Gathering Autonomous Mobile Robots with Dynamic Compasses: An Optimal Result

Let consider n autonomous mobile robots that can move in a two dimensional plane. The gathering problem is one of the most fundamental tasks of autonomous mobile robots. In short, given a set of robots with arbitrary initial locations, gathering must make all robots meet in finite time at a point that is not predefined. In this paper, we study about the feasibility of gathering by mobile robots that have ϕ-absolute error dynamic compasses. While the direction of each local coordinate system is fixed in usual systems, the dynamic compass model allows the angle difference between a local coordinate system and the global coordinate system to vary with time in the range of [0, ϕ]. This paper proposes a semi-synchronous gathering algorithm for n robots with (π/2-e)-absolute error dynamic compasses, where e is an arbitrary small constant larger than zero. To the best of our knowledge, the proposed algorithm is the first one that considers both inaccurate compass models and more than two robots. We also show the optimality of our algorithm. It is proved that for any ϕ ≥ π/2, there is no algorithm to gather two robots with ϕ-absolute error dynamic compasses.

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