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A metamorphic robotic system (MRS) is composed of anonymous, memoryless, andautonomous modules that execute an identical distributed algorithm to movewhile keeping the connectivity of the modules. For an MRS, the number ofmodules required to solve a given task is an important complexity measure.Here, we consider evacuation from a finite two-dimensional square grid field byan MRS. This study aims to establish the minimum number of modules required tosolve the evacuation problem under several conditions. We consider arectangular field surrounded by walls with at least one exit. Our results showthat two modules are necessary and sufficient for evacuation from anyrectangular field if equipped with a global compass, which provides the moduleswith a common sense of direction. After that, we focus on the case of moduleswithout a global compass and show that four (resp. seven) modules are necessaryand sufficient for restricted (resp. any) initial shapes of an MRS. We alsoshow that two modules are sufficient when an MRS is touching a wall in aninitial configuration. Then, we clarify the condition to stop an MRS afterevacuation of a rectangular field. Finally, we extend these results to mazesand convex fields.

Evacuation from Various Types of Finite 2D Square Grid Fields by a Metamorphic Robotic System