Exploration of finite 2D square grid by a metamorphic robotic system

Abstract

We consider exploration of a finite 2D square grid by a metamorphic robotic system consisting of anonymous oblivious modules. The number of possible shapes of the metamorphic robotic system grows as the number of modules increases. The shapes of the system serve as its memory and show its functionality. We consider the effect of global compass on the minimum number of modules for exploration of 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 limited initial configurations.