Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach
For safety-critical control systems, this provides a computationally efficient method to guarantee safety under arbitrary distributional uncertainties, addressing a key bottleneck in robust safety filtering.
This work ensures probabilistic safety for nonlinear systems under distributional ambiguity by using a backup-based safety filtering framework with Wasserstein ambiguity sets, reducing safety certification to a one-dimensional search. Simulations on three systems (Dubins vehicle, racing car, fighter jet) demonstrate broad applicability and computational efficiency.
In this work, 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 through simulations across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet, demonstrating the broad applicability and computational efficiency.