[Paper Review] Neural Graph Control Barrier Functions Guided Distributed Collision-avoidance Multi-agent Control

Songyuan Zhang, Kunal Garg+1 more|arXiv (Cornell University)|Nov 21, 2023

Bayesian Modeling and Causal Inference4 citations

TL;DR

This paper introduces Graph Control Barrier Functions (GCBF), a learning-based, decentralized multi-agent control framework that uses graph neural networks (GNNs) to encode collision avoidance constraints and distinguish between agents and obstacles. Trained on only 16 agents, GCBF achieves up to 3× higher success rates than MAPPO and MDCBF in large-scale scenarios (up to 1000+ agents), maintaining over 50% success even when baselines fail, and generalizes effectively to LiDAR-based, unseen obstacles and complex dynamics.

ABSTRACT

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.

Motivation & Objective

• To address the scalability, generalizability, and safety challenges in large-scale multi-agent systems with moving obstacles.
• To overcome limitations in existing CBF and MARL methods that rely on handcrafted constraints or treat all neighbors uniformly.
• To enable decentralized, local control that maintains safety while generalizing to unseen agents and obstacles.
• To integrate LiDAR point cloud observations for real-world applicability in dynamic, unknown environments.
• To achieve high success rates in large-scale multi-agent tasks where prior methods fail.

Proposed method

• Proposes Graph Control Barrier Functions (GCBF), a neural network-based CBF that encodes safety constraints using a dynamic graph structure of agent interactions.
• Uses graph neural networks (GNNs) to jointly learn a GCBF certificate and a distributed control policy that adapts to changing neighbor topologies.
• Incorporates LiDAR point clouds as input to detect and distinguish between controlled agents and uncontrolled obstacles (e.g., static or dynamic obstacles).
• Employs a continuous-time CBF formulation with time-derivative constraints to ensure forward invariance of safe sets, avoiding discrete approximations that degrade performance.
• Applies a smooth control input selection from a safe control set to maintain safety under time-varying graph structures and system dynamics.
• Uses theoretical CBF-based forward invariance arguments to prove safety guarantees under the proposed framework.

Experimental results

Research questions

• RQ1 Can a learning-based CBF framework maintain safety in large-scale multi-agent systems with dynamic, unknown obstacles?
• RQ2 Can GCBF generalize to unseen numbers of agents and obstacle configurations beyond the training distribution?
• RQ3 Does the integration of LiDAR observations improve robustness and performance in real-world-like environments?
• RQ4 How does GCBF compare to SOTA methods like MAPPO and MDCBF in terms of success rate and scalability?
• RQ5 Can GCBF maintain high performance under complex, realistic dynamics such as those of quadrotors?

Key findings

• Trained on only 16 agents, GCBF achieves up to 3× higher success rate than MAPPO and MDCBF in environments with fewer than 500 agents.
• For large-scale scenarios with over 1000 agents, where baseline methods achieve near 0% success rate, GCBF maintains a 50–100% success rate.
• In obstacle-rich environments with up to 32 large obstacles during testing (only 16 point-sized obstacles in training), GCBF improves success rate by over 15% compared to baselines.
• GCBF generalizes effectively to the CrazyFlie quadrotor dynamics, achieving a 98.9% success rate with 128 agents, demonstrating robustness to complex, realistic dynamics.
• The framework maintains safety guarantees through theoretical CBF-based forward invariance, even with changing graph topologies and LiDAR-based observations.
• Empirical results confirm that GCBF outperforms MDCBF and MAPPO in both obstacle-free and obstacle-embedded 2D and 3D environments across all tested scales.