# Multi-Robot Collision Avoidance under Uncertainty with Probabilistic Safety Barrier Certificates

arXiv: https://arxiv.org/abs/1912.09957 · HTML: https://mlsanity.com/paper/1912.09957/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 13 of 13)

- [Model-based Dynamic Shielding for Safe and Efficient Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2304.06281/) (2023)
- [Hierarchical Multi-Agent Reinforcement Learning with Control Barrier Functions for Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2507.14850/) (2025)
- [Computationally and Sample Efficient Safe Reinforcement Learning Using Adaptive Conformal Prediction](https://mlsanity.com/paper/2503.17678/) (2025)
- [Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions](https://mlsanity.com/paper/2207.14419/) (2022)
- [Risk-aware Safe Control for Decentralized Multi-agent Systems via Dynamic Responsibility Allocation](https://mlsanity.com/paper/2305.13467/) (2023)
- [DeCOM: Decomposed Policy for Constrained Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2111.05670/) (2021)
- [Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Merging](https://mlsanity.com/paper/2212.00618/) (2022)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [ARMOR: Robust Reinforcement Learning-based Control for UAVs under Physical Attacks](https://mlsanity.com/paper/2506.22423/) (2025)
- [Identification and Avoidance of Static and Dynamic Obstacles on Point Cloud for UAVs Navigation](https://mlsanity.com/paper/2105.06622/) (2021)
- [Is the Rush to Machine Learning Jeopardizing Safety? Results of a Survey](https://mlsanity.com/paper/2111.14324/) (2021)
- [ProBF: Learning Probabilistic Safety Certificates with Barrier Functions](https://mlsanity.com/paper/2112.12210/) (2021)
- [SRL-MPC: Shape-Aware Reinforcement Learned Model Predictive Control](https://mlsanity.com/paper/2608.21175/) (2026)

## Abstract (arXiv)

Safety in terms of collision avoidance for multi-robot systems is a difficult challenge under uncertainty, non-determinism and lack of complete information. This paper aims to propose a collision avoidance method that accounts for both measurement uncertainty and motion uncertainty. In particular, we propose Probabilistic Safety Barrier Certificates (PrSBC) using Control Barrier Functions to define the space of admissible control actions that are probabilistically safe with formally provable theoretical guarantee. By formulating the chance constrained safety set into deterministic control constraints with PrSBC, the method entails minimally modifying an existing controller to determine an alternative safe controller via quadratic programming constrained to PrSBC constraints. The key advantage of the approach is that no assumptions about the form of uncertainty are required other than finite support, also enabling worst-case guarantees. We demonstrate effectiveness of the approach through experiments on realistic simulation environments.