Harmonic path planning using Quarter-Sweep Boosted AOR iterative method

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Abstract
This paper presents the findings of a study that examined the effectiveness of the application of Quarter-Sweep Boosted AOR with the 9-Point Laplacian operator using the families of relaxation methods for computing the solutions of Laplace's equation to obtain the harmonic potentials+ This work is a continuation from the past study that applied the standard 5-Point Laplacian to solve path planning issue that a mobile robot faces when working in indoor environment. The robot can navigate from a given starting position to a goal position by following the safest path, ensuring it avoids any obstacles and minimizes the risk of collisions. By utilizing Laplace's equation and computing the distribution of potential values in the simulated environments, the robot can determine the safest path that avoids obstacles present in the environment. This method ensures that the robot moves along a path where the potential for collisions is minimized. The findings confirm that Quarter-Sweep Boosted AOR (QSBAOR) outperforms Half-Sweep Boosted AOR (HSBAOR) and Full-Sweep Boosted AOR (FSBAOR). QSBAOR and HSBAOR show 75% and 50% reduction respectively, compared to FSBAOR in terms of computational complexity.