Aiming at the problems of low success rate, long time and tortuous path of the traditional Rapidly-exploring Random Trees series of algorithms for path planning, this paper proposes the optimal path sampling algorithm based on the potential function (AP-RRT*), which solves the path planning problem of the manipulator in three-dimensional space. First, the potential function is defined and the concept of sampling termination distance is proposed. Second, a secondary sampling strategy is proposed in combination with the potential function to improve the planning speed and increase the coverage rate. Third, adaptive weights and adaptive step size are used to dynamically adjust the planning direction and distance, thereby improving the planning efficiency. Moreover, when performing node reconnection, dynamic retrieval circles are set to ensure path quality while reducing computational consumption. Finally, the improved algorithm, along with other algorithms, is simulated and experimentally verified in MATLAB and ROS. The results show that the AP-RRT* algorithm is superior in terms of path length, planning time, iterations, number of waypoints and success rate.

针对传统Rapidly-exploring Random Trees系列算法路径规划成功率低、时间长、路径曲折的问题，提出基于势函数的最优路径采样算法（AP-RRT*），解决了机械臂在三维空间中的路径规划问题。首先定义了势函数，提出了采样终止距离的概念。其次，结合势函数提出二次抽样策略，提高规划速度，提高覆盖率。第三，利用自适应权重和自适应步长动态调整规划方向和距离，从而提高规划效率。而且，在进行节点重连时，设置动态检索圈，保证路径质量的同时减少计算消耗。最后，改进算法与其他算法一起在MATLAB和ROS中进行了仿真和实验验证。结果表明，AP-RRT*算法在路径长度、规划时间、迭代次数、航点数量和成功率方面均具有优越性。