Autonomous Navigation on Modified AOR Iterative Method in Static Indoor Environment

Abstract

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.

A Modified Accelerated Overrelaxation (Maor) Scheme for Solving the Shifted Gr\"{u}nwald Estimation Fractional Poisson Equation

“…Research in [14,39] utilized the MAOR scheme on their respective problems, and both concluded that this scheme produces the least number of iterations. Thus, this research proposes an MAOR scheme based on the fractional finite difference iterative method for solving the fractional Poisson equation (1).…”

An Efficient Red–Black Skewed Modified Accelerated Arithmetic Mean Iterative Method for Solving Two-Dimensional Poisson Equation

“…Unlike the MAM method, which employs weighted parameters only, additional accelerated parameters are utilised for this newly proposed method. It can be constructed based on the AOR iterative scheme (15) to solve the given problem and is written as…”

“…Furthermore, it can be noted that the AOR can be treated as an extrapolation of the SOR method with overrelaxation parameter r and extrapolation parameter s = ω/r, as described in [12]. From Equations ( 13)- (15), u (k+1) denotes the unknown vector at iteration (k + 1), which we attempt to compute efficiently.…”

“…In Equation (14), the SOR scheme provides one overrelaxation parameter only to speed up the rate of convergence. Using Equation (15), two parameters can be adjusted to obtain the optimal convergence rate for solving the problem (1). Different values of ω and r can be chosen within the range between 1 and 2, in which good parameter values will give an acceptable optimum number of iterations.…”

“…As pointed out in [12], if fully exploited, the presence of two parameters in AOR and its variant [13,14] will provide a faster convergence rate than any other methods of the same type. Moreover, the red-black ordering strategy was applied in a previous work where two different weighted parameters were used for the calculation of red and black nodes to improve the execution time [15,16]. It is interesting to note that the numerical solutions to the fractional version of the partial differential equation were actively studied in recent works.…”