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.

This work has been performed while the first and third authors have been visiting ETH Zürich and while the second and fourth authors have been visiting Carleton University. We also gratefully acknowledge the partial support of the Swiss Natio- nal Science Foundation, the Natural Science and Engineering Research Council of Canada and the Fonds pour la Formation de Chercheurs et l’Aide à la Recherche du Québec.