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Optimal torus exploration by oblivious robots

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Abstract

We deal with a team of autonomous robots that are endowed with motion actuators and visibility sensors. Those robots are weak and evolve in a discrete environment. By weak, we mean that they are anonymous, uniform, unable to explicitly communicate, and oblivious. We first show that it is impossible to solve the terminating exploration of a simple torus of arbitrary size with less than 4 or 5 such robots, respectively depending on whether the algorithm is probabilistic or deterministic. Next, we propose in the SSYNC model a probabilistic solution for the terminating exploration of torus-shaped networks of size \(\ell \times L\), where \(7 \le \ell \le L\), by a team of 4 such weak robots. So, this algorithm is optimal w.r.t. the number of robots.

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Notes

  1. Obliviousness requires the set of initial configurations to be a proper subset of the set of all configurations to make termination possible in our model; following the literature [9] we assume that every possible initial configuration is towerless.

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Authors and Affiliations

  1. VERIMAG, Université Grenoble Alpes, Grenoble, France

    Stéphane Devismes

  2. Kyushu University, Fukuoka, Japan

    Anissa Lamani

  3. LIP6, UPMC Sorbonne Universités, Paris, France

    Franck Petit & Sébastien Tixeuil

Authors
  1. Stéphane Devismes
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  2. Anissa Lamani
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  3. Franck Petit
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  4. Sébastien Tixeuil
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Correspondence to Stéphane Devismes.

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Devismes, S., Lamani, A., Petit, F. et al. Optimal torus exploration by oblivious robots. Computing 101, 1241–1264 (2019). https://doi.org/10.1007/s00607-018-0595-8

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  • DOI: https://doi.org/10.1007/s00607-018-0595-8

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