Towards Swarm Calculus: Universal Properties of Swarm Performance and Collective Decisions

  • Heiko Hamann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7461)

Abstract

The search for generally applicable methods in swarm intelligence aims to gain new insights about natural swarms and to develop design methodologies for artificial swarms. The ideal would be a ‘swarm calculus’ that allows to calculate key features such as expected swarm performance and robustness on the basis of a few parameters. A path towards this ideal is to find methods and models that have maximal generality. We report two models that might be examples of exceptional generality. First, we present an abstract model that describes the performance of a swarm depending on the swarm density based on the dichotomy between cooperation and interference. Second, we give an abstract model for decision making that is inspired by urn models. A parameter, that controls the feedback based on the current consensus, allows to understand the effects of an increasing probability for positive feedback over time in a decision making system.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berman, S., Kumar, V., Nagpal, R.: Design of control policies for spatially inhomogeneous robot swarms with application to commercial pollination. In: IEEE Intern. Conf. on Robotics and Automation (ICRA 2011), pp. 378–385 (2011)Google Scholar
  2. 2.
    Bjerknes, J.D., Winfield, A.: On fault-tolerance and scalability of swarm robotic systems. In: Proc. Distributed Auton. Robotic Syst, DARS 2010 (2010)Google Scholar
  3. 3.
    Bjerknes, J.D., Winfield, A., Melhuish, C.: An analysis of emergent taxis in a wireless connected swarm of mobile robots. In: IEEE Swarm Intelligence Symposium, pp. 45–52. IEEE Press, Los Alamitos (2007)Google Scholar
  4. 4.
    Breder, C.M.: Equations descriptive of fish schools and other animal aggregations. Ecology 35(3), 361–370 (1954)CrossRefGoogle Scholar
  5. 5.
    Camazine, S., Deneubourg, J.L., Franks, N.R., Sneyd, J., Theraulaz, G., Bonabeau, E.: Self-Organizing Biological Systems. Princeton Univ. Press (2001)Google Scholar
  6. 6.
    Edelstein-Keshet, L.: Mathematical models of swarming and social aggregation. Robotica 24(3), 315–324 (2006)CrossRefGoogle Scholar
  7. 7.
    Ehrenfest, P., Ehrenfest, T.: Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem. Physikalische Zeitschrift 8, 311–314 (1907)MATHGoogle Scholar
  8. 8.
    Eigen, M., Winkler, R.: Laws of the game: how the principles of nature govern chance. Princeton University Press (1993)Google Scholar
  9. 9.
    Hamann, H.: Modeling and Investigation of Robot Swarms. Master’s thesis, University of Stuttgart, Germany (2006)Google Scholar
  10. 10.
    Hamann, H.: Space-Time Continuous Models of Swarm Robotics Systems: Supporting Global-to-Local Programming. Springer (2010)Google Scholar
  11. 11.
    Hamann, H., Meyer, B., Schmickl, T., Crailsheim, K.: A Model of Symmetry Breaking in Collective Decision-Making. In: Doncieux, S., Girard, B., Guillot, A., Hallam, J., Meyer, J.-A., Mouret, J.-B. (eds.) SAB 2010. LNCS (LNAI), vol. 6226, pp. 639–648. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Hamann, H., Schmickl, T., Wörn, H., Crailsheim, K.: Analysis of emergent symmetry breaking in collective decision making. Neural Computing & Applications 21(2), 207–218 (2012)CrossRefGoogle Scholar
  13. 13.
    Hamann, H., Wörn, H.: Embodied computation. Parallel Processing Letters 17(3), 287–298 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hamann, H., Wörn, H.: Aggregating Robots Compute: An Adaptive Heuristic for the Euclidean Steiner Tree Problem. In: Asada, M., Hallam, J.C.T., Meyer, J.-A., Tani, J. (eds.) SAB 2008. LNCS (LNAI), vol. 5040, pp. 447–456. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Lerman, K., Galstyan, A.: Mathematical model of foraging in a group of robots: Effect of interference. Autonomous Robots 13, 127–141 (2002)MATHCrossRefGoogle Scholar
  16. 16.
    Lighthill, M.J., Whitham, G.B.: On kinematic waves. II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London A 229(1178), 317–345 (1955)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Mahmassani, H.S., Dong, J., Kim, J., Chen, R.B., Park, B.: Incorporating weather impacts in traffic estimation and prediction systems. Tech. Rep. FHWA-JPO-09-065, U.S. Department of Transportation (September 2009)Google Scholar
  18. 18.
    Milutinovic, D., Lima, P.: Cells and Robots: Modeling and Control of Large-Size Agent Populations. Springer (2007)Google Scholar
  19. 19.
    Miramontes, O.: Order-disorder transitions in the behavior of ant societies. Complexity 1(1), 56–60 (1995)Google Scholar
  20. 20.
    Mondada, F., Bonani, M., Guignard, A., Magnenat, S., Studer, C., Floreano, D.: Superlinear Physical Performances in a SWARM-BOT. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds.) ECAL 2005. LNCS (LNAI), vol. 3630, pp. 282–291. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Nembrini, J., Winfield, A.F.T., Melhuish, C.: Minimalist coherent swarming of wireless networked autonomous mobile robots. In: Hallam, B., et al. (eds.) Proc. of the 7th Intern. Conf. on Simulation of Adaptive Behavior (SAB), pp. 373–382. MIT Press, Cambridge (2002)Google Scholar
  22. 22.
    Okubo, A.: Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds. Advances in Biophysics 22, 1–94 (1986)CrossRefGoogle Scholar
  23. 23.
    Okubo, A., Levin, S.A.: Diffusion and Ecological Problems: Modern Perspectives. Springer, Berlin (2001)CrossRefGoogle Scholar
  24. 24.
    Prorok, A., Correll, N., Martinoli, A.: Multi-level spatial models for swarm-robotic systems. The International Journal of Robotics Research 30(5), 574–589 (2011)CrossRefGoogle Scholar
  25. 25.
    Schmickl, T., Hamann, H.: BEECLUST: A swarm algorithm derived from honeybees. In: Xiao, Y. (ed.) Bio-inspired Computing and Communication Networks. CRC Press (March 2011)Google Scholar
  26. 26.
    Strogatz, S.H.: Exploring complex networks. Nature 410(6825), 268–276 (2001)CrossRefGoogle Scholar
  27. 27.
    Vicsek, T., Zafiris, A.: Collective motion. arXiv:1010.5017v1 (2010)Google Scholar
  28. 28.
    Yates, C.A., Erban, R., Escudero, C., Couzin, I.D., Buhl, J., Kevrekidis, I.G., Maini, P.K., Sumpter, D.J.T.: Inherent noise can facilitate coherence in collective swarm motion. PNAS 106(14), 5464–5469 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Heiko Hamann
    • 1
  1. 1.Artificial Life Laboratory of the Department of ZoologyKarl-Franzens University GrazAustria

Personalised recommendations