Rendezvous of two robots with visible bits

Abstract

We study the rendezvous problem for two robots moving in the plane (or on a line). Robots are autonomous, anonymous, oblivious, and carry colored lights that are visible to both. We consider deter-ministic distributed algorithms in which robots do not use distance information, but try to reduce (or increase) their distance by a constant factor, depending on their lights' colors. We give a complete characterization of the number of colors that are necessary to solve the rendezvous problem in every possible model, ranging from fully synchronous to semi-synchronous to asynchronous, rigid and non-rigid, with preset or arbitrary initial configuration. In particular, we show that three colors are sufficient in the non-rigid asynchronous model with arbitrary initial configuration. In contrast , two colors are insufficient in the rigid asynchronous model with arbitrary initial configuration and in the non-rigid asynchronous model with preset initial configuration. Additionally, if the robots are able to distinguish between zero and non-zero distances, we show how they can solve rendezvous and detect termination using only three colors, even in the non-rigid asynchronous model with arbitrary initial configuration.

DOI: 10.1007/978-3-642-45346-5_21

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Distributed computing for mobile robots: gathering

  • M Cieliebak, P Flocchini, G Prencipe, N Santoro
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