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Continuous vs. Discrete Asynchronous Moves: A Certified Approach for Mobile Robots

  • Thibaut Balabonski
  • Pierre Courtieu
  • Robin Pelle
  • Lionel Rieg
  • Sébastien Tixeuil
  • Xavier UrbainEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11704)

Abstract

Oblivious Mobile Robots have been studied both in continuous Euclidean spaces, and discrete spaces (that is, graphs). However the obtained literature forms distinct sets of results for the two settings. In our view, the continuous model reflects well the physicality of robots operating in some real environment, while the discrete model reflects well the digital nature of autonomous robots, whose sensors and computing capabilities are inherently finite.

We explore the possibility of bridging results between the two models. Our approach is certified using the Coq proof assistant and the Pactole framework, which we extend to the most general asynchronous model without compromising its genericity. Our extended framework is then used to formally prove the equivalence between atomic moves in a discrete space (the classical “robots on graphs” model) and non-atomic moves in a continuous unidimensional space when robot vision sensors are discrete (robots move in straigth lines between positions, but their observations are at source and destination positions only), irrespective of the problem being solved. Our effort consolidates the integration between the model, the problem specification, and its proof that is advocated by the Pactole framework.

Keywords

Formal proof Proof assistant Coq Mobile autonomous robots Distributed algorithms 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Thibaut Balabonski
    • 1
  • Pierre Courtieu
    • 2
  • Robin Pelle
    • 1
  • Lionel Rieg
    • 3
  • Sébastien Tixeuil
    • 4
  • Xavier Urbain
    • 5
    Email author
  1. 1.LRI, CNRS UMR 8623, Université Paris-Sud, Université Paris-SaclayOrsayFrance
  2. 2.CÉDRIC – Conservatoire national des arts et métiersParisFrance
  3. 3.Université Grenoble Alpes, Grenoble INP, VERIMAGSaint Martin d’HèresFrance
  4. 4.Sorbonne Université, CNRS, LIP6ParisFrance
  5. 5.Université Claude Bernard Lyon-1, LIRIS CNRS UMR 5205, Université de LyonLyonFrance

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