Gathering Asynchronous Mobile Robots with Inaccurate Compasses

This paper considers a system of asynchronous autonomous mobile robots that can move freely in a two-dimensional plane with no agreement on a common coordinate system. Starting from any initial configuration, the robots are required to eventually gather at a single point, not fixed in advance (gathering problem).

Prior work has shown that gathering oblivious (i.e., stateless) robots cannot be achieved deterministically without additional assumptions. In particular, if robots can detect multiplicity (i.e., count robots that share the same location) gathering is possible for

three or more

robots. Similarly, gathering of any number of robots is possible if they share a common direction, as given by compasses, with

no errors

.

Our work is motivated by the pragmatic standpoint that (1) compasses are error-prone devices in reality, and (2) multiplicity detection, while being easy to achieve, allows for gathering in situations with more than two robots. Consequently, this paper focusses on gathering two asynchronous mobile robots equipped with

inaccurate

compasses. In particular, we provide a self-stabilizing algorithm to gather, in a finite time, two oblivious robots equipped with compasses that can differ by as much as

π

/4.