Probabilistic collision detection (PCD) is essential in motion planning for robots operating in unstructured environments, where considering sensing uncertainty helps prevent damage. Existing PCD methods mainly used simplified geometric models and addressed only position estimation errors. This paper presents an enhanced PCD method with two key advancements: (a) using superquadrics for more accurate shape approximation and (b) accounting for both position and orientation estimation errors to improve robustness under sensing uncertainty. Our method first computes an enlarged surface for each object that encapsulates its observed rotated copies, thereby addressing the orientation estimation errors. Then, the collision probability under the position estimation errors is formulated as a chance-constraint problem that is solved with a tight upper bound. Both the two steps leverage the recently developed normal parameterization of superquadric surfaces. Results show that our PCD method is twice as close to the Monte-Carlo sampled baseline as the best existing PCD method and reduces path length by 30% and planning time by 37%, respectively. A Real2Sim pipeline further validates the importance of considering orientation estimation errors, showing that the collision probability of executing the planned path in simulation is only 2%, compared to 9% and 29% when considering only position estimation errors or none at all.

翻译：概率碰撞检测（PCD）对于在非结构化环境中运行的机器人运动规划至关重要，其中考虑感知不确定性有助于防止损伤。现有的PCD方法主要使用简化的几何模型，并且仅处理位置估计误差。本文提出了一种增强型PCD方法，具有两个关键进展：（a）使用超二次曲面实现更精确的形状近似；（b）同时考虑位置和姿态估计误差，以提高在感知不确定性下的鲁棒性。我们的方法首先为每个物体计算一个放大的表面，该表面封装了其观测到的旋转副本，从而处理姿态估计误差。然后，将位置估计误差下的碰撞概率表述为一个机会约束问题，并使用一个紧的上界进行求解。这两个步骤都利用了最近发展的超二次曲面法向参数化方法。结果表明，我们的PCD方法比现有最佳PCD方法更接近蒙特卡洛采样基准的两倍，并分别将路径长度减少了30%，规划时间减少了37%。一个Real2Sim流水线进一步验证了考虑姿态估计误差的重要性，显示在仿真中执行规划路径的碰撞概率仅为2%，而仅考虑位置估计误差或完全不考虑误差时，碰撞概率分别为9%和29%。