Timely Activation of Safety Filters via One-Step Reachability Expansion

Abstract:Least-restrictive safety filters based on Hamilton-Jacobi reachability provide strong safety guarantees by overriding a nominal controller only when the system reaches the boundary of the set of unsafe states defined as a Backward Reachable Tube (BRT). These guarantees, however, rely on the continuous-time nature of the underlying formulation. In practice, robotic systems apply control at discrete sampling intervals, which creates a mismatch where the system may jump into the unsafe BRT between updates, allowing failures that are theoretically avoidable. This work introduces a principled solution based on a one-step expanded BRT that predicts all states capable of reaching the true BRT within a single timestep. By using this expanded boundary as the activation condition for the safety filter, safety interventions occur early enough to ensure correctness under discrete-time execution. We formulate this expanded set as a modified reachability problem and compute it using standard continuous-time solvers.

Robotics (cs.RO)

arXiv:2609.17904 [cs.RO]

(or arXiv:2609.17904v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.17904 arXiv-issued DOI via DataCite (pending registration)

. Borquez, "Timely Activation of Safety Filters via One-Step Reachability Expansion," 2026 12th International Conference on Control, Automation and Robotics (ICCAR), Nagoya, Japan, 2026, pp. 125-130

https://doi.org/10.1109/ICCAR69571.2026.11549591 DOI(s) linking to related resources