Multi-robot motion planning is a hard problem. We investigate restricted variants of the problem where square robots are allowed to slide over an arbitrary curve to a new position only a constant number of times each. We show that the problem remains NP-hard in most cases, except when the squares have unit size and when the problem is unlabeled, i.e., the location of each square in the target configuration is left unspecified.

翻译：多机器人运动规划是一个困难问题。本文研究该问题的受限变体，其中正方形机器人仅允许沿任意曲线滑动至新位置，且每个机器人移动次数恒定。我们证明在大多数情况下该问题仍保持NP困难性，仅当正方形具有单位尺寸且问题为非标记化（即目标配置中每个正方形的位置未作指定）时例外。