Certified Universal Gathering in \(\mathbb {R} ^2\) for Oblivious Mobile Robots

  • Pierre Courtieu
  • Lionel Rieg
  • Sébastien Tixeuil
  • Xavier UrbainEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9888)


We present a unified formal framework for expressing mobile robots models, protocols, and proofs, and devise a protocol design/proof methodology dedicated to mobile robots that takes advantage of this formal framework.

As a case study, we present the first formally certified protocol for oblivious mobile robots evolving in a two-dimensional Euclidean space. In more details, we provide a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common orientation nor chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the Coq proof assistant.

This result demonstrates both the effectiveness of the approach to obtain new algorithms that use as few assumptions as necessary, and its manageability since the amount of developed code remains human readable.


Mobile Robot Execution Model Proof Assistant Advertise Model Multiplicity Detection 
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 2016

Authors and Affiliations

  • Pierre Courtieu
    • 1
  • Lionel Rieg
    • 2
  • Sébastien Tixeuil
    • 3
  • Xavier Urbain
    • 4
    • 5
    Email author
  1. 1.CÉDRIC – Conservatoire national des arts et métiersParisFrance
  2. 2.Collège de FranceParisFrance
  3. 3.UPMC Sorbonne Universités, LIP6-CNRS 7606, Institut Universitaire de FranceParisFrance
  4. 4.ENSIIEÉvryFrance
  5. 5.LRI, CNRS UMR 8623, Université Paris-Sud, Université Paris-SaclayOrsayFrance

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