{"ID":22918819,"CreatedAt":"2026-09-17T01:02:08.507062015Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.17904","arxiv_id":"2609.17904","title":"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.","short_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 th...","url_abs":"https://arxiv.org/abs/2609.17904","url_pdf":"https://arxiv.org/pdf/2609.17904v1","authors":"[\"Javier Borquez\"]","published":"2026-09-15T22:54:00Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}