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Infinite Grid Exploration by Disoriented Robots

  • Quentin BramasEmail author
  • Stéphane Devismes
  • Pascal Lafourcade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11639)

Abstract

We deal with a set of autonomous robots moving on an infinite grid. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global compass. Finally, they may use lights of different colors, but except from that, robots have neither persistent memories, nor communication mean. We consider the infinite grid exploration (IGE) problem. We first show that two robots are not sufficient in our settings to solve the problem, even when robots have a common coordinate system. We then show that if the robots’ coordinate systems are not self-consistent, three or four robots are not sufficient to solve the problem neither. Finally, we present three algorithms that solve the IGE problem in various settings. The first algorithm uses six robots with constant colors and a visibility range of one. The second one uses the minimum number of robots, i.e., five, as well as five modifiable colors, still under visibility one. The last algorithm requires seven oblivious anonymous robots, yet assuming visibility two. Notice that the two last algorithms also achieve exclusiveness.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Quentin Bramas
    • 1
    Email author
  • Stéphane Devismes
    • 2
  • Pascal Lafourcade
    • 3
  1. 1.University of Strasbourg, ICUBE, CNRSStrasbourgFrance
  2. 2.Université Grenoble Alpes, VERIMAGGrenobleFrance
  3. 3.University Clermont Auvergne, CNRS, UMR 6158, LIMOSClermont-FerrandFrance

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