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Continuous Protocols for Swarm Robotics

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Distributed Computing by Mobile Entities

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11340))

Abstract

We consider simple models of swarms of identical, anonymous robots: they are points in the plane and “see” only their neighbors (robots within distance one). We will deal with distributed local protocols of such swarms that result in formations like “gathering at one point”. The focus will be on protocols assuming a continuous time model. We present upper and lower bounds on their run time and energy consumption, and compare different protocols both theoretically and experimentally.

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Notes

  1. 1.

    Without loss of generality, we say an angle is positive if it is measured counterclockwise and negative if it is measured clockwise.

  2. 2.

    As in the proof of Theorem 6, we identify vertices with the robots positioned on them.

References

  1. Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: Proceedings of 10th International Symposium on Intelligent Control (ISIC), pp. 453–460, August 1995. https://doi.org/10.1109/ISIC.1995.525098

  2. Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the robots gathering problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1181–1196. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45061-0_90

    Chapter  Google Scholar 

  3. Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34(6), 1516–1528 (2005). https://doi.org/10.1137/S0097539704446475

    Article  MathSciNet  MATH  Google Scholar 

  4. Degener, B., Kempkes, B., Langner, T., Meyer auf der Heide, F., Pietrzyk, P., Wattenhofer, R.: A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In: Rajaraman R., Meyer auf der Heide, F., (eds.) SPAA 2011: Proceedings of the 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures, San Jose, CA, USA, 4–6 June 2011 (Co-located with FCRC 2011), pp. 139–148. ACM (2011). https://doi.org/10.1145/1989493.1989515

  5. Degener, B., Kempkes, B., Kempkes, P., Meyer auf der Heide, F.: Linear and competitive strategies for continuous robot formation problems. TOPC 2(1), 2:1–2:18 (2015). https://doi.org/10.1145/2742341

    Article  Google Scholar 

  6. Dieudonné, Y., Petit, F.: Self-stabilizing deterministic gathering. In: Dolev, S. (ed.) ALGOSENSORS 2009. LNCS, vol. 5804, pp. 230–241. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05434-1_23

    Chapter  Google Scholar 

  7. Gabriel, K.R., Sokal, R.R.: A new statistical approach to geographic variation analysis. Syst. Biol. 18(3), 259–278 (1969). https://doi.org/10.2307/2412323

    Article  Google Scholar 

  8. Gordon, N., Wagner, I.A., Bruckstein, A.M.: Gathering multiple robotic a(ge)nts with limited sensing capabilities. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) ANTS 2004. LNCS, vol. 3172, pp. 142–153. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28646-2_13

    Chapter  Google Scholar 

  9. Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: Gathering autonomous mobile robots with dynamic compasses: an optimal result. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 298–312. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75142-7_24

    Chapter  Google Scholar 

  10. Katayama, Y., Tomida, Y., Imazu, H., Inuzuka, N., Wada, K.: Dynamic compass models and gathering algorithms for autonomous mobile robots. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 274–288. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72951-8_22

    Chapter  MATH  Google Scholar 

  11. Katreniak, B.: Convergence with limited visibility by asynchronous mobile robots. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 125–137. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22212-2_12

    Chapter  Google Scholar 

  12. Li, S., Meyer auf der Heide, F., Podlipyan, P.: The impact of the gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots. In: Chrobak, M., Fernández Anta, A., Gąsieniec, L., Klasing, R. (eds.) ALGOSENSORS 2016. LNCS, vol. 10050, pp. 62–79. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-53058-1_5

    Chapter  Google Scholar 

  13. Li, S., Markarian, C., Meyer auf der Heide, F., Podlipyan, P.: A continuous strategy for collisionless gathering. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 182–197. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72751-6_14

    Chapter  Google Scholar 

  14. Nguyen, H.G., Pezeshkian, N., Raymond, S.M., Gupta, A., Spector, J.M.: Autonomous communication relays for tactical robots. In: Proceedings of the 11th International Conference on Advanced Robotics (ICAR), pp. 35–40 (2003)

    Google Scholar 

  15. Olver, F.W., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions, 1st edn. Cambridge University Press, New York (2010)

    MATH  Google Scholar 

  16. Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384(2–3), 222–231 (2007). https://doi.org/10.1016/j.tcs.2007.04.023

    Article  MathSciNet  MATH  Google Scholar 

  17. Souissi, S., Défago, X., Yamashita, M.: Gathering asynchronous mobile robots with inaccurate compasses. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 333–349. Springer, Heidelberg (2006). https://doi.org/10.1007/11945529_24

    Chapter  Google Scholar 

  18. Watton, A., Kydon, D.W.: Analytical aspects of the \(n\)-bug problem. Am. J. Phys. 37(2), 220–221 (1969). https://doi.org/10.1119/1.1975458

    Article  Google Scholar 

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Authors and Affiliations

  1. Universität Hamburg, Hamburg, Germany

    Peter Kling

  2. University of Paderborn, Paderborn, Germany

    Friedhelm Meyer auf der Heide

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  1. Peter Kling
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  2. Friedhelm Meyer auf der Heide
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Correspondence to Peter Kling .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Pisa, Pisa, Italy

    Giuseppe Prencipe

  3. Carleton University, Ottawa, ON, Canada

    Nicola Santoro

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Kling, P., Meyer auf der Heide, F. (2019). Continuous Protocols for Swarm Robotics. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_13

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  • DOI: https://doi.org/10.1007/978-3-030-11072-7_13

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  • Online ISBN: 978-3-030-11072-7

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