迈向运动规划中的运动学可执行不可行性检测
Towards Kinematic Actionable Infeasibility Detection in Motion Planning
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中文总结 AI 辅助
提出几何驱动框架，通过构型空间拓扑分析及GPU加速并行算法，实现高维运动规划中不可行性的快速证明与原因识别。
中文摘要 AI 辅助
机器人运动规划不仅需要计算无碰撞路径，还需要在不存在此类路径时证明不可行性。完备方法仅限于低维空间，而基于采样的规划器虽能高效扩展，却无法提供有限时间内的不可行性证明，使得该问题在高维空间中很大程度上仍未解决。本文提出了一种几何驱动的框架，通过对构型空间拓扑进行显式的分辨率相关分析来证明不可行性。利用有符号距离场表示，所提方法直接在构型空间中追踪由障碍物边界诱导的分隔流形，从而既能检测不可行性，又能识别具体的几何原因。为解决计算挑战，我们开发了一种并行前沿扩展算法，利用GPU加速在高维空间中进行高效的单纯形重构。我们在4自由度（4-DOF）和5自由度（5-DOF）机器人场景中验证了该方法，在4-DOF情况下能在数秒内证明不可行性，在5-DOF情况下能在四分钟内完成。我们进一步讨论了提高向更高维空间可扩展性的途径。
英文摘要
Motion planning in robotics requires not only computing collision-free paths but also certifying infeasibility when no such path exists. Complete methods are limited to low-dimensional spaces, while sampling-based planners scale efficiently but cannot provide finite-time infeasibility certificates, leaving this problem largely unresolved in high-dimensional spaces. In this letter, we present a geometry-driven framework for certifying infeasibility through an explicit resolution-dependent analysis of configuration space topology. Leveraging signed distance field representations, the proposed method traces separating manifolds induced by obstacle boundaries directly in configuration space, enabling both detection of infeasibility and identification of the specific geometric cause. To address computational challenges, we develop a parallel frontier-expansion algorithm that exploits GPU acceleration for efficient simplicial reconstruction in high-dimensional spaces. We validate the approach on 4-DOF and 5-DOF robot scenarios, certifying infeasibility within seconds for 4-DOF cases and under four minutes for 5-DOF cases. We further discuss avenues for improving scalability to higher-dimensional spaces.
