動的障害物存在下での確率バリア証明書
Stochastic Barrier Certificates in the Presence of Dynamic Obstacles
不確実性を伴う離散時間システムの安全性を、動的障害物を考慮した時間依存バリア証明書を用いて検証し、凸最適化で解けることを示した論文。
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著者: Rayan Mazouz, Luca Laurenti, Morteza Lahijanian
分類: cs.RO, math.PR
原文アブストラクト
Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time, continuous-space systems subject to uncertainty, which provide certified lower bounds on the probability of remaining within a safe set over a finite horizon. These certificates explicitly account for time-varying unsafe regions induced by obstacle dynamics. By leveraging Bellman's optimality perspective, the time-varying formulation directly captures temporal structure and yields less conservative bounds than state-of-the-art approaches. By restricting certificates to polynomial functions, we show that time-varying barrier synthesis can be formulated as a convex sum-of-squares program, enabling tractable optimization. Empirical evaluations on nonlinear systems with dynamic obstacles show that time-varying certificates consistently achieve tight guarantees, demonstrating improved accuracy and scalability over state-of-the-art methods.
