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Certified Gathering of Oblivious Mobile Robots: Survey of Recent Results and Open Problems

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Critical Systems: Formal Methods and Automated Verification (AVoCS 2017, FMICS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10471))

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Abstract

Swarms of mobile robots have recently attracted the focus of the Distributed Computing community. One of the fundamental problems in this context is that of gathering the robots: the robots must meet at a common location, not known beforehand. Despite its apparent simplicity, this problem proved quite hard to characterise fully, due to many model variants, leading to informal error-prone reasoning.

Over the past few years, a significant effort has resulted in the set up of a formal framework, relying on the Coq proof assistant, that was used to provide certified results related to the gathering problem. We survey the main abstractions that permit to reason about oblivious mobile robots that evolve in a bidimensional Euclidean space, the distributed executions they can perform, and the variants of the gathering problem they can solve, while certifying all obtained results. We also describe the remaining steps to obtain a certified full characterisation of the problem.

This work was partially funded by the CNRS PEPS OCAAA 2017 project CYBORG and the Université Claude Bernard Lyon 1 BQR 2017 project PREFER.

The original version of this chapter was revised. The author corrections were updated. The erratum to this chapter is available at https://doi.org/10.1007/978-3-319-67113-0_15

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Notes

  1. 1.

    http://pactole.lri.fr.

  2. 2.

    http://coq.inria.fr.

  3. 3.

    A demon is k -fair when any robot is activated within k consecutive activations of any other robot.

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Author information

Authors and Affiliations

  1. CÉDRIC, Conservatoire National des Arts et Métiers, Paris, France

    Pierre Courtieu

  2. Yale University, New Haven, USA

    Lionel Rieg

  3. Université de Lyon, Université Claude Bernard Lyon 1, CNRS, LIRIS UMR 5205, Lyon, France

    Xavier Urbain

  4. UPMC Sorbonne Universités, LIP6-CNRS 7606, Paris, France

    Sébastien Tixeuil

  5. Institut Universitaire de France, Paris, France

    Sébastien Tixeuil

  6. Université Paris-Sud, LRI, CNRS UMR 8623, Université Paris-Saclay, Paris, France

    Thibaut Balabonski

Authors
  1. Thibaut Balabonski
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  2. Pierre Courtieu
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  3. Lionel Rieg
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  4. Sébastien Tixeuil
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  5. Xavier Urbain
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Corresponding author

Correspondence to Xavier Urbain .

Editor information

Editors and Affiliations

  1. Paris 13 University, Villetaneuse, France

    Laure Petrucci

  2. Mälardalen University, Västerås, Sweden

    Cristina Seceleanu

  3. University of York, York, United Kingdom

    Ana Cavalcanti

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Balabonski, T., Courtieu, P., Rieg, L., Tixeuil, S., Urbain, X. (2017). Certified Gathering of Oblivious Mobile Robots: Survey of Recent Results and Open Problems. In: Petrucci, L., Seceleanu, C., Cavalcanti, A. (eds) Critical Systems: Formal Methods and Automated Verification. AVoCS FMICS 2017 2017. Lecture Notes in Computer Science(), vol 10471. Springer, Cham. https://doi.org/10.1007/978-3-319-67113-0_11

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  • DOI: https://doi.org/10.1007/978-3-319-67113-0_11

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