Problem
Research questions and friction points this paper is trying to address.
Safety Filters
Discrete-Time Execution
Backward Reachable Tube (BRT)
Timely Activation of Safety Filters via One-Step Reachability Expansion
🤖 AI Summary
通过一步可达性扩展方法预测并提前激活安全过滤器，以解决离散时间执行下的机器人系统安全问题。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
One-Step Reachability Expansion
Backward Reachable Tube (BRT)
Safety Filters
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