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

arXiv: https://arxiv.org/abs/2609.28364 · HTML: https://mlsanity.com/paper/2609.28364/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 30 of 33)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions](https://mlsanity.com/paper/2010.16001/) (2020)
- [Robustness of Control Barrier Functions for Safety Critical Control](https://mlsanity.com/paper/1612.01554/) (2016)
- [ISAACS: Iterative Soft Adversarial Actor-Critic for Safety](https://mlsanity.com/paper/2212.03228/) (2022)
- [GCBF+: A Neural Graph Control Barrier Function Framework for Distributed Safe Multi-Agent Control](https://mlsanity.com/paper/2401.14554/) (2024)
- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)
- [Input-to-State Safety With Control Barrier Functions](https://mlsanity.com/paper/1803.03035/) (2018)
- [Refining Control Barrier Functions through Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2204.12507/) (2022)
- [Predictive control barrier functions: Enhanced safety mechanisms for learning-based control](https://mlsanity.com/paper/2105.10241/) (2021)
- [Solving Minimum-Cost Reach Avoid using Reinforcement Learning](https://mlsanity.com/paper/2410.22600/) (2024)
- [Backup Control Barrier Functions: Formulation and Comparative Study](https://mlsanity.com/paper/2104.11332/) (2021)
- [Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theory](https://mlsanity.com/paper/2306.04026/) (2023)
- [Safe Controller Synthesis with Tunable Input-to-State Safe Control Barrier Functions](https://mlsanity.com/paper/2103.08041/) (2021)
- [Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning](https://mlsanity.com/paper/2604.13192/) (2026)
- [Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraints](https://mlsanity.com/paper/2108.10491/) (2021)
- [Patching Approximately Safe Value Functions Leveraging Local Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2304.09850/) (2023)
- [Safety on the Fly: Constructing Robust Safety Filters via Policy Control Barrier Functions at Runtime](https://mlsanity.com/paper/2410.11157/) (2024)
- [MADR: MPC-guided Adversarial DeepReach](https://mlsanity.com/paper/2510.18845/) (2025)
- [Reachability Analysis Using Dissipation Inequalities For Uncertain Nonlinear Systems](https://mlsanity.com/paper/1808.02585/) (2018)

## 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.