发表机构
Universidad de Santiago de Chile（智利圣地亚哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对离散时间执行下安全过滤器激活延迟导致系统可能跳入不安全区域的问题，提出基于单步扩张BRT的激活条件，确保及时干预并保持安全保证。
AI 中文摘要
基于Hamilton-Jacobi可达性的最小限制安全过滤器通过仅在系统到达定义为后向可达管（BRT）的不安全状态集合边界时覆盖标称控制器，提供了强大的安全保证。然而，这些保证依赖于底层公式的连续时间特性。在实践中，机器人系统在离散采样间隔内施加控制，这会产生不匹配，系统可能在更新之间跳入不安全的BRT，从而导致理论上可避免的故障。本文提出了一种基于单步扩张BRT的原理性解决方案，该BRT预测所有能在单个时间步内到达真实BRT的状态。通过使用此扩张边界作为安全过滤器的激活条件，安全干预足够早地发生，以确保在离散时间执行下的正确性。我们将此扩张集表述为一个修改后的可达性问题，并使用标准连续时间求解器进行计算。
英文摘要
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.
Journal ref. 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
DOI：10.1109/ICCAR69571.2026.11549591
