In this work, we systematically examine the application of spatio-temporal splitting heuristics to the Multi-Robot Motion Planning (MRMP) problem in a graph-theoretic setting: a problem known to be NP-hard to optimally solve. Following the divide-and-conquer principle, we design multiple spatial and temporal splitting schemes that can be applied to any existing MRMP algorithm, including integer programming solvers and Enhanced Conflict Based Search, in an orthogonal manner. The combination of a good baseline MRMP algorithm with a proper splitting heuristic proves highly effective, allowing the resolution of problems 10+ times than what is possible previously, as corroborated by extensive numerical evaluations. Notably, spatial partition of problem fusing with the temporal splitting heuristic and the enhanced conflict based search (ECBS) algorithm increases the scalability of ECBS on large and challenging DAO maps by 5--15 folds with negligible impact on solution optimality.
翻译:在这项工作中,我们系统地研究对多机器人动力规划(MRMP)问题应用时空分裂理论的问题在图形理论环境中的应用:一个已知难以以最佳方式解决问题的问题。根据分而治之原则,我们设计了多种空间和时间分解计划,可以以正向方式适用于任何现有的MRMP算法,包括整数编程求解器和强化冲突搜索。将良好的基准MRMP算法与适当的分解超模率混合在一起,证明非常有效,使得问题比以前可能解决的10倍以上,这一点得到了广泛的数字评估的证实。 值得注意的是,随着时间分解的超常态和基于搜索(ECBS)的强化冲突,问题的空间分解使欧洲央行在大型和具有挑战性的DAO地图上的可扩展性增加了5-15倍,对解决方案的最佳性影响微乎其微。