Learning Verified Safe Neural Network Controllers for Multi-Agent Path Finding

Multi-agent path finding (MAPF) is a safety-critical scenario where the goal is to secure collision-free trajectories from initial to desired locations. However, due to system complexity and uncertainty, integrating learning-based controllers with MAPF is challenging and cannot theoretically guarantee the safety of the learned controllers. In response, our study proposes a verified safe multi-agent neural control (VSMANC) approach for MAPF, focusing on the unified training of Decentralized Control Barrier Functions (DCBF) and controllers to enhence safety. VSMANC enables all agents to concurrently learn controllers and DCBFs using a unified loss function designed to maximize safety, adhere to standard control policies, and incorporate path-finding-related heuristics. We also propose a formal verification-guided retraining process to both verify the properties of the learned DCBFs and generate counterexamples for retraining, thereby providing a verified safety guarantee. We validate our approach through shape formation experiments and UAV simulations, demonstrating significant improvements in safety and effectiveness in complex multi-agent environments.