Ring Exploration of Myopic Luminous Robots with Visibility More Than One

Abstract

In this paper, we investigate ring exploration algorithms for autonomous myopic luminous robots. Myopic robots mean that they can observe nodes only within a certain fixed distance, and luminous robots mean that they have light devices that can emit a color from a set of constant number of colors. We consider the constraint that the visible distance is any constant of at least two and the number of colors of light devices is two. As a main contribution, in the fully synchronous, semi-synchronous, and asynchronous models, we prove that (1) two robots are necessary and sufficient to achieve perpetual exploration and (2) three robots are necessary and sufficient to achieve terminating exploration, where perpetual exploration requires every robot to visit every node infinitely many times and terminating exploration requires robots to terminate after every node is visited by a robot at least once. These results show the power of large visibility for luminous robots because, when the visible distance is one and the number of colors is two, three and four robots are necessary to achieve perpetual and terminating exploration, respectively, in the semi-synchronous and asynchronous models. We also show that the proposed perpetual exploration algorithm is universal, that is, the algorithm achieves perpetual exploration from any solvable initial configuration with two robots. On the other hand, we show that no universal algorithm exists for terminating exploration with three robots.