The main purpose of this paper is to examine the application of complexity reduction approach based on half-sweep iteration concept with Alternating Group Explicit (AGE) method namely Half-Sweep AGE (HSAGE) method for solving system of linear equations generated from the discretization of two-point fuzzy boundary value problems (FBVPs). To form the linear system, the corresponding second order finite difference scheme has been used to derive the half-sweep finite difference approximation equation of the problems. The formulation and implementation of the proposed iterative method are discussed. Furthermore, numerical results of two test problems are also included in order to verify performance of the method compared to Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep AGE (FSAGE) methods. The findings show that the proposed HSAGE method is superior to other tested methods in the sense of number of iterations, execution time and Hausdorff distance.

One of the key issues in mobile robot navigation is the ability for the robot to move from an arbitrary start location to a specified goal location without colliding with any obstacles while traveling, also known as mobile robot path planning problem. In this paper, however, we examined the performance of a robust searching algorithm that relies on the use of harmonic potentials of the environment to generate smooth and safe path for mobile robot navigation in a static known indoor environment. The harmonic potentials will be discretized by using Laplacian's operator to form a system of algebraic approximation equations. This algebraic linear system will be computed via 4-Point Explicit Group Accelerated Over-Relaxation (4-EGAOR) iterative method for rapid computation. The performance of the proposed algorithm will then be compared and analyzed against the existing algorithms in terms of number of iterations and execution time. The result shows that the proposed algorithm performed better than the existing methods.

One of the main issues when dealing with mobile robot navigation is that we have to resolve the obstacle avoidance problem, where when moving from a starting point to the goal point, the mobile robot will have to generate a collision-free path in order ensure that it can move efficiently in the environment. In this study, we attempt to resolve the issue by solving it iteratively via numerical technique. This solution is based on the potential field method that utilizes the Laplace’s equation to constrain the generation of potential functions over the regions in the configuration space where the mobile robot operates in. This paper proposed Modified Accelerated Over-Relaxation (MAOR) iterative method for solving robot path planning problem. Through the application of finite-difference technique in it, the experiment shows that the mobile robot is able to generate a smooth path from starting point to goal point. Furthermore, the results obtained from the simulation has shown that this numerical method was able to perform faster solution and generated smoother path comparing the previous works on the similar problem.

Mobile robots are often in a situation where they need to find a bump-free path or navigation in their environment from any starting to a specific target point. Within this study, improving the navigation problem of a mobile robot iteratively by using a numerical method based on the potential field method is one of the main aims. This potential field will lean on the use of Laplace’s equation to restrain the formation of a potential function across regions within the mobile robot configuration area. The present paper proposed a Quarter-Sweep Modified Accelerated Overrelaxation (QSMAOR) approach to improve the pathfinding of mobile robots in a given environment. The experiment shows that, by using a finite difference method, it is capable of producing an optimal path and creating a smooth path between the starting and target point. The results of the simulation also show that this numerical approach works more rapidly and provides a smoother/clearer direction than the previous study.