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

TL;DR

This paper investigates the minimum number of modules needed for a metamorphic robotic system to evacuate various finite 2D grid fields, establishing bounds based on the presence of a global compass and initial configurations.

Contribution

It provides the first comprehensive analysis of module requirements for evacuation in finite 2D fields, considering different initial conditions and the presence of a global compass.

Findings

Two modules are necessary and sufficient with a global compass.

Four to seven modules are needed without a global compass depending on initial shape.

Two modules suffice when touching a wall initially.

Abstract

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.