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

**Authors:** Songyuan Zhang, Oswin So, Kunal Garg, Chuchu Fan  
**arXiv:** [2401.14554](https://arxiv.org/abs/2401.14554)  
**Date:** 2024-01-25  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2401.14554v1/

## Key points

- A team of researchers led by Songyuan Zhang, Oswin So, Kunal Garg, and Chuchu Fan developed the groundbreaking GCBF+ framework for safe control of multi-agent systems.
- The framework utilizes graph neural networks (GNNs) to enable distributed safe control in large-scale environments with obstacles.
- It introduces a new class called graph control barrier functions (GCBFs) that build upon the theory of control barrier functions (CBFs).
- By parameterizing both a candidate GCBF and a distributed control policy using GNNs, the framework efficiently processes data from LiDAR sensors without relying on actual state information.
- Hardware experiments with drones and extensive numerical experiments validated the effectiveness of the method.
- GCBF+ outperformed traditional CBF-based methods by up to 20% for relatively small-scale multi-agent systems (MAS) with 256 agents like Crazyflie drones in complex environments with nonlinear agents.
- When compared to leading reinforcement learning methods, GCBF+ showed improvements of up to 40% for MAS involving 1024 agents while maintaining high levels of safety.

## Summary

In the field of robotics and multi-agent systems, ensuring safe and efficient control of large-scale environments with obstacles presents a significant challenge. To address this challenge, a team of researchers led by Songyuan Zhang, Oswin So, Kunal Garg, and Chuchu Fan has developed the groundbreaking <kw>GCBF+ framework</kw>, which utilizes <kw>graph neural networks (GNNs)</kw> to enable distributed safe control of multi-agent systems. This innovative approach builds upon the established theory of <kw>control barrier functions (CBFs)</kw>, introducing a new class called <kw>graph control barrier functions (GCBFs)</kw>. By parameterizing both a candidate GCBF and a distributed control policy using GNNs, the framework can efficiently process data from LiDAR sensors without relying on actual state information. The effectiveness of this method was validated through hardware experiments with drones and extensive numerical experiments under varying conditions. Results showed that in complex environments with nonlinear agents like Crazyflie drones, GCBF+ outperformed traditional CBF-based methods by up to 20% for relatively small-scale MAS with 256 agents. Furthermore, when compared to leading reinforcement learning methods, GCBF+ showed improvements of up to 40% for MAS involving 1024 agents while maintaining high levels of safety. Overall, the GCBF+ framework represents a significant advancement in distributed safe multi-agent control and offers an innovative solution for managing large-scale robotic systems in complex environments with obstacles.