发表机构
University of California, Berkeley; Norwegian University of Science and Technology（加州大学伯克利分校; 挪威科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨了TCPA、DCPA和速度障碍在碰撞风险表征中的关系，并扩展至有界不确定性下的凸相对状态集，证明了不确定性感知速度障碍能保持等价性。
AI 中文摘要
最近接近点时间（TCPA）、最近接近点距离（DCPA）和速度障碍（VOs）被广泛用于自主导航中的碰撞风险评估与缓解，然而它们之间的关系及其在不确定性下的行为在很大程度上仍未得到探索。假设完美的状态信息，我们在有限和无限预测范围内建立了这些表示之间的联系，并推导出它们提供碰撞风险等价表征的条件。在有界不确定性下，我们将最近接近点（CPA）度量和速度障碍扩展到凸相对状态集。我们表明，在这种情况下，独立计算的TCPA和DCPA界限失去了速度障碍成员资格所需的联合关系，而不确定性感知的速度障碍通过碰撞诱导速度的集值表示保持了这种关系。
英文摘要
Time to Closest Point of Approach (TCPA), Distance to Closest Point of Approach (DCPA), and Velocity Obstacles (VOs), are widely used to assess and mitigate collision risk in autonomous navigation, yet their relationship and behavior under uncertainty remain largely unexplored. Assuming perfect state information, we establish a relationship between these representations over finite and infinite prediction horizons and derive conditions under which they provide equivalent characterizations of collision risk. Under bounded uncertainty, we extend the Closest Point of Approach (CPA) metrics and VO to convex relative-state sets. We show that in this setting, independently computed TCPA and DCPA bounds lose the joint relationship required for VO membership, while uncertainty-aware VOs preserve this relationship through a set-valued representation of collision-inducing velocities.
