# GCBF+: A Neural Graph Control Barrier Function Framework for Distributed Safe Multi-Agent Control

arXiv: https://arxiv.org/abs/2401.14554 · HTML: https://mlsanity.com/paper/2401.14554/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2024.

## Built on by (most cited first, 22 of 22)

- [Learning Control Barrier Functions and their application in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2404.16879/) (2024)
- [Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control](https://mlsanity.com/paper/2502.03640/) (2025)
- [MAGICS: Adversarial RL with Minimax Actors Guided by Implicit Critic Stackelberg for Convergent Neural Synthesis of Robot Safety](https://mlsanity.com/paper/2409.13867/) (2024)
- [Solving Multi-Agent Safe Optimal Control with Distributed Epigraph Form MARL](https://mlsanity.com/paper/2504.15425/) (2025)
- [Collision- and Reachability-Aware Multi-Robot Control with Grounded LLM Planners](https://mlsanity.com/paper/2505.20573/) (2025)
- [Foundation Models to the Rescue: Deadlock Resolution in Connected Multi-Robot Systems](https://mlsanity.com/paper/2404.06413/) (2024)
- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [Reliable and Efficient Multi-Agent Coordination via Graph Neural Network Variational Autoencoders](https://mlsanity.com/paper/2503.02954/) (2025)
- [Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions](https://mlsanity.com/paper/2502.15006/) (2025)
- [Robust Multi-Agent Reinforcement Learning for Small UAS Separation Assurance under GPS Degradation and Spoofing](https://mlsanity.com/paper/2603.28900/) (2026)
- [Distributed Model Predictive Control with Adaptive Safety Zones for Multi-Fleet Drone Operations](https://mlsanity.com/paper/2606.20651/) (2026)
- [AttentionSwarm: Reinforcement Learning with Attention Control Barier Function for Crazyflie Drones in Dynamic Environments](https://mlsanity.com/paper/2503.07376/) (2025)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)
- [Distributed Control of Network Systems in the Space of Stabilizing Graph Neural Network Policies](https://mlsanity.com/paper/2512.18540/) (2025)
- [Safer Trajectory Planning with CBF-guided Diffusion Model for Unmanned Aerial Vehicles](https://mlsanity.com/paper/2604.17527/) (2026)
- [Safe and Generalizable Hierarchical Multi-Agent RL via Constraint Manifold Control](https://mlsanity.com/paper/2606.24010/) (2026)
- [Discriminative Barrier Functions for Safe Adversarial Imitation Learning from Observation](https://mlsanity.com/paper/2607.13938/) (2026)
- [Safe and Scalable Multi-Drone Payload Transport via CBF-based Reinforcement Learning with Zero-Shot Sim-to-Real Transfer](https://mlsanity.com/paper/2607.20665/) (2026)
- [Generalizable Multi-Agent Planning from Signal Temporal Logic Specifications via Diffusion](https://mlsanity.com/paper/2608.29490/) (2026)
- [Conflict-Predictive Variable Horizons in Multi-Drone Distributed Model Predictive Control](https://mlsanity.com/paper/2609.13270/) (2026)
- [LEAP-CBF: A Safety Filter for Uncertain Systems with Least-Effort Adversarial Potentials](https://mlsanity.com/paper/2609.28364/) (2026)
- [CollisionGAT: Controller-Agnostic One-Step Collision Screening for Multi-Agent Motion](https://mlsanity.com/paper/2609.32783/) (2026)

## Abstract (arXiv)

Distributed, scalable, and safe control of large-scale multi-agent systems is a challenging problem. In this paper, we design a distributed framework for safe multi-agent control in large-scale environments with obstacles, where a large number of agents are required to maintain safety using only local information and reach their goal locations. We introduce a new class of certificates, termed graph control barrier function (GCBF), which are based on the well-established control barrier function theory for safety guarantees and utilize a graph structure for scalable and generalizable distributed control of MAS. We develop a novel theoretical framework to prove the safety of an arbitrary-sized MAS with a single GCBF. We propose a new training framework GCBF+ that uses graph neural networks to parameterize a candidate GCBF and a distributed control policy. The proposed framework is distributed and is capable of taking point clouds from LiDAR, instead of actual state information, for real-world robotic applications. We illustrate the efficacy of the proposed method through various hardware experiments on a swarm of drones with objectives ranging from exchanging positions to docking on a moving target without collision. Additionally, we perform extensive numerical experiments, where the number and density of agents, as well as the number of obstacles, increase. Empirical results show that in complex environments with agents with nonlinear dynamics (e.g., Crazyflie drones), GCBF+ outperforms the hand-crafted CBF-based method with the best performance by up to 20% for relatively small-scale MAS with up to 256 agents, and leading reinforcement learning (RL) methods by up to 40% for MAS with 1024 agents. Furthermore, the proposed method does not compromise on the performance, in terms of goal reaching, for achieving high safety rates, which is a common trade-off in RL-based methods.