Abstract
Recent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and correctness proofs.
This paper is the first to propose a formal framework to automatically design distributed algorithms that are dedicated to autonomous mobile robots evolving in a discrete space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. Our contribution is threefold. First, we propose an encoding of the gathering problem as a reachability game. Then, we automatically generate an optimal distributed algorithm for three robots evolving on a fixed size uniform ring. Finally, we prove by induction that the generated algorithm is also correct for any ring size except when an impossibility result holds (that is, when the number of robots divides the ring size).
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References
Abadi, M., Lamport, L., Wolper, P.: Realizable and unrealizable specifications of reactive systems. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 1–17. Springer, Heidelberg (1989)
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.) SSS 2013. LNCS, vol. 8255, pp. 178–190. Springer, Heidelberg (2013)
Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: UPPAAL-Tiga: Time for playing games! In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 121–125. Springer, Heidelberg (2007)
Bérard, B., Millet, L., Potop-Butucaru, M., Tixeuil, S., Thierry-Mieg, Y.: Vérification formelle et robots mobiles. In: Proc. of Algotel 2013 (2013)
Bonnet, F., Défago, X., Petit, F., Potop-Butucaru, M.G., Tixeuil, S.: Brief announcement: Discovering and assessing fine-grained metrics in robot networks protocols. In: Richa, A.W., Scheideler, C. (eds.) SSS 2012. LNCS, vol. 7596, pp. 282–284. Springer, Heidelberg (2012)
Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc. 138, 295–311 (1969)
Church, A.: Logic, arithmetics, and automata. In: Proc. of Int. Congr. of Mathematicians, pp. 23–35 (1963)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)
D’Angelo, G., Navarra, A., Nisse, N.: Gathering and exclusive searching on rings under minimal assumptions. In: Chatterjee, M., Cao, J.-N., Kothapalli, K., Rajsbaum, S. (eds.) ICDCN 2014. LNCS, vol. 8314, pp. 149–164. Springer, Heidelberg (2014)
D’Angelo, G., Di Stefano, G., Navarra, A.: How to gather asynchronous oblivious robots on anonymous rings. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 326–340. Springer, Heidelberg (2012)
D’Angelo, G., Stefano, G.D., Navarra, A., Nisse, N., Suchan, K.: A unified approach for different tasks on rings in robot-based computing systems. In: IPDPS Workshops, pp. 667–676 (2013)
Devismes, S., Lamani, A., Petit, F., Raymond, P., Tixeuil, S.: Optimal grid exploration by asynchronous oblivious robots. In: Richa, A.W., Scheideler, C. (eds.) SSS 2012. LNCS, vol. 7596, pp. 64–76. Springer, Heidelberg (2012)
Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool Publishers (2012)
Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Mobile robots gathering algorithm with local weak multiplicity in rings. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 101–113. Springer, Heidelberg (2010)
Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Asynchronous mobile robot gathering from symmetric configurations without global multiplicity detection. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 150–161. Springer, Heidelberg (2011)
Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Gathering an even number of robots in an odd ring without global multiplicity detection. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 542–553. Springer, Heidelberg (2012)
Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390(1), 27–39 (2008)
Manna, Z., Wolper, P.: Synthesis of communicating processes from temporal logic specifications. ACM Trans. Program. Lang. Syst. 6(1), 68–93 (1984)
Mazala, R.: Infinite games. In: Grädel, E., Thomas, W., Wilke, T. (eds.) Automata, Logics, and Infinite Games. LNCS, vol. 2500, pp. 23–38. Springer, Heidelberg (2002)
Ooshita, F., Tixeuil, S.: On the self-stabilization of mobile oblivious robots in uniform rings. In: Richa, A.W., Scheideler, C. (eds.) SSS 2012. LNCS, vol. 7596, pp. 49–63. Springer, Heidelberg (2012)
Peterson, G.L., Reif, J.H.: Multiple-person alternation. In: Proc. of FOCS 1979, pp. 348–363. IEEE Computer Society Press (1979)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. of POPL 1989, pp. 179–190. ACM (1989)
Di Stefano, G., Navarra, A.: Optimal gathering of oblivious robots in anonymous graphs. In: Moscibroda, T., Rescigno, A.A. (eds.) SIROCCO 2013. LNCS, vol. 8179, pp. 213–224. Springer, Heidelberg (2013)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal on Computing, 1347–1363 (1999)
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Millet, L., Potop-Butucaru, M., Sznajder, N., Tixeuil, S. (2014). On the Synthesis of Mobile Robots Algorithms: The Case of Ring Gathering. In: Felber, P., Garg, V. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2014. Lecture Notes in Computer Science, vol 8756. Springer, Cham. https://doi.org/10.1007/978-3-319-11764-5_17
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DOI: https://doi.org/10.1007/978-3-319-11764-5_17
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