Symmetry-Breaking in Multi-Agent Navigation: Winding Number-Aware MPC with a Learned Topological Strategy
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908869828018176 |
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| author | Nakao, Tomoki Kasaura, Kazumi Kozuno, Tadashi |
| author_facet | Nakao, Tomoki Kasaura, Kazumi Kozuno, Tadashi |
| contents | In distributed multi-agent navigation without explicit communication, agents can fall into symmetry-induced deadlocks because each agent must autonomously decide how to pass others. To address this problem, we propose WNumMPC, a hierarchical navigation method that quantifies cooperative symmetry-breaking strategies via a topological invariant, the winding number, and learns such strategies through reinforcement learning. The learning-based Planner outputs continuous-valued signed target winding numbers and dynamic importance weights to prioritize critical interactions in dense crossings. Then, the model-based Controller generates collision-free and efficient motions based on the strategy and weights provided by the Planner. Simulation and real-world robot experiments indicate that WNumMPC effectively avoids deadlocks and collisions and achieves better performance than the baselines, particularly in dense and symmetry-prone scenarios. These experiments also suggest that explicitly leveraging winding numbers yields robust sim-to-real transfer with minimal performance degradation. The code for the experiments is available at https://github.com/omron-sinicx/WNumMPC. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry-Breaking in Multi-Agent Navigation: Winding Number-Aware MPC with a Learned Topological Strategy Nakao, Tomoki Kasaura, Kazumi Kozuno, Tadashi Robotics Multiagent Systems In distributed multi-agent navigation without explicit communication, agents can fall into symmetry-induced deadlocks because each agent must autonomously decide how to pass others. To address this problem, we propose WNumMPC, a hierarchical navigation method that quantifies cooperative symmetry-breaking strategies via a topological invariant, the winding number, and learns such strategies through reinforcement learning. The learning-based Planner outputs continuous-valued signed target winding numbers and dynamic importance weights to prioritize critical interactions in dense crossings. Then, the model-based Controller generates collision-free and efficient motions based on the strategy and weights provided by the Planner. Simulation and real-world robot experiments indicate that WNumMPC effectively avoids deadlocks and collisions and achieves better performance than the baselines, particularly in dense and symmetry-prone scenarios. These experiments also suggest that explicitly leveraging winding numbers yields robust sim-to-real transfer with minimal performance degradation. The code for the experiments is available at https://github.com/omron-sinicx/WNumMPC. |
| title | Symmetry-Breaking in Multi-Agent Navigation: Winding Number-Aware MPC with a Learned Topological Strategy |
| topic | Robotics Multiagent Systems |
| url | https://arxiv.org/abs/2511.15239 |