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A Continuous Strategy for Collisionless Gathering

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Algorithms for Sensor Systems (ALGOSENSORS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 10718))

Abstract

We consider continuous strategies for swarms of robots in the Euclidean plane. In such a strategy, each robot continuously observes its local neighborhood, and continuously adapts speed and direction following a local rule. We present two main results. The first defines a class of strategies, the contracting strategies, that perform gathering in time O(nd), where d is a diameter of the initial configuration. Several well-known strategies belong to this class. Our second result is about collisions in such strategies. We present a contracting strategy which ensures that no collisions occur. This strategy needs the robots to have some additional capabilities.

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901) and the International Graduate School “Dynamic Intelligent Systems”.

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References

  1. Abshoff, S., Cord-Landwehr, A., Fischer, M., Jung, D., Meyer auf der Heide, F.: Gathering a closed chain of robots on a grid. In: Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS), pp. 689–699. IEEE, May 2016

    Google Scholar 

  2. Agathangelou, C., Georgiou, C., Mavronicolas, M.: A distributed algorithm for gathering many fat mobile robots in the plane. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013. ACM, New York, pp. 250–259 (2013)

    Google Scholar 

  3. Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: Proceedings of the 1995 IEEE International Symposium on Intelligent Control, 1995, pp. 453–460 (1995)

    Google Scholar 

  4. Chrystal, G.: On the problem to construct the minimum circle enclosing n given points in a plane. In: Proceedings of the Edinburgh Mathematical Society, Third Meeting, pp. 30–35 (1885)

    Google Scholar 

  5. Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 228–239. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30140-0_22

    Chapter  Google Scholar 

  6. Cord-Landwehr, A., Fischer, M., Jung, D., Meyer auf der Heide, F.: Asymptotically optimal gathering on a grid. In: Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 301–312. ACM, July 2016

    Google Scholar 

  7. Czyzowicz, J., Gąsieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 350–364. Springer, Heidelberg (2006). https://doi.org/10.1007/11945529_25

    Chapter  Google Scholar 

  8. Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: The power of lights: synchronizing asynchronous robots using visible bits. In: 2012 IEEE 32nd International Conference on Distributed Computing Systems, Macau, China, June 18–21, pp. 506–515 (2012)

    Google Scholar 

  9. Degener, B., Kempkes, B., Meyer auf der Heide, F.: A local O(n2) gathering algorithm. In: Proceedings of the 22nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2010, pp. 217–223. ACM, New York (2010)

    Google Scholar 

  10. 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: Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2011. ACM, New York, pp. 139–148 (2011)

    Google Scholar 

  11. Fischer, M., Jung, D., Meyer auf der Heide, F.: Gathering anonymous, oblivious robots on a grid. CoRR, abs/1702.03400 (2017)

    Google Scholar 

  12. Flocchini, P.: Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory, no. 10. Morgan and Claypool, San Rafael (2012)

    Google Scholar 

  13. Gabriel, R.K., Sokal, R.R.: A new statistical approach to geographic variation analysis. Syst. Biol. 18(3), 259–278 (1969)

    Google Scholar 

  14. 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 

  15. Kempkes, B., Kling, P., Meyer auf der Heide, F.: Optimal and competitive runtime bounds for continuous, local gathering of mobile robots. In: Proceedinbgs of the 24th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2012. ACM, New York, pp. 18–26 (2012)

    Google Scholar 

  16. Li, S., Markarian, C., Meyer auf der Heide, F., Podlipyan, P.: A continuous strategy for collisionless gathering. Full version, March 2017. https://www.hni.uni-paderborn.de/pub/9531

  17. 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 

  18. Lukovszki, T., Meyer auf der Heide, F.: Fast collisionless pattern formation by anonymous, position-aware robots. In: Aguilera, M.K., Querzoni, L., Shapiro, M. (eds.) OPODIS 2014. LNCS, vol. 8878, pp. 248–262. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-14472-6_17

    Google Scholar 

  19. Megiddo, N.: Linear-time algorithms for linear programming in \(\mathbb{R}^3\) and related problems. SIAM J. Comput. 12(4), 759–776 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pagli, L., Prencipe, G., Viglietta, G.: Getting close without touching. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 315–326. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31104-8_27

    Chapter  Google Scholar 

  21. Singer, I.: Abstract Convex Analysis. Wiley, Hoboken (1997)

    MATH  Google Scholar 

  22. Toussaint, G.T.: The relative neighbourhood graph of a finite planar set. Pattern Recogn. 12, 261–268 (1980)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Heinz Nixdorf Institute, Paderborn University, Fürstenallee 11, 33102, Paderborn, Germany

    Shouwei Li, Christine Markarian, Friedhelm Meyer auf der Heide & Pavel Podlipyan

Authors
  1. Shouwei Li
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  2. Christine Markarian
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  3. Friedhelm Meyer auf der Heide
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  4. Pavel Podlipyan
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Corresponding author

Correspondence to Pavel Podlipyan .

Editor information

Editors and Affiliations

  1. IMDEA Networks Institute, Leganés, Spain

    Antonio Fernández Anta

  2. University of Wrocław, Wroclaw, Poland

    Tomasz Jurdzinski

  3. Pace University, New York, USA

    Miguel A. Mosteiro

  4. Rutgers University, North Brunswick, New Jersey, USA

    Yanyong Zhang

A Appendix

A Appendix

1.1 A.1 Safe-Go-To-The-Relative-Center algorithm

figure a

1.2 A.2 Go-To-The-Relative-Center algorithm

figure b

1.3 A.3 Figures

Fig. 1.
figure 1

Lenses of the Relative neighborhood graph

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Fig. 2.
figure 2

The construction of target arc \(A \subset D\).

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Fig. 3.
figure 3

Robot r in the safe state moves towards target point M(r) the mid point of the target arc \(A \subset D\). Black arcs \(C_1\), \(C_2\) are the parts of according RNG lenses.

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Fig. 4.
figure 4

Robots w with RNG lenses that correspond to RNG edges \(\{w, m_1\}\) and \( \{w, m_2 \} \). Both robots are inside of the circle B with the center at the crash point p(w) and radius . If robot r performs safe move, then the target point during the safe move belongs to the circle D.

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Li, S., Markarian, C., Meyer auf der Heide, F., Podlipyan, P. (2017). A Continuous Strategy for Collisionless Gathering. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M., Zhang, Y. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2017. Lecture Notes in Computer Science(), vol 10718. Springer, Cham. https://doi.org/10.1007/978-3-319-72751-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-72751-6_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72750-9

  • Online ISBN: 978-3-319-72751-6

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