Asynchronous Exclusive Perpetual Grid Exploration without Sense of Direction

  • François Bonnet
  • Alessia Milani
  • Maria Potop-Butucaru
  • Sébastien Tixeuil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7109)

Abstract

In this paper, we investigate the exclusive perpetual exploration of grid shaped networks using anonymous, oblivious and fully asynchronous robots. Our results hold for robots without sense of direction (i.e. they do not agree on a common North, nor do they agree on a common left and right ; furthermore, the “North” and “left” of each robot is decided by an adversary that schedules robots for execution, and may change between invocations of particular robots). We focus on the minimal number of robots that are necessary and sufficient to solve the problem in general grids.

In more details, we prove that three deterministic robots are necessary and sufficient, provided that the size of the grid is n ×m with 3 ≤ n ≤ m or n = 2 and m ≥ 4. Perhaps surprisingly, and unlike results for the exploration with stop problem (where grids are “easier” to explore and stop than rings with respect to the number of robots), exclusive perpetual exploration requires as many robots in the ring as in the grid.

Furthermore, we propose a classification of configurations such that the space of configurations to be checked is drastically reduced. This pre-processing lays the bases for the automated verification of our algorithm for general grids as it permits to avoid combinatorial explosion.

Keywords

Mobile Robot General Grid Grid Graph Robot Position Circular Permutation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • François Bonnet
    • 1
  • Alessia Milani
    • 2
  • Maria Potop-Butucaru
    • 3
  • Sébastien Tixeuil
    • 3
  1. 1.JAISTSchool of Information ScienceJapan
  2. 2.LaBRIUniversité de Bordeaux 1France
  3. 3.LIP6UPMC Sorbone UniversitésFrance

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