Mobile robots often have to discover a path of collision-free towards a specific goal point in their environment. We are trying to resolve the mobile robot problem iteratively by means of numerical technique. It is built on a method of potential field that count on the use of Laplace’s equation in the mobile robot’s configuration space to constrain/which reduces the generation of a potential function over regions. This paper proposed an iterative approach in solving robot path finding problem known as Accelerated Over-Relaxation (AOR). The experiment shows that these suggested approach can establish a smooth path between the starting and goal points by engaging with a finite-difference technique. The simulation results also show that a more rapidly solution with smoother path than the previous work is achieved via this numerical approach.
In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods.