Terminating grid exploration with myopic luminous robots

Abstract: We investigate the terminating grid exploration 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 colors. First, we prove that, in the semi-synchronous and asynchronous models, three myopic robots are necessary to achieve the terminating grid exploration if the visible distance is one. Next, we give fourteen algorithms for the terminating grid exploration in various assumptions of synchrony (fully-synchronous, semi-synchronous, and asynchronous models), visible distance, the number of colors, and a chirality. Six of them are optimal in terms of the number of robots.