Optimum Algorithm for Mutual Visibility Among Asynchronous Robots with Lights

This paper addresses the constrained version of the mutual visibility problem for a set of asynchronous, opaque robots in the Euclidean plane. The mutual visibility problem asks the robots to form a configuration, within finite time and without collision, in which no three robots are collinear. The constrained mutual visibility problem in addition aims to minimize the maximum number of movements by a single robot. One of the implications of this constrained version of mutual visibility problem is that it also addresses issue of energy efficiency. The robots have a constant amount of persistent memory and they are equipped with externally visible lights which can assume a constant number of predefined colors. The colors represent different states of the robots and are used both for internal memory and communication. The colors of the lights do not change automatically. A distributed algorithm is proposed to solve the constrained mutual visibility problem for a set of asynchronous robots using only seven colors. The proposed algorithm does not impose any other restriction on the capability of the robots and guarantees collision-free movements for the robots.

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