[Paper Review] CTRMs: Learning to Construct Cooperative Timed Roadmaps for Multi-agent Path Planning in Continuous Spaces

Keisuke Okumura, Ryo Yonetani+2 more|arXiv (Cornell University)|Jan 24, 2022

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes Cooperative Timed Roadmaps (CTRMs), a data-driven method that learns to construct agent-specific, collision-aware, time-augmented roadmaps for multi-agent path planning in continuous spaces. By training a conditional variational autoencoder on MAPP demonstrations, CTRMs enable efficient, high-quality planning with significantly reduced search effort compared to baseline methods.

ABSTRACT

Multi-agent path planning (MAPP) in continuous spaces is a challenging problem with significant practical importance. One promising approach is to first construct graphs approximating the spaces, called roadmaps, and then apply multi-agent pathfinding (MAPF) algorithms to derive a set of conflict-free paths. While conventional studies have utilized roadmap construction methods developed for single-agent planning, it remains largely unexplored how we can construct roadmaps that work effectively for multiple agents. To this end, we propose a novel concept of roadmaps called cooperative timed roadmaps (CTRMs). CTRMs enable each agent to focus on its important locations around potential solution paths in a way that considers the behavior of other agents to avoid inter-agent collisions (i.e., "cooperative"), while being augmented in the time direction to make it easy to derive a "timed" solution path. To construct CTRMs, we developed a machine-learning approach that learns a generative model from a collection of relevant problem instances and plausible solutions and then uses the learned model to sample the vertices of CTRMs for new, previously unseen problem instances. Our empirical evaluation revealed that the use of CTRMs significantly reduced the planning effort with acceptable overheads while maintaining a success rate and solution quality comparable to conventional roadmap construction approaches.

Motivation & Objective

• To address the challenge of efficient multi-agent path planning (MAPP) in continuous spaces, where conventional roadmap methods are not optimized for multiple agents.
• To reduce the search space for MAPF algorithms by constructing sparse yet effective roadmaps that capture plausible solution paths.
• To improve planning efficiency and solution quality by incorporating inter-agent cooperation and temporal awareness into roadmap construction.
• To develop a generalizable, learning-based approach that can be applied across diverse scenarios with varying numbers of agents and obstacles.

Proposed method

• A conditional variational autoencoder (CVAE) is trained on a dataset of MAPP problem instances and their corresponding conflict-free solution paths to model agent behavior over time.
• The trained CVAE serves as a vertex sampler $F_{\rm CTRM}$ to generate space-time vertices for constructing agent-specific CTRMs for new, unseen problem instances.
• CTRMs are directed acyclic graphs that encode both spatial positions and time steps, enabling timed path planning with reduced inter-agent collision risk.
• The method integrates communication features $\mathbf{x}_{\rm comm}$ and indicator features $\mathbf{x}_{\rm ind}$ to improve agent coordination and sampling accuracy.
• A random walk strategy is used during CTRM construction to explore diverse path candidates while maintaining high success rates.
• The resulting CTRMs are used as input to a standard MAPF solver, enabling fast and efficient conflict-free path computation.

Experimental results

Research questions

• RQ1 How can roadmaps be constructed to effectively support multi-agent path planning in continuous spaces while minimizing search effort?
• RQ2 What characteristics of roadmap construction are essential for achieving high success rates and solution quality in multi-agent systems?
• RQ3 To what extent can a learned generative model improve the efficiency and effectiveness of roadmap-based MAPP compared to random or uniform sampling?
• RQ4 How do communication and indicator features influence the performance of the learned sampling model in CTRM construction?
• RQ5 Can a single trained model generalize across different scenarios with varying numbers of agents and obstacle configurations?

Key findings

• CTRMs achieved a success rate of 80% on the Basic scenario with $N_{\rm traj} = 25$, significantly outperforming variants without communication features (23%) or random walk (3%).
• The sum-of-costs per agent was 21.2 (95% CI: 20.3–22.0), comparable to or better than baseline methods, even when accounting for reduced sampling effort.
• The number of expanded nodes was reduced to 612.4 on average, a substantial improvement over baselines, indicating a much smaller search space.
• The total planning time, including CTRM construction overhead, remained practical and competitive, with solution generation completing immediately after CTRM creation.
• The model demonstrated generalization: a single model trained on one scenario successfully solved problems in other scenarios with different agent counts and obstacle layouts.
• Ablation studies confirmed that all components—communication features, indicator features, and random walk—were critical for high performance, with their absence leading to drastic drops in success rate and solution quality.