Uniform Circle Formation for Fully, Semi-, and Asynchronous Opaque Robots with Lights

In the field of robotics, a lot of theoretical models have been settled to formalize multi-agent systems and design distributed algorithms for autonomous robots. Among the most investigated problems for such systems, the study of the Uniform Circle Formation (UCF) problem earned a lot of attention for the properties of such a convenient disposition. Such a problem asks robots to move on the plane to form a regular polygon, running a deterministic and distributed algorithm by executing a sequence of look–compute–move cycles. This work aims to solve the UCF problem for a very restrictive model of robots: they are punctiform, anonymous, and indistinguishable. They are completely disoriented, i.e., they share neither the coordinate system nor chirality. Additionally, they are opaque, so collinearities can hide important data for a proper computation. To tackle these system limitations, robots are equipped with a persistent light used to communicate and store a constant amount of information. For such a robot model, this paper presents a solution for UCF for each of the three scheduling modes usually studied in the literature: fully synchronous, semi-synchronous, and asynchronous. Regarding the time complexity, the proposed algorithms use a constant number of cycles (epochs) for fully synchronous (semi-synchronous) robots, and linearly, many epochs in the worst case for asynchronous robots.