使用反应式圆形场的运动规划：碰撞避免与目标收敛的二维分析
Motion Planning using Reactive Circular Fields: A 2D Analysis of Collision Avoidance and Goal Convergence
AI总结：
本文针对反应式规划难以同时保证避碰与目标收敛的问题，严格分析基于CF的二维运动规划器，给出覆盖全算法的充要避碰条件、多障碍扩展及目标收敛充分条件，并通过非凸点云障碍仿真验证。
摘要：
近来，文献中提出了许多反应式轨迹规划方法，因为它们在机器人系统日益复杂、杂乱且不可预测的环境中具有固有的即时适应能力。然而，这些方法通常仅具有局部反应性，未考虑全局路径规划，并且无法给出同时实现碰撞避免与目标收敛的保证。本文研究了一种近期开发的基于圆形场（CF）的运动规划器，该规划器通过调整人工磁场来评估障碍物周围的多条轨迹，从而将局部反应控制与全局轨迹生成相结合。特别地，我们在平面环境中对该规划器进行了数学上严格的分析，以确保受控机器人的安全运动。与现有结果不同，所推导的碰撞避免分析覆盖了整个CF运动规划算法，包括用于目标收敛的吸引力，并且不限于旋转场的特定选择，即我们的保证不限于某条可能次优的特定轨迹。我们的Lyapunov型碰撞避免分析基于一个（等价的）二维辅助系统的定义，这使我们能够针对与点障碍物发生碰撞的情况给出紧的、当且仅当条件。此外，我们展示了该分析如何自然地扩展到多个障碍物，并明确给出目标收敛的充分条件。最后，我们提供了一个具有多个非凸点云障碍物的具有挑战性的仿真场景，并证明了碰撞避免与目标收敛。
英文摘要：
Recently, many reactive trajectory planning approaches were suggested in the literature because of their inherent immediate adaption in the ever more demanding cluttered and unpredictable environments of robotic systems. However, typically those approaches are only locally reactive without considering global path planning and no guarantees for simultaneous collision avoidance and goal convergence can be given. In this paper, we study a recently developed circular field (CF)-based motion planner that combines local reactive control with global trajectory generation by adapting an artificial magnetic field such that multiple trajectories around obstacles can be evaluated. In particular, we provide a mathematically rigorous analysis of this planner in a planar environment to ensure safe motion of the controlled robot. Contrary to existing results, the derived collision avoidance analysis covers the entire CF motion planning algorithm including attractive forces for goal convergence and is not limited to a specific choice of the rotation field, i.e., our guarantees are not limited to a specific potentially suboptimal trajectory. Our Lyapunov-type collision avoidance analysis is based on the definition of an (equivalent) two-dimensional auxiliary system, which enables us to provide tight, if and only if conditions for the case of a collision with point obstacles. Furthermore, we show how this analysis naturally extends to multiple obstacles and we specify sufficient conditions for goal convergence. Finally, we provide a challenging simulation scenario with multiple non-convex point cloud obstacles and demonstrate collision avoidance and goal convergence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
