任意の不確実性下での分布的ロバスト安全性：安全フィルタリングアプローチ
Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach
非線形システムの確率的安全性を、分布の曖昧さがある状況で保証する手法を提案。バックアップベースの安全フィルタリングとWasserstein曖昧集合を用いた分布的ロバスト最適化を組み合わせ、切り替え時間の1次元探索とサンプリングベースの検証で安全性を確保する。
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著者: Daniel M. Cherenson, Haejoon Lee, Taekyung Kim, Dimitra Panagou
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
We study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a certified backup policy to ensure safety. To handle arbitrary uncertainties from ambiguous distributions, i.e., where the distribution is not of specific structure and the true distribution is unknown, we adopt a distributionally robust (DR) formulation using Wasserstein ambiguity sets. Rather than solving a high-dimensional DR trajectory optimization problem online, we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold. We validate our method across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet, demonstrating the broad applicability and computational efficiency.
