Uniform circle formation for swarms of opaque robots with lights

Abstract

The Uniform Circle Formation problem requires a swarm of mobile agents, arbitrarily positioned onto the plane, to move on the vertices of a regular polygon. Each agent, customarily called robot, acts through a sequence of look-compute-move cycles. The robots do not store past actions/system snapshots. They are anonymous and cannot be distinguished by their appearance and do not have a common coordinate system (origin and axis) and chirality. The system is fully synchronous in that all robots have a common clock/notion of time regulating cycles. From the literature, the Uniform Circle Formation problem is recently known to be solvable in a system where robots are punctiform or fat, but in both cases transparent: no robot obstructs the visibility of any other robot. Here, we solve the Uniform Circle Formation problem within a more realistic opaque robot system, i.e., robots may have obstructed visibility due to collinearities. Yet, our robots are assumed to be punctiform and luminous, i.e., equipped with a persistent light assuming different colors. This latter peculiarity represents the only way robots have to communicate. Our proposed algorithm uses a constant number of look-compute-move cycles as well as a constant number of colors.