用神经网络加速安全规划，实现可证明的实时避障。
Contingency-Aware Planning via Certified Neural Hamilton-Jacobi Reachability
- 用FNO逼近变障碍物下的哈密顿-雅可比方程解算器
- 理论保证学习后的可达集是安全集的下界
- 适合对安全性要求高的机器人实时导航场景
哈密顿-雅可比（HJ）可达性为动态系统提供形式化安全保证，但求解高维HJ偏微分方程限制了其在实时规划中的应用。本文提出一种考虑突发情况的多目标导航框架，将基于学习的可达性与采样规划结合于未知环境。采用傅里叶神经算子（FNO）近似不同障碍配置下哈密顿-雅可比-伊萨克斯变分不等式的解算子。首先提供了安全后向可达-规避集的理论下界保证，使学习得到的可达集可被正式认证为安全。随后，将经认证的可达集与增量式多目标规划器集成，强制执行可达集约束，并引入恢复策略以保证有限时间内返回安全区域。整体上，该框架实现了渐近最优导航并具备可证明的突发应对能力，在KUKA youBot机器人上通过Webots仿真完成实时部署验证。
原文摘要 · Abstract (English)
Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems, but solving high-dimensional HJ partial differential equations limits its use in real-time planning. This paper presents a contingency-aware multi-goal navigation framework that integrates learning-based reachability with sampling-based planning in unknown environments. We use Fourier Neural Operator (FNO) to approximate the solution operator of the Hamilton-Jacobi-Isaacs variational inequality under varying obstacle configurations. We first provide a theoretical under-approximation guarantee on the safe backward reach-avoid set, which enables formal safety certification of the learned reachable sets. Then, we integrate the certified reachable sets with an incremental multi-goal planner, which enforces reachable-set constraints and a recovery policy that guarantees finite-time return to a safe region. Overall, we demonstrate that the proposed framework achieves asymptotically optimal navigation with provable contingency behavior, and validate its performance through real-time deployment on KUKA's youBot in Webots simulation.
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