Gathering Two Stateless Mobile Robots Using Very v

This paper considers two asynchronous identical mobile robots in an environment devoid of any landmarks or common coordinate system. The robots, executing their own instance of the same algorithm, must cooperate to end up at the exact same location (not predetermined) within a finite time. The problem, known as gathering, is the simplest form of spontaneous agreement that can be reached between the robots. This simple problem is however notoriously impossible with two such robots. Surprisingly, the problem was shown to be solvable for three robots or more, adding a weak assumption to help break any potential symmetry in the system. Prior work has shown that the problem could be solved by letting each robot have access to some compass, provided that the divergence between the compasses is at most 45◦. The question remained open, however, as to whether the problem could still be solved with a larger divergence. In this paper, we present a distributed algorithm that solves the gathering problem with two asynchronous robots, when their compasses can differ by any angle less than 180◦, which is obviously the largest divergence for which the compasses can still bring any useful information.