Safely handling occlusions is a fundamental challenge for autonomous mobile robots operating in dynamic environments. This issue is especially prominent in autonomous valet parking (AVP), where traffic rules are lax, occlusions are frequent and cluttered, and overly conservative behavior can leave vehicles stuck. However, existing methods either lack formal safety guarantees, assume agents follow road structures, or introduce conservatism, leaving occlusion-aware planning for AVP an open challenge. In this paper, we propose APRO (AH-Polyhedron Reachability for Occlusions), an exact and efficient occlusion-aware planning framework based on game-theoretic active perception and AH-polyhedron reachability analysis with AVP as our canonical use case. Our key insight is to reformulate set-based safety conditions in prior work as unions of AH-polyhedrons, enabling exact safety verification through linear programming (LP) without any additional conservatism in set computations or assumptions on road topology. We further show how the resulting safety conditions can be integrated into optimization-based planners or a bisection search scheme for real-time applications. We validate our method in simulation and hardware experiments, including data replay on a real-world parking lot dataset. Experimental results demonstrate that our method consistently achieved a 100% safety rate across all evaluated scenarios while maintaining real-time performance, resulting in safer and more optimal decisions than existing methods with formal safety guarantees.

翻译：安全处理遮挡是自主移动机器人在动态环境中运行的基础性挑战。这一问题在自主代客泊车（AVP）中尤为突出，因为该场景下交通规则松散、遮挡情况频繁且杂乱，过度保守的行为可能导致车辆陷入困境。然而，现有方法要么缺乏形式化安全保障，要么假设智能体遵循道路结构，或者引入保守性，使得AVP中的遮挡感知规划仍是一个开放挑战。本文基于博弈论主动感知和AH-多面体可达性分析，以AVP为典型应用场景，提出APRO（遮挡场景的AH-多面体可达性分析）——一种精确且高效的遮挡感知规划框架。我们的关键洞察是将先前工作中基于集合的安全性条件重构为AH-多面体的并集，从而通过线性规划（LP）实现精确的安全验证，无需在集合计算或道路拓扑假设中引入任何额外保守性。我们进一步展示了如何将生成的安全条件集成到基于优化的规划器或二分搜索方案中，以实现实时应用。我们在仿真和硬件实验中验证了该方法，包括在真实停车场数据集上的数据重放。实验结果表明，我们的方法在所有评估场景中始终达到100%的安全率，同时保持实时性能，相比具有形式化安全保障的现有方法，能做出更安全且更优的决策。