Context-Conditioned Hamilton-Jacobi Reachability for Adaptive Safety Filtering

2026-10-06

AI Summary

This study addresses the limitation of conventional safety certificates requiring re-synthesis under varying operating conditions by proposing a conditional Hamilton-Jacobi reachability framework that enables adaptive, universal safety certificates across diverse scenarios. Methodologically, leveraging an eight-state vehicle dynamics model and boundary observation encoding, this work constructs the first context-conditioned single-certificate mechanism. Through conditional value function learning and discrete-time control barrier function filtering, the certificate dynamically generalizes across friction, geometry, and disturbances without re-synthesis, adapting seamlessly to unseen deployment environments. Real-world vehicle experiments under extreme handling maneuvers demonstrate that the proposed approach maintains zero lateral constraint violations with only 3.1% performance degradation, validating its highly efficient transferability.

Abstract

Hamilton-Jacobi reachability constructs safety certificates for specified dynamics and safety constraints, tying each certificate to the deployment context for which it is synthesized. We ask whether a single certificate can instead represent a family of context-dependent safety problems and be queried across deployment conditions without re-synthesis. We learn a backward reachable tube for an eight-state vehicle model conditioned on local boundary geometry, friction coefficient, and adversarial disturbance scale. Geometry enters through an ego-frame boundary observation that defines the local containment constraint, while friction and disturbance scale enter as explicit operating-condition variables. This allows the same value function to be queried across friction coefficients from 0.4 to 2.0 and on geometries absent from synthesis. On 11 held-out evaluation geometries, the certificate maintains containment across the full tested friction range, including simultaneous geometry and grip shifts, while remaining within 1.2 percentage points in intervention rate and 0.09 m/s in speed of certificates re-synthesized with knowledge of the test geometry. We then deploy the certificate as a sampled discrete-time control barrier function filter on a full-scale vehicle near the handling limit. Lateral containment holds in every hardware session under both adversarial driving and autonomous racing, with 99th-percentile acceleration magnitude reaching 0.99 g. Across three certificates evaluated under a fixed autonomous racing controller, lap time varies by only 3.1%, demonstrating that a context-conditioned reachability certificate can transfer to deployment geometries absent from synthesis with modest performance cost.

Problem

• Hamilton-Jacobi reachability
• safety certificates
• context-conditioned
• adaptive safety filtering
• backward reachable tube

Innovation

• Context-Conditioned Reachability
• Hamilton-Jacobi
• Safety Filtering
• Control Barrier Function
• Backward Reachable Tube