produced more accurate approximation solution compared to combination of repeated trapezoidal-central difference schemes

Numerical solutions of first kind Linear Fredholm Integral Equations using quarter-sweep successive over-relaxation (QSSOR) Iterative Method

In this paper, an experimental study is conducted to show the efficiency of the Quarter-Sweep Successive Over-Relaxation (QSSOR) iterative method by using the quadrature approximation equations to obtain numerical solutions of the first kind linear Fredholm integral equations. Furthermore, the derivation and implementation of the QSSOR method in solving first kind linear Fredholm integral equations are also presented. Numerical examples and comparisons with other existing methods are given to illustrate the effectiveness of the proposed method

Path planning for mobile robot using 4EGSOR via Nine-Point Laplacian (4EGSOR9L) iterative method

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 finite difference 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

Robot path planning using Laplacian behaviour-based control via half-sweep Gauss-Seidel (LBBC-HSGS) Iterative method

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

Half-sweep geometric mean method for solution of linear Fredholm equations

The objective of this paper is to examine the application of the Half-Sweep Geometric Mean (HSGM) method by using the half-sweep approximation equation based on quadrature formula to solve linear integral equations of Fredholm type. The formulation and implementation of the Full-Sweep Geometric Mean (FSGM) and HalfSweep Geometric Mean (HSGM) methods are also presented. Some numerical tests were carried out to show that the HSGM method is superior to the FSGM method in the sense of complexity and execution time

Algorithm solution for space-fractional diffusion equations

In this study, we propose approximate algorithm solution of the space-fractional diffusion equation (SFDE's) based on a quarter-sweep (QS) implicit finite difference approximation equation. To derive this approximation equation, the Caputo's space-fractional derivative has been used to discretize the proposed problems. By using the Caputo's finite difference approximation equation, a linear system will be generated and solved iteratively. In addition to that, formulation and implementation algorithm the Quarter-Sweep AOR (QSAOR) iterative method are also presented. Based on numerical results of the proposed iterative method, it can be concluded that the proposed iterative method is superior to the FSAOR and HSAOR iterative method

A fast, parallel performance of fourth order iterative algorithm on shared memory multiprocessors (SMP) architecture

The rotated fourth order iterative algorithm of O(h 4) accuracy which was applied to the linear system was introduced by Othman et al. [OTH01] and it was shown to be the fastest compared to the standard fourth order iterative algorithm. Meanwhile the parallel standard fourth order iterative algorithms with difference strategies were implemented successfully by many researchers for solving large scientific and engineering problems. In this paper, the implementation of the parallel rotated fourth order iterative algorithm on SMP architecture is discussed. The performance results of all the parallel algorithms were compared in order to show their outstanding performances

Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems

Objective - Conjugate Gradient (CG) method is used to solve two-point boundary value problems together with non-polynomial spline approach at cubic degree. Methodology/Technique - To develop a system of linear equations in a matrix form, cubic non-polynomial splines are used to descretize the two-point boundary value problems so that the approximation can be computed using CG method. Since many previous researchers attempt to obtain the approximate solution for the two-point boundary value-problems at different degree of non-polynomial splines only, then the present paper aims to look into method which is best used with the cubic non-polynomial splines in order to approximate the solution of these problem Findings - According to the performance analysis results in term of iterations number, execution time and maximum absolute error at different grid sizes, the application of CG method together with the cubic non-polynomial spline give the best approximation to the solution of two-point boundary value problems compared to the approximation shown by Successive Over Relaxation (SOR) method and Gauss-Seidel (GS) method. Novelty - the performance of CG iterative method is found to be superior in respect of iterations number, execution time and maximum absolute error on various grid sizes

Performance numerical method half-sweep preconditioned gauss-seidel for solving fractional diffusion equation

The main purpose, we derive a finite difference approximation equation from the discretization of the one-dimensional linear space-fractional diffusion equations by using the space fractional derivative of Caputo's. The linear system will be generated by the Caputo's finite difference approximation equation. The resulting linear system was then resolved using Half-Sweep Preconditioned Gauss-Seidel (HSPGS) iterative method, which compares its effectiveness with the existing Preconditioned Gauss- Seidel (PGS) or call named (Full-Sweep Preconditioned Gauss-Seidel (FSPGS)) and Gauss-Seidel (HSPGS) methods. Two examples of the issue are provided in order to check the performance efficacy of the proposed approach. The findings of this study show that the proposed iterative method is superior to FSPGS and GS. © 2020 International Information and Engineering Technology Association