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Finding Water on Poleless Using Melomaniac Myopic Chameleon Robots

Authors Quentin Bramas , Pascal Lafourcade , Stéphane Devismes

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Author Details

Quentin Bramas
  • University of Strasbourg, ICUBE, France
Pascal Lafourcade
  • LIMOS, University Clermont Auvergne, Aubière, France
Stéphane Devismes
  • Université Grenoble Alpes, VERIMAG, France

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Quentin Bramas, Pascal Lafourcade, and Stéphane Devismes. Finding Water on Poleless Using Melomaniac Myopic Chameleon Robots. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 6:1-6:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


In 2042, the exoplanet exploration program, launched in 2014 by NASA, finally discovers a new exoplanet so-called Poleless, due to the fact that it is not subject to any magnetism. A new generation of autonomous mobile robots, called M2C (for Melomaniac Myopic Chameleon), have been designed to find water on Poleless. To address this problem, we investigate optimal (w.r.t., visibility range and number of used colors) solutions to the infinite grid exploration problem (IGE) by a small team of M2C robots. Our first result shows that minimizing the visibility range and the number of used colors are two orthogonal issues: it is impossible to design a solution to the IGE problem that is optimal w.r.t. both parameters simultaneously. Consequently, we address optimality of these two criteria separately by proposing two algorithms; the former being optimal in terms of visibility range, the latter being optimal in terms of number of used colors. It is worth noticing that these two algorithms use a very small number of robots, respectively six and eight.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Luminous Robots
  • Grid
  • Infinite Exploration
  • Treasure Search Problem


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