Using eventually consistent compasses to gather oblivious mobile robots with limited visibility

Reaching agreement between a set of mobile robots is one of the most fundamental issues in distributed robotic systems. This problem is often illustrated by the gathering problem, where the robots must self-organize and meet at some (not predetermined) location, without a global coordinate system. While being very simple to express, this problem has the advantage of retaining the inherent difficulty of agreement, namely the question of breaking symmetry between robots. In previous works, it was proved that gathering is solvable in asynchronous model with oblivious robots and limited visibility, as long as the robots share the knowledge of some direction, as provided by a compass. However, the problem has no solution in the semi-synchronous model when robots do not share a compass and cannot detect multiplicity. In this paper, we define a model in which compasses may be unreliable, and study the solvability of gathering oblivious mobile robots with limited visibility in a semi-synchronous model. In particular, we give an algorithm that solves the problem in finite time in a system where compasses are unstable for some arbitrary long periods, provided that they stabilize eventually. In addition, our algorithm is self-stabilizing.