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 oper...
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| Vydáno v: | Theory of computing systems Ročník 63; číslo 2; s. 200 - 218 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Springer US
01.02.2019
Springer Nature B.V Springer Verlag |
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| ISSN: | 1432-4350, 1433-0490 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Tixeuil, Sébastien Rieg, Lionel Balabonski, Thibaut Urbain, Xavier Delga, Amélie |
| Author_xml | – sequence: 1 givenname: Thibaut surname: Balabonski fullname: Balabonski, Thibaut organization: LRI, Université Paris-Sud, CNRS, Université Paris-Saclay – sequence: 2 givenname: Amélie surname: Delga fullname: Delga, Amélie organization: École Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise (ENSIIE), UPMC Sorbonne Universités – sequence: 3 givenname: Lionel surname: Rieg fullname: Rieg, Lionel organization: Collège de France, Yale University – sequence: 4 givenname: Sébastien orcidid: 0000-0002-0948-7172 surname: Tixeuil fullname: Tixeuil, Sébastien email: Sebastien.Tixeuil@lip6.fr organization: UPMC Sorbonne Universités, Institut Universitaire de France – sequence: 5 givenname: Xavier surname: Urbain fullname: Urbain, Xavier organization: Université Claude Bernard Lyon-1, LIRIS CNRS UMR 5205, Université de Lyon |
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| Cites_doi | 10.1145/3154273.3154321 10.1007/978-3-319-11764-5_17 10.1016/j.tcs.2007.04.023 10.1007/978-3-319-25524-8_12 10.1007/978-3-319-03089-0_13 10.1007/978-3-319-67113-0_15 10.1007/3-540-52335-9_47 10.23919/FMCAD.2017.8102262 10.2200/S00440ED1V01Y201208DCT010 10.1137/S009753979628292X 10.1007/s00446-016-0271-1 10.1007/978-3-662-07964-5 10.1007/978-3-662-53426-7_14 10.1016/j.ipl.2014.11.001 10.1007/978-3-540-27796-5_8 10.1017/CBO9780511777110 10.1007/978-3-642-33536-5_7 10.1137/S0097539704446475 10.1007/978-3-319-39570-8_3 10.1109/SRDSW.2014.34 |
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| Keywords | Proof assistant Gathering Mobile robots Certification Multiplicity detection |
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| References | Balabonski, T., Pelle, R., Rieg, L., Tixeuil, S.: A foundational framework for certified impossibility results with mobile robots on graphs. In: Proceedings of International Conference on Distributed Computing and Networking. Varanasi (2018) Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge University Press (2012) Altisen, K., Corbineau, P., Devismes, S.: A framework for certified self-stabilization. In: Albert, E, Lanese, I (eds.) Formal Techniques for Distributed Objects, Components, and Systems - 36th IFIP WG 6.1 International Conference, FORTE 2016, Held as Part of the 11th International Federated Conference on Distributed Computing Techniques, DisCoTec 2016, Heraklion, Crete, Greece, June 6-9, 2016, Proceedings, volume 9688 of Lecture Notes in Computer Science, pp. 36–51. Springer (2016) Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers (2012) SuzukiIYamashitaMDistributed Anonymous Mobile Robots: Formation of Geometric PatternsSIAM J. Comput.199928413471363168101010.1137/S009753979628292X0940.68145 Rubin, S., Zuleger, F., Murano, A., Aminof, B.: Verification of asynchronous mobile-robots in partially-known environments. In: Chen, Q., Torroni, P., Villata, S., Hsu, J.Y.-j., Omicini, A. (eds.) PRIMA 2015: Principles and Practice of Multi-Agent Systems - 18th International Conference, Bertinoro, Italy, October 26-30, 2015, Proceedings, volume 9387 of Lecture Notes in Computer Science, pp. 185–200. Springer (2015) Coquand, T., Paulin-Mohring, C.: Inductively defined types. In: Martin-Löf, P, Mints, G (eds.) International Conference on Computer Logic (Colog’88), volume 417 of Lecture Notes in Computer Science, pp. 50–66. Springer (1990) BérardBLafourcadePMilletLPotop-ButucaruMThierry-MiegYTixeuilSFormal verification of mobile robot protocolsDistrib. Comput.2016296459487357332010.1007/s00446-016-0271-106734694 Millet, L., Potop-Butucaru, M., Sznajder, N., Tixeuil, S.: On the synthesis of mobile robots algorithms: The case of ring gathering. In: Felber, P., Garg, V.K. (eds.) Stabilization, Safety, and Security of Distributed Systems - 16th International Symposium, (SSS 2014), volume 8756 of Lecture Notes in Computer Science, pp. 237–251. Springer, Paderborn (2014) CastėranPFilouVTasks, types and tactics for local computation systemsStudia Informatica Universalis2011913986 Auger, C., Bouzid, Z., Courtieu, P., Tixeuil, S., Urbain, X.: Certified impossibility results for byzantine-tolerant mobile robots. In: Higashino, T, Katayama, Y, Masuzawa, T, Potop-Butucaru, M, Yamashita, M (eds.) Stabilization, Safety, and Security of Distributed Systems - 15th International Symposium (SSS 2013), volume 8255 of Lecture Notes in Computer Science, pp. 178–186. Springer, Osaka (2013) Bonnet, F., Dėfago, X., Petit, F., Potop-Butucaru, M., Tixeuil, S.: Discovering and assessing fine-grained metrics in robot networks protocols. In: 33rd IEEE International Symposium on Reliable Distributed Systems Workshops, SRDS Workshops 2014, pp. 50–59. IEEE, Nara (2014) Bertot, Y., Castéran, P.: Interactive theorem proving and program development. Coq’Art: The calculus of inductive constructions. Texts in Theoretical Computer Science. Springer (2004) Courtieu, P., Rieg, L., Tixeuil, S., Urbain, X.: Certified universal gathering algorithm in ℝ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {R}^{2}$\end{document} for oblivious mobile robots. In: Gavoille, C, Ilcinkas, D (eds.) Distributed Computing - 30th International Symposium, (DISC 2016), volume 9888 of Lecture Notes in Computer Science. Springer, Paris (2016) CohenRPelegDConvergence properties of the gravitational algorithm in asynchronous robot systemsSIAM J. Comput.200534615161528216575310.1137/S00975397044464751081.68110 Cohen, R., Peleg, D.: Robot convergence via center-of-gravity algorithms. In: Kralovic, R, Sýkora, O (eds.) Structural Information and Communication Complexity - 11th International Colloquium (SIROCCO 2004), volume 3104 of Lecture Notes in Computer Science, pp. 79–88. Springer, Smolenice Castle (2004) Devismes, S., Lamani, A., Petit, F., Raymond, P., Tixeuil, S.: Optimal Grid Exploration by Asynchronous Oblivious Robots. In: Richa, A W, Scheideler, C (eds.) Stabilization, Safety, and Security of Distributed Systems - 14th International Symposium (SSS 2012), volume 7596 of Lecture Notes in Computer Science, pp. 64–76. Springer, Toronto (2012) Balabonski, T., Courtieu, P., Rieg, L., Tixeuil, S., Urbain, X.: 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 - Joint 22nd International Workshop on Formal Methods for Industrial Critical Systems - and - 17th International Workshop on Automated Verification of Critical Systems, (FMICS-AVoCS 2017), volume 10471 of Lecture Notes in Computer Science, pp. 165–181. Springer, Turin (2017) BérardBCourtieuPMilletLPotop-ButucaruMRiegLSznajderNTixeuilSUrbainXFormal methods for mobile robots: Current results and open problemsInt. J. Inf. Soc.201573101114Invited Paper Doan, HTT., Bonnet, F., Ogata, K.: Model checking of robot gathering. In: Aspnes, J., Felber, P. (eds.) Principles of Distributed Systems - 21th International Conference (OPODIS 2017), Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Lisbon (2017) PrencipeGImpossibility of gathering by a set of autonomous mobile robotsTheor. Comput. Sci.20073842-3222231235330310.1016/j.tcs.2007.04.0231125.68124 Sangnier, A., Sznajder, N., Potop-Butucaru, M., Tixeuil, S.: Parameterized verification of algorithms for oblivious robots on a ring. In: Formal Methods in Computer Aided Design. Vienna (2017) CourtieuPRiegLTixeuilSUrbainXImpossibility of gathering, a certificationInf. Process. Lett.2015115447452329042110.1016/j.ipl.2014.11.0011317.68264 B Bérard (9828_CR5) 2016; 29 P Castėran (9828_CR9) 2011; 9 R Cohen (9828_CR11) 2005; 34 9828_CR18 9828_CR17 9828_CR16 B Bérard (9828_CR8) 2015; 7 9828_CR15 9828_CR14 I Suzuki (9828_CR23) 1999; 28 9828_CR12 G Prencipe (9828_CR19) 2007; 384 9828_CR22 9828_CR10 9828_CR21 9828_CR4 9828_CR20 9828_CR3 9828_CR2 9828_CR1 P Courtieu (9828_CR13) 2015; 115 9828_CR7 9828_CR6 |
| References_xml | – reference: Coquand, T., Paulin-Mohring, C.: Inductively defined types. In: Martin-Löf, P, Mints, G (eds.) International Conference on Computer Logic (Colog’88), volume 417 of Lecture Notes in Computer Science, pp. 50–66. Springer (1990) – reference: Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers (2012) – reference: Balabonski, T., Courtieu, P., Rieg, L., Tixeuil, S., Urbain, X.: 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 - Joint 22nd International Workshop on Formal Methods for Industrial Critical Systems - and - 17th International Workshop on Automated Verification of Critical Systems, (FMICS-AVoCS 2017), volume 10471 of Lecture Notes in Computer Science, pp. 165–181. Springer, Turin (2017) – reference: SuzukiIYamashitaMDistributed Anonymous Mobile Robots: Formation of Geometric PatternsSIAM J. Comput.199928413471363168101010.1137/S009753979628292X0940.68145 – reference: Bertot, Y., Castéran, P.: Interactive theorem proving and program development. Coq’Art: The calculus of inductive constructions. Texts in Theoretical Computer Science. Springer (2004) – reference: Courtieu, P., Rieg, L., Tixeuil, S., Urbain, X.: Certified universal gathering algorithm in ℝ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {R}^{2}$\end{document} for oblivious mobile robots. In: Gavoille, C, Ilcinkas, D (eds.) Distributed Computing - 30th International Symposium, (DISC 2016), volume 9888 of Lecture Notes in Computer Science. Springer, Paris (2016) – reference: Balabonski, T., Pelle, R., Rieg, L., Tixeuil, S.: A foundational framework for certified impossibility results with mobile robots on graphs. In: Proceedings of International Conference on Distributed Computing and Networking. Varanasi (2018) – reference: CohenRPelegDConvergence properties of the gravitational algorithm in asynchronous robot systemsSIAM J. Comput.200534615161528216575310.1137/S00975397044464751081.68110 – reference: PrencipeGImpossibility of gathering by a set of autonomous mobile robotsTheor. Comput. Sci.20073842-3222231235330310.1016/j.tcs.2007.04.0231125.68124 – reference: CastėranPFilouVTasks, types and tactics for local computation systemsStudia Informatica Universalis2011913986 – reference: Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge University Press (2012) – reference: Auger, C., Bouzid, Z., Courtieu, P., Tixeuil, S., Urbain, X.: Certified impossibility results for byzantine-tolerant mobile robots. In: Higashino, T, Katayama, Y, Masuzawa, T, Potop-Butucaru, M, Yamashita, M (eds.) Stabilization, Safety, and Security of Distributed Systems - 15th International Symposium (SSS 2013), volume 8255 of Lecture Notes in Computer Science, pp. 178–186. Springer, Osaka (2013) – reference: Sangnier, A., Sznajder, N., Potop-Butucaru, M., Tixeuil, S.: Parameterized verification of algorithms for oblivious robots on a ring. In: Formal Methods in Computer Aided Design. Vienna (2017) – reference: Cohen, R., Peleg, D.: Robot convergence via center-of-gravity algorithms. In: Kralovic, R, Sýkora, O (eds.) Structural Information and Communication Complexity - 11th International Colloquium (SIROCCO 2004), volume 3104 of Lecture Notes in Computer Science, pp. 79–88. Springer, Smolenice Castle (2004) – reference: CourtieuPRiegLTixeuilSUrbainXImpossibility of gathering, a certificationInf. Process. 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