Contingency-Aware Planning via Certified Neural Hamilton-Jacobi Reachability

• URL: http://arxiv.org/abs/2603.17022v1
• Date: Tue, 17 Mar 2026 18:04:20 GMT
• Title: Contingency-Aware Planning via Certified Neural Hamilton-Jacobi Reachability
• Abstract summary: Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems.<n>We present a contingency-aware multi-goal navigation framework that integrates learning-based reachability with sampling-based planning.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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