Complete Visibility for Mobile Agents with Lights Tolerating a Faulty Agent
We revisit the problem of gathering autonomous robots in the plane. In particular, we consider non-transparent unit-disc robots (i.e., <i>fat</i>) 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>i</i>) The robots' centers form a convex hull in which all robots are on the convex hull's boundary; (<i>ii</i>) Each robot can see all other robots; (<i>iii</i>) The configuration is <i>connected</i>: 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.