[论文解读] MAPP: a Scalable Multi-Agent Path Planning Algorithm with Tractability and Completeness Guarantees

Ko-Hsin Cindy Wang, Adi Botea|arXiv (Cornell University)|Jan 16, 2014

Robotic Path Planning Algorithms参考文献 28被引用 167

一句话总结

MAPP 是一种适用于无向图的可扩展、可 tractable 的多智能体路径规划算法，即使在一般情况下不完全，也能提供可解性和性能的正式保证。它通过具有有界复杂度的集中式搜索分解问题，在解覆盖度（99.86% 对比 FAR 和 WHCA* 的 18–22% 更优）和初始规划阶段将 98.82% 的单位标记为可证明可解方面表现优异，同时保持了具有竞争力的速度和解的质量。

ABSTRACT

Multi-agent path planning is a challenging problem with numerous real-life applications. Running a centralized search such as A* in the combined state space of all units is complete and cost-optimal, but scales poorly, as the state space size is exponential in the number of mobile units. Traditional decentralized approaches, such as FAR and WHCA*, are faster and more scalable, being based on problem decomposition. However, such methods are incomplete and provide no guarantees with respect to the running time or the solution quality. They are not necessarily able to tell in a reasonable time whether they would succeed in finding a solution to a given instance. We introduce MAPP, a tractable algorithm for multi-agent path planning on undirected graphs. We present a basic version and several extensions. They have low-polynomial worst-case upper bounds for the running time, the memory requirements, and the length of solutions. Even though all algorithmic versions are incomplete in the general case, each provides formal guarantees on problems it can solve. For each version, we discuss the algorithms completeness with respect to clearly defined subclasses of instances. Experiments were run on realistic game grid maps. MAPP solved 99.86% of all mobile units, which is 18--22% better than the percentage of FAR and WHCA*. MAPP marked 98.82% of all units as provably solvable during the first stage of plan computation. Parts of MAPPs computation can be re-used across instances on the same map. Speed-wise, MAPP is competitive or significantly faster than WHCA*, depending on whether MAPP performs all computations from scratch. When data that MAPP can re-use are preprocessed offline and readily available, MAPP is slower than the very fast FAR algorithm by a factor of 2.18 on average. MAPPs solutions are on average 20% longer than FARs solutions and 7--31% longer than WHCA*s solutions.

研究动机与目标

• 为解决基于集中式 A* 的多智能体路径规划在可扩展性和完全性方面的局限性，后者因状态空间呈指数级增长而受限。
• 克服 FAR 和 WHCA* 等去中心化方法在不完全性和运行时/解质量保证方面的不足。
• 设计一种可扩展的算法，为多智能体路径规划问题的特定子类提供可解性的正式保证。
• 在保持竞争性解质量并可在相似地图实例间复用的前提下，实现低多项式时间与内存复杂度。

提出的方法

• MAPP 在分解后的状态空间上执行集中式搜索，采用有界成本搜索策略以降低计算复杂度。
• 它引入了两阶段规划流程：首先，通过可 tractable 的可行性检查将单位标记为可证明可解；其次，计算实际路径。
• 该算法利用预处理数据在相似地图实例间复用，提升了重复规划场景下的效率。
• 它采用问题分解方法，在确保时间、内存和路径长度的低多项式最坏情况边界的同时，维持了解质量。
• 其核心方法依赖于经过修改的类似 A* 的搜索，结合剪枝和有界扩展，以确保可 tractability。
• 它为特定实例子类定义了正式的完全性保证，确保在适用情况下可解。

实验结果

研究问题

• RQ1 多智能体路径规划算法是否能在有意义的实例子类上同时实现可 tractability 和正式完全性保证？
• RQ2 如何在不牺牲可解情况下的解质量或完全性的情况下，提升集中式 A* 的可扩展性？
• RQ3 在相似地图间，预处理数据能在多大程度上复用，以加速动态环境中的规划？
• RQ4 MAPP 的解质量与覆盖度与现有去中心化方法（如 FAR 和 WHCA*）相比如何？
• RQ5 在使用可 tractable、有界复杂度算法时，解长度与规划速度之间的权衡如何？

主要发现

• MAPP 在真实游戏网格地图上解决了所有移动单位中的 99.86%，解覆盖度相比 FAR 和 WHCA* 提高了 18–22%。
• MAPP 在规划第一阶段将 98.82% 的所有单位标记为可证明可解，表明其具备强大的可行性检测能力。
• 当存在预处理数据时，MAPP 平均仅比快速的 FAR 算法慢 2.18 倍，显示出优异的复用性能。
• MAPP 的解平均比 FAR 长 20%，比 WHCA* 长 7–31%，表明其在解质量上实现了合理的权衡。
• 该算法在运行时间、内存使用和解长度方面均实现了低多项式最坏情况边界，确保了可 tractability。
• 与仅依赖去中心化方法（不提供此类保证）不同，MAPP 为特定实例子类提供了正式的完全性保证。