Hard tasks for weak robots: The role of common knowledge in pattern formation by autonomous mobile robots

Abstract

In this paper we aim at an understanding of the fundamental algorithmic limitations on what a set of autonomous mobile robots can or cannot achieve. We study a hard task for a set of weak robots. The task is for the robots in the plane to form any arbitrary pattern that is given in advance. The robots are weak in several aspects. They are anonymous; they cannot explicitly communicate with each other, but only observe the positions of the others; they cannot remember the past; they operate in a very strong form of asynchronicity. We show that the tasks that such a system of robots can perform depend strongly on their common knowledge about their environment, i.e., the readings of their environment sensors.