提出新方法减少机器人路径弯曲,提升运动效率和控制稳定性。
Smooth Feedback Motion Planning with Reduced Curvature
- 通过局部向量场对齐与几何算法构建目标区域大
- 路径弯曲减少91.40%,控制能耗降低45.47%
- 适合低维空间下需快速安全规划的机器人应用
基于单元分解的反馈运动规划可生成无碰撞且具有形式保证的机器人路径,但现有方法常产生不必要的弯曲,导致运动缓慢、控制代价高。本文提出一种计算高效的改进方法,针对给定单纯形分解,引入启发式策略系统性地对齐并分配局部向量场,生成更直接的轨迹;同时设计一种新型几何算法,在目标周围构建最大星形单纯形链,形成大“漏斗”区域,使最优直指目标的控制律可安全应用。仿真显示,该方法使路径总弯曲度平均降低91.40%,LQR控制努力平均减少45.47%。与采样及优化类规划器对比,验证了其时间效率与鲁棒性。虽适用于任意有限维单纯形复形,实际应用聚焦于低维(d≤3)配置空间,此时单纯形分解计算可行。
原文摘要 · Abstract (English)
Feedback motion planning over cell decompositions provides a robust method for generating collision-free robot motion with formal guarantees. However, existing algorithms often produce paths with unnecessary bending, leading to slower motion and higher control effort. This paper presents a computationally efficient method to mitigate this issue for a given simplicial decomposition. A heuristic is introduced that systematically aligns and assigns local vector fields to produce more direct trajectories, complemented by a novel geometric algorithm that constructs a maximal star-shaped chain of simplexes around the goal. This creates a large ``funnel'' in which an optimal, direct-to-goal control law can be safely applied. Simulations demonstrate that our method generates measurably more direct paths, reducing total bending by an average of 91.40\% and LQR control effort by an average of 45.47\%. Furthermore, comparative analysis against sampling-based and optimization-based planners confirms the time efficacy and robustness of our approach. While the proposed algorithms work over any finite-dimensional simplicial complex embedded in the collision-free subset of the configuration space, the practical application focuses on low-dimensional ($d\le3$) configuration spaces, where simplicial decomposition is computationally tractable.
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