基于全局引导力的分数阶人工势场的路径规划算法研究

Research on Path Planning Algorithm Based on Fractional-Order Artificial Potential Field with Global Guiding Force

摘要: 本文针对传统A算法在路径规划中存在扩展节点多、搜索时间长、路径转折频繁及易陷入局部最优等问题，提出一种融合全局引导的分数阶人工势场法(APF)的改进A路径规划算法。该算法通过引入分数阶微积分增强势场力的连续性与记忆性，并结合全局路径趋势引导力，动态约束搜索邻域，减少冗余搜索方向。在MATLAB平台上进行仿真实验，结果表明：在30 × 30和50 × 50栅格地图中，改进算法相较于传统A*算法，搜索时间分别减少38.67%和47.31%，扩展节点数降低22.97%和33.46%，路径转折次数减少15.38%和18.18%，路径长度缩短1.94%和2.95%。实验验证了所提算法在复杂环境中具有更高的规划效率和路径质量。

Abstract: To address the issues of excessively expanded nodes, long search time, frequent path turns, and susceptibility to local optima in traditional A* algorithm-based path planning, this paper proposes an improved A* path planning algorithm that integrates globally-guided fractional-order artificial potential field (APF). By introducing fractional calculus to enhance the continuity and memory of potential field forces, and incorporating global path trend guidance to dynamically constrain the search neighborhood, the algorithm effectively reduces redundant search directions. Simulation experiments conducted on the MATLAB platform show that in 30 × 30 and 50 × 50 grid maps, the improved algorithm reduces search time by 38.67% and 47.31%, decreases the number of expanded nodes by 22.97% and 33.46%, and reduces the number of path turns by 15.38% and 18. 18%, and shortens the path length by 1.94% and 2.95%, respectively, compared to the traditional A* algorithm. The results verify that the proposed algorithm achieves higher planning efficiency and path quality in complex environments.