SIGMA: Sheaf-Informed Geometric Multi-Agent Pathfinding

TL;DR

SIGMA introduces a sheaf-theoretic framework for decentralized multi-agent pathfinding, enabling agents to learn geometric dependencies and achieve better cooperation, scalability, and collision avoidance in complex environments.

Contribution

The paper presents a novel sheaf theory-based approach integrated with deep reinforcement learning for decentralized MAPF, improving cooperation and scalability.

Findings

Significant performance improvements over state-of-the-art methods.

Effective in large-scale and complex scenarios.

Validated through simulations and real-world robot experiments.

Abstract

The Multi-Agent Path Finding (MAPF) problem aims to determine the shortest and collision-free paths for multiple agents in a known, potentially obstacle-ridden environment. It is the core challenge for robotic deployments in large-scale logistics and transportation. Decentralized learning-based approaches have shown great potential for addressing the MAPF problems, offering more reactive and scalable solutions. However, existing learning-based MAPF methods usually rely on agents making decisions based on a limited field of view (FOV), resulting in short-sighted policies and inefficient cooperation in complex scenarios. There, a critical challenge is to achieve consensus on potential movements between agents based on limited observations and communications. To tackle this challenge, we introduce a new framework that applies sheaf theory to decentralized deep reinforcement learning, enabling agents to learn geometric cross-dependencies between each other through local consensus and utilize them for tightly cooperative decision-making. In particular, sheaf theory provides a mathematical proof of conditions for achieving global consensus through local observation. Inspired by this, we incorporate a neural network to approximately model the consensus in latent space based on sheaf theory and train it through self-supervised learning. During the task, in addition to normal features for MAPF as in previous works, each agent distributedly reasons about a learned consensus feature, leading to efficient cooperation on pathfinding and collision avoidance. As a result, our proposed method demonstrates significant improvements over state-of-the-art learning-based MAPF planners, especially in relatively large and complex scenarios, demonstrating its superiority over baselines in various simulations and real-world robot experiments. The code is available at https://github.com/marmotlab/SIGMA