# Hamilton-Jacobi Reachability

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arXiv Nov 5, 2026
Neural reachability now errs on the safe side: ConDR pushes the learned value below the true one and gives the lowest closed-loop collision rates
DeepReach replaces the grid in Hamilton–Jacobi reachability with a neural value function but penalizes both sides of the residual equally, so the learned value can sit above the true one and unsafe states get labeled safe. ConDR instead trains toward a subsolution of the HJI variational inequality: the obstacle branch and terminal condition hold by construction, a one-sided loss pushes the differential residual below a safety margin, and a complementarity term blocks the degenerate all-unsafe solution. On Air3D, Air6D, a 9D multi-vehicle system and a 13D quadrotor, ConDR reports the lowest false-negative rate and the lowest closed-loop collision rates, with at most a small rise in intervention.
DeepReach replaces the grid in Hamilton–Jacobi reachability with a neural value function but penalizes both sides of the residual equally, so the learned value can sit above the true one and unsafe states get labeled safe. ConDR instead trains toward a subsolution of the HJI variational inequality: the obstacle branch and terminal condition hold by construction, a one-sided loss pushes the differential residual below a safety margin, and a complementarity term blocks the degenerate all-unsafe solution. On Air3D, Air6D, a 9D multi-vehicle system and a 13D quadrotor, ConDR reports the lowest false-negative rate and the lowest closed-loop collision rates, with at most a small rise in intervention.
Vanderbilt University Universität Ulm
Kendra Givens（First author）
ConDR Hamilton-Jacobi Reachability Safety-Critical Control
arXiv Sep 28, 2026
ShieldVLA gates VLA fine-tuning with Hamilton-Jacobi reachability, cutting cumulative safety cost by 57% and lifting success rate by 0.13
ShieldVLA is a safety-aligned fine-tuning framework for vision-language-action (VLA) models that learns a model-free Hamilton-Jacobi reachability value function from visual observations as a safety critic, uses that critic to gate policy optimization into reward maximization inside feasible regions and recovery near unsafe states, and replaces manual per-step cost labels with rubric-based VLM safety scores; across five navigation and manipulation benchmarks (Dubins-VL, TurtleBot-Nav, Safety-CHORES Nav/Fetch, Franka-Reach) and multiple VLA backbones it reduces cumulative safety cost by 57% on average and improves task success rate by 0.13 over SafeVLA.
ShieldVLA is a safety-aligned fine-tuning framework for vision-language-action (VLA) models that learns a model-free Hamilton-Jacobi reachability value function from visual observations as a safety critic, uses that critic to gate policy optimization into reward maximization inside feasible regions and recovery near unsafe states, and replaces manual per-step cost labels with rubric-based VLM safety scores; across five navigation and manipulation benchmarks (Dubins-VL, TurtleBot-Nav, Safety-CHORES Nav/Fetch, Franka-Reach) and multiple VLA backbones it reduces cumulative safety cost by 57% on average and improves task success rate by 0.13 over SafeVLA.
Microsoft (United States)Indian Institute of Science Bangalore
Manan Tayal（First author）
ShieldVLA Hamilton-Jacobi Reachability Vision-Language-Action Models Safe Reinforcement Learning Rubric-Based Evaluation

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Neural reachability now errs on the safe side: ConDR pushes the learned value below the true one and gives the lowest closed-loop collision rates

ShieldVLA gates VLA fine-tuning with Hamilton-Jacobi reachability, cutting cumulative safety cost by 57% and lifting success rate by 0.13