A distributed algorithm for gathering many fat mobile robots in the plane

Abstract

We revisit the problem of gathering autonomous robots in the plane. In particular, we consider non-transparent unit-disc robots (i.e., fat) in an asynchronous setting with vision as the only means of coordination and robots only make local decisions. We use a state-machine representation to formulate the gathering problem and develop a distributed algorithm that solves the problem for any number of fat robots. The main idea behind the algorithm is to enforce the robots to reach a configuration in which all the following hold: (i) The robots' centers form a convex hull in which all robots are on the convex hull's boundary

(ii) Each robot can see all other robots

(iii) The configuration is connected: every robot touches another robot and all robots form together a connected formation. We show that starting from any initial configuration, the fat robots eventually reach such a configuration and terminate yielding a solution to the gathering problem. Copyright 2013 ACM.