Mutual visibility on grid by asynchronous luminous robots

Abstract

For a team of autonomous opaque point robots on the plane, the Mutual Visibility problem asks for a distributed algorithm that allows the robots to reposition themselves, without colliding, to a configuration where they all can see each other, i.e., no three of them are collinear. In this paper, we investigate the problem on a grid based terrain where the movements of the robots are restricted only along the grid lines and only to a neighboring grid point in each step. The robots operate in Look-Compute-Move cycles under an asynchronous scheduler. They have no agreement in coordinate system and do not know the total number of robots in the team. We assume the luminous robots model where each robot is equipped with an externally visible light which can assume a constant number of predefined colors. These colors serve both as memory and as a form of communication. We give an algorithm that solves the problem from any initial configuration using 9 colors.