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

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... rea. 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.