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Gradient-Free Neural Hamilton-Jacobi Reachability for Scalable Safety-Critical Control

arXiv · AI, language, vision and robotics · article · Sep 12, 2026 · UTC

Hamilton-Jacobi (HJ) reachability provides a principled framework for synthesizing safety certificates and robust controllers for safety-critical robotic systems. However, applying reachability analysis to high-dimensional nonlinear systems remains challenging: classical grid-based solvers suffer from the curse of dimensionality, continuous-time neural solvers require accurate spatial value gradients, and reinforcement-learning-based approaches often suffer from weak boundary anchoring and non-stationary adversarial policy optimization. We propose a discrete-time neural reachability framework

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