A Guaranteed Global Minimum Mobile Robots Navigation based on Khatib’s Potential Function

The Artificial Potential Field (APF) methodology, first proposed by Khatib, has garnered significant attention as a prevalent technique for the navigation of mobile robots, attributed to its inherent simplicity and capacity for real-time application. This approach directs robots through the utilization of virtual attractive and repulsive forces; however, it is not without significant drawbacks, including the emergence of local minima, particularly the struggle of reaching the goal when confronted by close obstacles. Such challenges can result in the robot becoming ensnared or displaying oscillatory dynamics in proximity to obstacles. This manuscript introduces an amended potential function that mitigates these shortcomings while preserving computational efficiency. The proposed APF incorporates corrective terms that reformulate the potential landscape, thereby effectively abolishing undesirable local minima and guaranteeing convergence towards the goal, even when situated close to obstacles. Two control strategies, namely static and dynamic control laws, are proposed in conjunction with the revised APF, incorporating linear damping to enhance stability. A thorough mathematical analysis is provided, demonstrating the stability and efficacy of the suggested solution. Simulations conducted within complex environments reveal that the new function engenders smooth and successful trajectories, surpassing the original APF methodology in terms of dependability and robustness. The findings underscore the appropriateness of the proposed function for real-time navigation endeavors within dynamic and cluttered settings. This research contributes to the progression of autonomous navigation by improving the reliability of path planning based on potential fields.