<![CDATA[Path planning for autonomous mobile robots remains a critical challenge, particularly in environments with obstacles and constraints. Efficient navigation requires a robust algorithm capable of generating smooth, collision-free trajectories while ensuring computational efficiency. This study addresses the problem of indoor mobile robot navigation by leveraging harmonic potential fields, a solution derived from Laplace’s equation, to formulate an effective path-planning strategy. Conventional numerical methods for solving Laplace’s equation, such as Successive Over-Relaxation and Accelerated Over-Relaxation, often require extensive computational resources, especially in large-scale environments. To overcome this limitation, this research introduces an improved iterative approach, the Explicit Decoupled Group Modified Accelerated Over-Relaxation (EDGMAOR) method, which enhances computational efficiency and convergence speed. The EDGMAOR method incorporates a half-sweep block approach, significantly reducing the number of computations required per iteration while maintaining accuracy. To validate the effectiveness of the proposed method, simulations were conducted in a static, enclosed environment with various configurations of obstacles. Different starting and goal positions were tested to assess the efficiency, accuracy, and computational cost of the generated paths. The results indicate that the EDGMAOR method outperforms conventional approaches by achieving faster convergence rates and reduced computational time, demonstrating its suitability for real-time robot pathfinding applications. Furthermore, the study highlights that with greater obstacles proliferation, the EDGMAOR method maintains its efficiency, as obstacle regions are automatically excluded from unnecessary computations. This characteristic makes the method particularly useful for complex indoor environments where real-time processing is crucial. In conclusion, this research establishes EDGMAOR as a practical and effective solution for solving mobile robot path-planning problems, providing a balance between computational speed, accuracy, and robustness. The findings contribute to the ongoing advancements in autonomous robotics and artificial intelligence-driven navigation systems, with potential applications in industrial automation, smart transportation, and defence sectors.]]>
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