Contingency-Aware Planning via Certified Neural Hamilton-Jacobi Reachability

2026-03-17

AI Summary

This work addresses the challenge of real-time solution of high-dimensional Hamilton-Jacobi partial differential equations, which has hindered their application in safe motion planning within unknown environments. The authors propose a multi-objective navigation framework that integrates learning-based approximation with sampling-based planning. Specifically, a Fourier Neural Operator (FNO) is employed to approximate the solution operator of the Hamilton-Jacobi-Isaacs variational inequality, yielding a neural reachable set endowed with formal safety guarantees. This set is embedded into an incremental planner to achieve asymptotically optimal navigation with provably correct emergency response capabilities. The approach is successfully deployed on a KUKA youBot platform in Webots simulations, demonstrating real-time performance, safety, and formal correctness.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Hamilton-Jacobi reachability
• contingency-aware planning
• multi-goal navigation
• safe backward reach-avoid set
• real-time planning

Innovation

• Hamilton-Jacobi reachability
• Fourier Neural Operator
• safety certification
• contingency-aware planning
• multi-goal navigation