Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911695762358272 |
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| author | Cherenson, Daniel M. Lee, Haejoon Kim, Taekyung Panagou, Dimitra |
| author_facet | Cherenson, Daniel M. Lee, Haejoon Kim, Taekyung Panagou, Dimitra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12974 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach Cherenson, Daniel M. Lee, Haejoon Kim, Taekyung Panagou, Dimitra Robotics Systems and Control 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. |
| title | Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach |
| topic | Robotics Systems and Control |
| url | https://arxiv.org/abs/2605.12974 |