引用本文: 兰鸿辉, 卢海林, 乔璐等. 基于力流和有限元法的路径规划. 力学与实践, xxxx, x(x): 1-7.
Lan Honghui, Lu Hailin, Qiao Lu, et al. Path planning based on force flow and finite element method. Mechanics in Engineering, xxxx, x(x): 1-7.
 Citation: Lan Honghui, Lu Hailin, Qiao Lu, et al. Path planning based on force flow and finite element method. Mechanics in Engineering, xxxx, x(x): 1-7.

## PATH PLANNING BASED ON FORCE FLOW AND FINITE ELEMENT METHOD

• 摘要: 提出了一种基于力流和有限元法的路径规划方法，旨在解决复杂环境下全局路径规划的问题。将地图等效为由杆单元构成的桁架结构，在起点和终点处施加静定约束条件和相互作用力，通过捕捉点到点的力流解决避障和路径规划问题。力在物体中的传递遵循最短路径原则，因此力流路径不会偏离最优路径太远。根据上述原理设计了基于杆单元的路径规划算法，以简单桁架模型对路径计算过程进行详细演示，并分析了网格对计算效率的影响，证明了算法的可行性。在复杂迷宫地图中用本文算法与A*算法进行对比，结果显示本方法在解决大规模和复杂地图上具有优势，有限元法的网格构建方式比A*算法更自由，因此使计算规模更加容易控制。

Abstract: This paper proposes a path planning method based on force flow and finite element method to address the challenges of global path planning in complex environments. The map is treated as a truss structure composed of bar elements, static constraints and interaction forces are applied at the starting and ending points. The avoidance of obstacles and path planning issues are resolved by capturing the force flow from point to point. The transfer of force within the objects follows the principle of the shortest path, ensuring that the force flow path does not deviate too far from the optimal path. Based on these principles, a path planning algorithm using bar elements is designed. The process is demonstrated in detail using a simple truss model, and the impact of the grid on computational efficiency is analyzed, proving the feasibility of the algorithm. In comparison with the A* algorithm on complex maze maps, the results indicate the advantages of this method, especially in addressing large-scale and intricate maps. The grid construction approach of the finite element method provides more flexibility than the A* algorithm, making it easier to control the computational scale.

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