# Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties

arXiv: https://arxiv.org/abs/2004.05273 · HTML: https://mlsanity.com/paper/2004.05273/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2020.

## Built on by (most cited first, 20 of 20)

- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [SABLAS: Learning Safe Control for Black-box Dynamical Systems](https://mlsanity.com/paper/2201.01918/) (2022)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Beyond Robustness: A Taxonomy of Approaches towards Resilient Multi-Robot Systems](https://mlsanity.com/paper/2109.12343/) (2021)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Learning Interaction-aware Guidance Policies for Motion Planning in Dense Traffic Scenarios](https://mlsanity.com/paper/2107.04538/) (2021)
- [Provably Correct Training of Neural Network Controllers Using Reachability Analysis](https://mlsanity.com/paper/2102.10806/) (2021)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions](https://mlsanity.com/paper/2207.14419/) (2022)
- [Learning Adaptive Safety for Multi-Agent Systems](https://mlsanity.com/paper/2309.10657/) (2023)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems](https://mlsanity.com/paper/2407.08868/) (2024)
- [Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty](https://mlsanity.com/paper/2501.04757/) (2025)
- [Robust Action Governor for Uncertain Piecewise Affine Systems with Non-convex Constraints and Safe Reinforcement Learning](https://mlsanity.com/paper/2207.08240/) (2022)
- [Safe Learning of Uncertain Environments](https://mlsanity.com/paper/2103.01413/) (2021)
- [Learning Safety Filters for Unknown Discrete-Time Linear Systems](https://mlsanity.com/paper/2111.00631/) (2021)
- [ProBF: Learning Probabilistic Safety Certificates with Barrier Functions](https://mlsanity.com/paper/2112.12210/) (2021)
- [Barrier Function Overrides For Non-Convex Fixed Wing Flight Control and Self-Driving Cars](https://mlsanity.com/paper/2505.05548/) (2025)
- [Distributed Risk-Sensitive Safety Filters for Uncertain Discrete-Time Systems](https://mlsanity.com/paper/2506.07347/) (2025)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)

## Abstract (arXiv)

Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties