  We consider the problem of designing distributed collision-avoidance
multi-agent control in large-scale environments with potentially moving
obstacles, where a large number of agents are required to maintain safety using
only local information and reach their goals. This paper addresses the problem
of collision avoidance, scalability, and generalizability by introducing graph
control barrier functions (GCBFs) for distributed control. The newly introduced
GCBF is based on the well-established CBF theory for safety guarantees but
utilizes a graph structure for scalable and generalizable decentralized
control. We use graph neural networks to learn both neural a GCBF certificate
and distributed control. We also extend the framework from handling state-based
models to directly taking point clouds from LiDAR for more practical robotics
settings. We demonstrated the efficacy of GCBF in a variety of numerical
experiments, where the number, density, and traveling distance of agents, as
well as the number of unseen and uncontrolled obstacles increase. Empirical
results show that GCBF outperforms leading methods such as MAPPO and
multi-agent distributed CBF (MDCBF). Trained with only 16 agents, GCBF can
achieve up to 3 times improvement of success rate (agents reach goals and never
encountered in any collisions) on <500 agents, and still maintain more than 50%
success rates for >1000 agents when other methods completely fail.
