mlsanityData to 14 Oct 2026

LEAP-CBF: A Safety Filter for Uncertain Systems with Least-Effort Adversarial Potentials

arXiv 2609.28364 ↗First posted 23 Sep 2026cs.RO cs.LG math.OCcited by 0

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Abstract (arXiv)

Control barrier functions (CBF) are a popular safety filter to ensure safety for nonlinear dynamical systems. However, when the system is subject to uncertainties and disturbances, this requires the use of robust variants of CBFs, which can be difficult to construct and can be overly conservative, especially for high-dimensional systems under input constraints. In this work, we propose a new approach to solve these challenges by introducing Least-Effort Adversarial Potentials (LEAP), a certificate that quantifies the robustness of a given state against disturbances in terms of the effort required by the disturbance to cause failure. We show that LEAP is a CBF for the undisturbed system, but can also be used to construct a safety filter that is robust to disturbances whose cumulative effort is bounded. We propose a method for constructing LEAPs with on-policy deep reinforcement learning. Next, we demonstrate LEAPs in simulation on a variety of multi-agent systems with disturbances and uncertainties. Finally, hardware experiments on a quadruped and quadrotors validate that LEAPs are well suited to tackle the disturbances and uncertainties from real-world robotic systems.

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33 of 44 references.

References · 33

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2017Robust Adversarial Reinforcement Learningcited by 451
  3. 2019Control Barrier Functions: Theory and Applicationscited by 372
  4. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 287
  5. 2017Hamilton-Jacobi Reachability: A Brief Overview and Recent Advancescited by 201
  6. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
  7. 2018A predictive safety filter for learning-based control of constrained nonlinear dynamical systemscited by 118
  8. 2020DeepReach: A Deep Learning Approach to High-Dimensional Reachabilitycited by 91
  9. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 88
  10. 2019Learning for Safety-Critical Control with Control Barrier Functionscited by 69
  11. 2021Robust Control Barrier-Value Functions for Safety-Critical Controlcited by 51
  12. 2023How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systemscited by 44
21 more
  1. 2020Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functionscited by 33
  2. 2016Robustness of Control Barrier Functions for Safety Critical Controlcited by 30
  3. 2022ISAACS: Iterative Soft Adversarial Actor-Critic for Safetycited by 28
  4. 2024GCBF+: A Neural Graph Control Barrier Function Framework for Distributed Safe Multi-Agent Controlcited by 22
  5. 2024Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imaginationcited by 16
  6. 2018Input-to-State Safety With Control Barrier Functionscited by 15
  7. 2022Refining Control Barrier Functions through Hamilton-Jacobi Reachabilitycited by 15
  8. 2021Predictive control barrier functions: Enhanced safety mechanisms for learning-based controlcited by 14
  9. 2024Solving Minimum-Cost Reach Avoid using Reinforcement Learningcited by 14
  10. 2021Backup Control Barrier Functions: Formulation and Comparative Studycited by 12
  11. 2023Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theorycited by 6
  12. 2021Safe Controller Synthesis with Tunable Input-to-State Safe Control Barrier Functionscited by 5
  13. 2026Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learningcited by 5
  14. 2021Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraintscited by 4
  15. 2023Patching Approximately Safe Value Functions Leveraging Local Hamilton-Jacobi Reachability Analysiscited by 3
  16. 2024Safety on the Fly: Constructing Robust Safety Filters via Policy Control Barrier Functions at Runtimecited by 2
  17. 2025MADR: MPC-guided Adversarial DeepReachcited by 2
  18. 2018Reachability Analysis Using Dissipation Inequalities For Uncertain Nonlinear Systemscited by 1
  19. 2020Backward Reachability using Integral Quadratic Constraints for Uncertain Nonlinear Systemscited by 1
  20. 2021Computation of Reachable Sets Based on Hamilton-Jacobi-Bellman Equation with Running Cost Functioncited by 1
  21. 2026A Time-to-Collision Barrier Function Approach to Collision Avoidance for Stochastic Systemscited by 1

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