Timely Activation of Safety Filters via One-Step Reachability Expansion
arXiv:2609.17904v1 Announce Type: new 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
Overview
arXiv:2609.17904v1 Announce Type: new 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.
Source
Originally published at arxiv.org.
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Source: https://arxiv.org/abs/2609.17904