[论文解读] Pairwise Symmetry Reasoning for Multi-Agent Path Finding Search

Jiaoyang Li, Daniel Harabor+2 more|arXiv (Cornell University)|Mar 12, 2021

Robotic Path Planning Algorithms参考文献 38被引用 26

一句话总结

本论文将成对对称性识别为MAPF难度的主要来源之一，并在CBS中开发了打破对称性的技术，解决矩形、目标和走廊对称性，从而大幅减少节点扩展并提升可扩展性。

ABSTRACT

Multi-Agent Path Finding (MAPF) is a challenging combinatorial problem that asks us to plan collision-free paths for a team of cooperative agents. In this work, we show that one of the reasons why MAPF is so hard to solve is due to a phenomenon called pairwise symmetry, which occurs when two agents have many different paths to their target locations, all of which appear promising, but every combination of them results in a collision. We identify several classes of pairwise symmetries and show that each one arises commonly in practice and can produce an exponential explosion in the space of possible collision resolutions, leading to unacceptable runtimes for current state-of-the-art (bounded-sub)optimal MAPF algorithms. We propose a variety of reasoning techniques that detect the symmetries efficiently as they arise and resolve them by using specialized constraints to eliminate all permutations of pairwise colliding paths in a single branching step. We implement these ideas in the context of the leading optimal MAPF algorithm CBS and show that the addition of the symmetry reasoning techniques can have a dramatic positive effect on its performance - we report a reduction in the number of node expansions by up to four orders of magnitude and an increase in scalability by up to thirty times. These gains allow us to solve to optimality a variety of challenging MAPF instances previously considered out of reach for CBS.

研究动机与目标

• 识别并描述在MAPF中导致组合爆炸的成对对称现象。
• 发展高效的对称性破坏约束以解决对称冲突。
• 证明所提出的对称性推理保持CBS的完备性与最优性。
• 在4-连通网格上实现并在CBS及其变体中评估对称性技术。

提出的方法

• 定义并分类导致指数级搜索增长的成对对称类型（矩形、目标、走廊）。
• 推导屏障和基于约束的对称性破坏技术，在单次分支步骤中解决对称冲突。
• 证明约束集合的互相互斥性以保持CBS保证（完备性和最优性）。
• 将基于矩形的推理整合到CBSH和CBSH2框架中，并扩展到广义场景。
• 在MAPF实例上进行经验评估，报告节点扩展的减少和可解性提升。

实验结果

研究问题

• RQ1 MAPF 中存在哪些成对对称性，以及它们如何影响最优搜索性能？
• RQ2 如何设计对称性破坏约束，以在不丢失完备性或最优性的情况下消除对称路径组合？
• RQ3 所提出的基于矩形、目标和走廊的推理技术在实际中对 CBS及其变体有何影响？
• RQ4 将对称性推理应用于CBS及其变体时能获得哪些经验增益（如节点扩展、可解实例）？

主要发现

• 对称性推理可以将CBS节点扩展减少多达四个数量级。
• 增加对称性技术显著提升可扩展性，在某些情况下约多达三十倍。
• CBSH及其变体（CBSH2、Mutex Propagation）在具挑战性的实例上看到显著的运行时间和可解性提升。
• 矩形对称性推理可以在一次分支步骤中解决大多数两代理冲突。
• 该等技术在互斥性约束框架下保持CBS的完备性与最优性。