Perpetual torus exploration by myopic luminous robots

Abstract

We study perpetual torus exploration for swarms of autonomous, anonymous, uniform, and luminous robots. We consider robots with only few capabilities. They have a finite limited vision (myopic), they can only see robots at distance one or two. We show that the problem is impossible with only two luminous robots and also with three oblivious robots (without light). We then address the problem assuming luminous robots (resp. oblivious) with visibility range one (resp. two). We design optimal solutions with respect to both the number of robots and colors when robots share a common chirality and have, respectively, vision one and two. We also present an optimal solution with respect to the number of robots when they are endowed with vision one and share no common chirality. Finally, we propose a solution for the case in which robots are oblivious, have vision two, and no common chirality that uses one additional robot.