A metamorphic robotic system (MRS) is composed of anonymous, memoryless, and autonomous modules that execute an identical distributed algorithm to move while keeping the connectivity of the modules. For an MRS, the number of modules required to solve a given task is an important complexity measure. Here, we consider evacuation from a finite two-dimensional square grid field by an MRS. This study aims to establish the minimum number of modules required to solve the evacuation problem under several conditions. We consider a rectangular field surrounded by walls with at least one exit. Our results show that two modules are necessary and sufficient for evacuation from any rectangular field if equipped with a global compass, which provides the modules with a common sense of direction. After that, we focus on the case of modules without a global compass and show that four (resp. seven) modules are necessary and sufficient for restricted (resp. any) initial shapes of an MRS. We also show that two modules are sufficient when an MRS is touching a wall in an initial configuration. Then, we clarify the condition to stop an MRS after evacuation of a rectangular field. Finally, we extend these results to mazes and convex fields.

翻译：一个变形机器人系统(MRS)由匿名的、没有记忆的和自主的模块组成,这些模块在保持模块连接的同时执行相同的分布式算法来移动模块。对于 MRS, 解决特定任务所需的模块数量是一个重要复杂度。 这里, 我们考虑用 MRS 从一个有限的二维方格网格字段中进行疏散。 这项研究旨在确定在若干条件下解决疏散问题所需的模块最低数量。 我们考虑用至少一个出口的墙包围一个矩形场。 我们的结果显示, 如果配有全球指南针, 两个模块对于从任何矩形场中进行疏散是必要和充分的, 并且为模块提供了共同的方向感。 之后, 我们把重点放在没有全球指南的模块中, 并显示四个模块( 重复的七) 是必要的, 足以限制 MRS 的初始形状( 重写任何) 。 我们还表明, 当一个MSS 在初始配置中触动墙壁时, 两个模块就足够了。 然后, 我们澄清了在矩形场撤离后停止一个 MRS的条件, 我们将这些结果扩大到磁场和组合场。 最后, 我们将这些结果扩大到磁场。