Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach

TL;DR

This paper presents a distributionally robust safety filtering method for nonlinear systems under arbitrary uncertainties, using Wasserstein ambiguity sets and a one-dimensional search for efficient safety certification.

Contribution

It introduces a novel backup-based safety filtering framework that reduces complex distributionally robust safety certification to a simple one-dimensional search, with finite-sample guarantees.

Findings

Validated on three systems: Dubins vehicle, racing car, fighter jet.

Achieved broad applicability and computational efficiency.

Provided finite-sample safety guarantees with empirical failure probability control.

Abstract

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.