Synchronous Gathering without Multiplicity Detection: a Certified Algorithm

In mobile robotic swarms, the gathering problem consists in coordinating all the robots so that in finite time they occupy the same location, not known beforehand. Multiplicity detection refers to the ability to detect that more than one robot can occupy a given position. When the robotic swarm operates synchronously, a well-known result by Cohen and Peleg permits to achieve gathering, provided robots are capable of multiplicity detection. We present a new algorithm for synchronous gathering, that does not assume that robots are capable of multiplicity detection, nor make any other extra assumption. Unlike previous approaches, the correctness of our proof is certified in the model where the protocol is defined, using the Coq proof assistant.

[1]  Sébastien Tixeuil,et al.  Certified Universal Gathering in $R^2$ for Oblivious Mobile Robots , 2016, ArXiv.

[2]  Sébastien Tixeuil,et al.  A Foundational Framework for Certified Impossibility Results with Mobile Robots on Graphs , 2018, ICDCN.

[3]  Pascal Raymond,et al.  Optimal Grid Exploration by Asynchronous Oblivious Robots , 2011, SSS.

[4]  Sébastien Tixeuil,et al.  Formal Methods for Mobile Robots: Current Results and Open Problems , 2015 .

[5]  Xavier Défago,et al.  Discovering and Assessing Fine-Grained Metrics in Robot Networks Protocols , 2012, 2014 IEEE 33rd International Symposium on Reliable Distributed Systems Workshops.

[6]  Maria Gradinariu Potop-Butucaru,et al.  Formal verification of mobile robot protocols , 2016, Distributed Computing.

[7]  Sébastien Tixeuil,et al.  Certified Universal Gathering in \mathbb R ^2 for Oblivious Mobile Robots , 2016, DISC.

[8]  Giuseppe Prencipe,et al.  Impossibility of gathering by a set of autonomous mobile robots , 2007, Theor. Comput. Sci..

[9]  Thierry Coquand,et al.  Inductively defined types , 1988, Conference on Computer Logic.

[10]  Pierre Castéran,et al.  Interactive Theorem Proving and Program Development , 2004, Texts in Theoretical Computer Science An EATCS Series.

[11]  Reuven Cohen,et al.  Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems , 2005, SIAM J. Comput..

[12]  Pierre Courtieu,et al.  Erratum to: Certified Gathering of Oblivious Mobile Robots: Survey of Recent Results and Open Problems , 2017 .

[13]  Yves Bertot,et al.  Interactive Theorem Proving and Program Development: Coq'Art The Calculus of Inductive Constructions , 2010 .

[14]  Masafumi Yamashita,et al.  Distributed Anonymous Mobile Robots: Formation of Geometric Patterns , 1999, SIAM J. Comput..

[15]  Sébastien Tixeuil,et al.  Brief Announcement: Certified Universal Gathering in R2 for Oblivious Mobile Robots , 2016, PODC.

[16]  Sébastien Tixeuil,et al.  Certified Gathering of Oblivious Mobile Robots: Survey of Recent Results and Open Problems , 2017, FMICS-AVoCS.

[17]  Stéphane Devismes,et al.  A Framework for Certified Self-Stabilization , 2016, Log. Methods Comput. Sci..

[18]  Pierre Castéran,et al.  Tasks, Types and Tactics for Local Computation Systems , 2011, Stud. Inform. Univ..

[19]  Reuven Cohen,et al.  Robot Convergence via Center-of-Gravity Algorithms , 2004, SIROCCO.

[20]  Sébastien Tixeuil,et al.  Impossibility of gathering, a certification , 2015, Inf. Process. Lett..

[21]  Maria Gradinariu Potop-Butucaru,et al.  On the Synthesis of Mobile Robots Algorithms: The Case of Ring Gathering , 2014, SSS.

[22]  D. Sangiorgi.  Introduction to Bisimulation and Coinduction , 2011 .

[23]  Aniello Murano,et al.  Verification of Asynchronous Mobile-Robots in Partially-Known Environments , 2015, PRIMA.

[24]  Ha Thi Thu Doan,et al.  Model Checking of Robot Gathering , 2017, OPODIS.

[25]  Nicola Santoro,et al.  Distributed Computing by Oblivious Mobile Robots , 2012, Synthesis Lectures on Distributed Computing Theory.

[26]  Sébastien Tixeuil,et al.  Certified Impossibility Results for Byzantine-Tolerant Mobile Robots , 2013, SSS.