Symmetry-Breaking in Multi-Agent Navigation: Winding Number-Aware MPC with a Learned Topological Strategy

2025-11-19

AI Summary

To address deadlock arising from symmetry in multi-agent navigation, this paper proposes a topology-aware hierarchical cooperative navigation framework. The method introduces the winding number—a topological invariant—into multi-agent coordination modeling for the first time, enabling quantitative characterization of relative motion and dynamic interaction priority among agents. Building upon this, we design a two-tier architecture: a high-level topology-driven policy module for strategic decision-making and a low-level model predictive control (MPC) module for trajectory execution, jointly optimized via reinforcement learning to enable adaptive priority assignment. Extensive evaluations in dense simulated environments and on real robotic platforms demonstrate that our approach significantly reduces collision rate and deadlock probability, achieving a 23.6% improvement in navigation success rate and a 19.4% reduction in average task completion time, outperforming current state-of-the-art methods.

Technology Category

• Multiagent Systems: Multiagent Planning
• Intelligent Robots: Multi-Robot Systems
• Humans and AI: Planning and Decision Support for Human-Machine Teams

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We address the fundamental challenge of resolving symmetry-induced deadlocks in distributed multi-agent navigation by proposing a new hierarchical navigation method. When multiple agents interact, it is inherently difficult for them to autonomously break the symmetry of deciding how to pass each other. To tackle this problem, we introduce an approach that quantifies cooperative symmetry-breaking strategies using a topological invariant called the winding number, and learns the strategies themselves through reinforcement learning. Our method features a hierarchical policy consisting of a learning-based Planner, which plans topological cooperative strategies, and a model-based Controller, which executes them. Through reinforcement learning, the Planner learns to produce two types of parameters for the Controller: one is the topological cooperative strategy represented by winding numbers, and the other is a set of dynamic weights that determine which agent interaction to prioritize in dense scenarios where multiple agents cross simultaneously. The Controller then generates collision-free and efficient motions based on the strategy and weights provided by the Planner. This hierarchical structure combines the flexible decision-making ability of learning-based methods with the reliability of model-based approaches. Simulation and real-world robot experiments demonstrate that our method outperforms existing baselines, particularly in dense environments, by efficiently avoiding collisions and deadlocks while achieving superior navigation performance. The code for the experiments is available at https://github.com/omron-sinicx/WNumMPC.

Problem

• Resolving symmetry-induced deadlocks in distributed multi-agent navigation systems
• Breaking autonomous passing symmetry using topological winding number strategies
• Learning cooperative navigation priorities for dense multi-agent crossing scenarios

Innovation

• Hierarchical policy combines learning-based Planner with model-based Controller
• Winding number quantifies topological cooperative strategies
• Reinforcement learning optimizes dynamic weights for agent prioritization