Computational algorithm for indoor mobile robot path searching via TOR 9-Point Laplacian iteration family

Mobile robot path navigation is a subject that has been a crucial study in the robotics field. The ability of robots to navigate successfully demands high performance path searching algorithms. The room for improvements to raise the potential of autonomous path searching is far from seeing its limits. Any approach that bears potential needs to be explored. Thus, the objective of this study is to investigate the performance of a combined set of numerical techniques based on Laplacian potential values in producing path searching algorithm for mobile robots. This technique set comprised of Quarter-Sweep approach (QS) for complexity reduction, family of Twoparameter Overrelaxation iterative method (TOR) for reducing the cost of computations, and 9-Point Laplacian operator (9P) for improving computational
efficiency. This study is conducted in a robot path searching simulator, namely Robot 2D Simulator. The configuration space in the simulator is set up accordingly to resemble a 2D heat transfer environment, and numerical analysis via Laplace’s equation can be applied to the resulting heat distributions. The proposed numerical
techniques are used to solve and obtain Laplacian potential values, and their corresponding path searching algorithms are tested for their performance. Results show that the proposed numerical techniques outperform their predecessors.
Integration of family of TOR-9P iterative method and QS approach, i.e.,QuarterSweep Two-parameter Overrelaxation 9-Point Laplacian method (QSTOR-9P) has produced the best results. The method succeeded in reducing the number of iteration and CPU time to approximately 62.27% to 87.64% and 83.30% to 95.20%, respectively compared to the standard. Thus, it is concluded that the proposed numerical techniques have the potential to enable higher path searching performance.