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

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

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

Implementation of the half-sweep AOR iterative algorithm for space-fractional diffusion equations

In this paper, we consider the numerical solution of one dimensional space-fractional diffusion equation. The half-sweep AOR (HSAOR) iterative method is applied to solve linear system generated from discretization of one dimensional space-fractional diffusion equation using Caputo’s derivative operator and half-sweep implicit finite difference scheme. Furthermore, the formulation and implementation of HSAOR iterative method to solve the problem are also presented. Two examples and comparisons with FSAOR iterative method are given to show the effectiveness of the proposed method. From numerical results obtained, it has shown that the HSAOR iterative method is superior as compared with the FSAOR methods

SOR method for the implicit finite difference solution of time-fractional diffusion equations

In this study, we derive an unconditionally implicit finite difference approximation equation from the discretization of the one-dimensional linear time fractional diffusion equations by using the Caputo’s time fractional derivative. Then this approximation equation hence will be used to generate the corresponding system of linear equations. The approximation solution of the linear system is described via the implementation of Successive Over-Relaxation (SOR) iterative method. An example of the problem is presented to illustrate the effectiveness of SOR method. The findings of this study show that the proposed iterative method is superior compared with the Gauss-Seidel iterative method

Implementation of Quarter-Sweep Approach in Poisson Image Blending Problem

The quarter-sweep scheme has been used in solving boundary value problems efficiently. In this paper, we aim to determine the capability of the family of Gauss-Seidel iterative methods to solve the Poisson image blending problem, which are the Full-Sweep Gauss-Seidel (FSGS), Half-Sweep Gauss-Seidel (HSGS) and Quarter-Sweep Gauss-Seidel (QSGS). Second order finite difference approximation is used for the discretization of Poisson equation. Finally, the numerical results show that QSGS iterative scheme is more competent as compared with the full- and half-sweep approaches while obtaining the same quality of output images

Numerical Solutions for Poisson Image Blending Problem using 4-EDGSOR Iteration

Poisson image blending is an operation in image processing to generate a new image by using Poisson partial differential equation. In this paper, 4-EDGSOR iteration is used to solve the Poisson image blending problem and its efficiency in solving the proposed problem is illustrated. The approximation Poisson equation is formed by applying a finite difference method. Then, the rotated Laplacian operator which is constructed by a rotated finite difference scheme is used in this paper. Then a linear system is formed and solved using the 4-EDGSOR iterative method. The performance of the 4-EDGSOR iterative method in solving the proposed problem is compared to the SOR and 4-EGSOR iterative methods. The results obtained from numerical solutions showed that the 4-EDGSOR iterative method required lesser time and number of iterations to blend an image. From quality point of view, all images obtained the same natural look

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

This paper proposed a behaviour-based paradigm approach known as Laplacian Behaviour-Based Control (LBBC) for solving path planning problem for a mobile robot operating in a structured indoor environment. LBBC relies on the use of Laplace’s Equation to model the potential function in th eenvironment model. For solving the Laplace’s Equation, a numerical technique using a weighted block technique based on a block of four points known as Four Point-EGSOR (4EGSOR) iterative method is used to provide guidance in generating path for the robot. The simulation results show that LBBC provides robust motion for the robot, whilst 4EGSOR ensure faster computation than the previous methods

Using MySQL for learning management system

The Internet provides a new way of getting access to knowledge resources and materials.The Internet platform is proven provides an efficient way of communication among instructors, students and management using computers via network. However, an integrated learning management system (LMS) is required in order to have an efficient and effective communication, and to fully utilize the facilities provided by the Internet.There are already several implementations of such system, which are developed for commercial purpose, specifically for an organization or even provided in the public domain.This paper describes our work in utilizing open source tools particularly MySQL database, to develop web-based learning management system. The main focus is to evaluate the performance of MySQL, ease of usage, and platform dependency in a medium scale project

Application of harmonic functions through Modified SOR (MSOR) method for robot path planning in indoor structured environment

This paper presents the application of harmonic functions computed through MSOR iterative method to solve path planning problem in indoor environment. It is known that harmonic functions are very suitable to be used as a global approach for robot path planning. There exist a number of numerical techniques for obtaining the harmonic functions. This paper conducts an investigation of using MSOR method to discover its efficiency in computing the harmonic functions. It is found that MSOR method offer faster approach to the computation of harmonic functions, thus improve the overall performance of the path planning algorithm