Consensus reaching in swarms ruled by a hybrid metric-topological distance

Regular Article

Abstract

Recent empirical observations of three-dimensional bird flocks and human crowds have challenged the long-prevailing assumption that a metric interaction distance rules swarming behaviors. In some cases, individual agents are found to be engaged in local information exchanges with a fixed number of neighbors, i.e. a topological interaction. However, complex system dynamics based on pure metric or pure topological distances both face physical inconsistencies in low and high density situations. Here, we propose a hybrid metric-topological interaction distance overcoming these issues and enabling a real-life implementation in artificial robotic swarms. We use network- and graph-theoretic approaches combined with a dynamical model of locally interacting self-propelled particles to study the consensus reaching process for a swarm ruled by this hybrid interaction distance. Specifically, we establish exactly the probability of reaching consensus in the absence of noise. In addition, simulations of swarms of self-propelled particles are carried out to assess the influence of the hybrid distance and noise.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    S. Camazine, J.-L. Deneubourg, N.R. Franks, J. Sneyd, G. Theraulaz, E. Bonabeau, Self-Organization in Biological Systems (Princeton University Press, Princeton, 2001)Google Scholar
  2. 2.
    T. Vicsek, A. Zafeiris, Phys. Rep. 517, 71 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    R. Bouffanais, D.K.P. Yue, Phys. Rev. E 81, 041920 (2010) ADSCrossRefGoogle Scholar
  4. 4.
    D.J.T. Sumpter, Phil. Trans. R. Soc. B 361, 5 (2006)CrossRefGoogle Scholar
  5. 5.
    D.J.T. Sumpter, Collective Animal Behavior (Princeton University Press, Princeton, 2010)Google Scholar
  6. 6.
    M.A. Hsieh, V. Kumar, L. Chaimowicz, Robotica 26, 691 (2008)CrossRefGoogle Scholar
  7. 7.
    K. Naruse, in Intelligent Autonomous Systems, edited by S. Lee, H.S. Cho, K.J. Yoon, J.M. Lee (Advances in Intelligent Systems and Computing, 2013), Vol. 12, pp. 843–851Google Scholar
  8. 8.
    C.K. Hemelrijk, H. Hildenbrandt, Ethology 114, 245 (2008) CrossRefGoogle Scholar
  9. 9.
    C.K. Hemelrijk, H. Hildenbrandt, Interface Focus 2, 726 (2012)CrossRefGoogle Scholar
  10. 10.
    C.K. Hemelrijk, H. Hildenbrandt, PLoS One 6, e22479 (2011) ADSCrossRefGoogle Scholar
  11. 11.
    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, V. Zdravkovic, Proc. Natl. Acad. Sci. USA 105, 1232 (2008) ADSCrossRefGoogle Scholar
  12. 12.
    F. Ginelli, H. Chaté, Phys. Rev. Lett. 105, 168103 (2010) ADSCrossRefGoogle Scholar
  13. 13.
    M. Moussaïd, D. Helbing, G. Theraulaz, Proc. Natl. Acad. Sci. USA 108, 6884 (2011) ADSCrossRefGoogle Scholar
  14. 14.
    S. Coombs, J.C. Montgomery, in Comparative Hearing: Fish and Amphibians, edited by R.R. Fay, A.N. Popper (Springer Handbook of Auditory Research, Springer-Verlag, New York, 1999), pp. 319–362 Google Scholar
  15. 15.
    R. Bouffanais, G.D. Weymouth, D.K.P. Yue, Proc. R. Soc. A 467, 19 (2011)ADSCrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    D.B. Dusenbery, Sensory Ecology: How organisms acquire and respond to information (W.H. Freeman, Co., New York, 1992)Google Scholar
  17. 17.
    J. Emmerton, J. Delius, Vision, Brain, in Beyond Sensation: Visual Cognition in Pigeons, edited by H. Zeigler, H.J. Bischof (MIT Press, Cambridge, 1993), pp. 377–390Google Scholar
  18. 18.
    T. Niizato, Y.-P. Gunji, Ecol. Model. 222, 3041 (2011) CrossRefGoogle Scholar
  19. 19.
    L. Barberis, E.V. Albano, Phys. Rev. E 89, 012139 (2014) ADSCrossRefGoogle Scholar
  20. 20.
    H.G. Tanner, A. Jadbabaie, J.P. Pappas, in Proc. of the 42nd IEEE Conference on Decision and Control, IEEE, Maui, Hawaii USA, 2003, pp. 2010–2015Google Scholar
  21. 21.
    H.G. Tanner, A. Jadbabaie, J.P. Pappas, IEEE Trans. Automat. Control 52, 863 (2007)CrossRefMathSciNetGoogle Scholar
  22. 22.
    M. Komareji, R. Bouffanais, PLoS One 8, e82578 (2013) ADSCrossRefGoogle Scholar
  23. 23.
    Y. Shang, R. Bouffanais, Sci. Rep. 4, 4184 (2014)ADSGoogle Scholar
  24. 24.
    P. Miller, The Smart Swarm (Penguin Group, 2010)Google Scholar
  25. 25.
    M. Aldana, V. Dossetti, C. Huepe, V.M. Kenkre, H. Larralde, Phys. Rev. Lett. 98, 095702 (2007) ADSCrossRefGoogle Scholar
  26. 26.
    R. Olfati-Saber, J.A. Fax, R.M. Murray, Proc. IEEE 95, 215 (2007)CrossRefGoogle Scholar
  27. 27.
    D. Eppstein, M.S. Paterson, F.F. Yao, Discrete Computational Geometry 17, 263 (1997)CrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    P. Balister, B. Bollobás, A. Sarkar, M. Walters, Adv. Appl. Probab. 37, 1 (2005)CrossRefMATHGoogle Scholar
  29. 29.
    P. Balister, B. Bollobás, A. Sarkar, M. Walters, Adv. Appl. Probab. 41, 1 (2009)CrossRefMATHGoogle Scholar
  30. 30.
    W. Ren, R.W. Beard, IEEE Trans. Autom. Control 50, 655 (2005)CrossRefMathSciNetGoogle Scholar
  31. 31.
    H. Chaté, F. Ginelli, G. Grégoire, F. Peruani, F. Raynaud, Eur. Phys. J. B 64, 451 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    G. Grégoire, H. Chaté, Y.H. Tu, Physica D 181, 157 (2003) ADSCrossRefMATHMathSciNetGoogle Scholar
  33. 33.
    G. Grégoire, H. Chaté, Phys. Rev. Lett. 92, 025702 (2004) ADSCrossRefGoogle Scholar
  34. 34.
    I. Matei, J. Baras, C. Somarakis, SIAM J. Control Optim. 51, 1574 (2013) CrossRefMATHMathSciNetGoogle Scholar
  35. 35.
    I. Matei, N. Martins, J. Baras, in Proc. of the 47th IEEE Conference on Decision and Control, Cancún, Mexico, 2008, pp. 3535–3540Google Scholar
  36. 36.
    M. Huang, S. Dey, G.N. Nair, J.H. Manton, Automotica 46, 1571 (2010) CrossRefMATHMathSciNetGoogle Scholar
  37. 37.
    T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995) ADSCrossRefGoogle Scholar
  38. 38.
    M. Komareji, Y. Shang, R. Bouffanais, arXiv:1409.7207 (2014)Google Scholar
  39. 39.
    D.S. Calovi, U. Lopez, P. Schuhmacher, H. Chaté, C. Sire, G. Theraulaz, arXiv:1409.6430 (2014)Google Scholar
  40. 40.
    A. Attanasi, A. Cavagna, L. Del Castello, I. Giardina, T.S. Grigera, A. Jelić, S. Melillo, L. Parisi, O. Pohl, E. Shen, M. Viale, Nat. Phys. 10, 691 (2014)CrossRefGoogle Scholar
  41. 41.
    H. Chaté, F. Ginelli, G. Grégoire, F. Raynaud, Phys. Rev. E 77, 046113 (2008) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Singapore University of Technology and DesignSingaporeSingapore

Personalised recommendations