Improved Path Planning and Controller Design Based on PRM

This paper introduces the application of the Probabilistic Road Map (PRM) method in path planning and designs a path tracking controller based on the Lyapunov function. To enhance the smoothness of the paths generated by the PRM, Bézier curves are employed. Additionally, to address the path detection challenges encountered by the PRM algorithm in complex environments, this paper introduces normal distribution sampling and adaptive cost factors. By dynamically adjusting the PRM sampling points, the success rate of path detection is improved. The Improved PRM (IPRM) algorithm demonstrates better performance in terms of shorter path generation compared to the original PRM, RRT* and Bi-RRT algorithms. A path tracking controller is designed by integrating the curvature polynomial of the exploration path with the Lyapunov function. In complex mapping scenarios, dynamic obstacle avoidance strategies are incorporated to prevent collisions between the robot and obstacles. Experimental results indicate that the proposed controller achieves faster convergence, smaller tracking errors, and greater stability compared to traditional PD and PI controllers.