Exploration of Finite 2D Square Grid by a Metamorphic Robotic System

TL;DR

This paper investigates how a metamorphic robotic system with anonymous modules explores finite 2D grids, highlighting the impact of global compass agreement on the minimum modules needed.

Contribution

It establishes the minimum number of modules required for exploration depending on whether modules share a global compass direction.

Findings

Three modules suffice with a global compass for arbitrary initial configurations.

Five modules are necessary without a global compass for restricted initial configurations.

The shape of the system encodes memory and functionality.

Abstract

We consider exploration of finite 2D square grid by a metamorphic robotic system consisting of anonymous oblivious modules. The number of possible shapes of a metamorphic robotic system grows as the number of modules increases. The shape of the system serves as its memory and shows its functionality. We consider the effect of global compass on the minimum number of modules necessary to explore a finite 2D square grid. We show that if the modules agree on the directions (north, south, east, and west), three modules are necessary and sufficient for exploration from an arbitrary initial configuration, otherwise five modules are necessary and sufficient for restricted initial configurations.