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.
Keywords
- Positive Feedback
- Collective Decision
- Pitchfork Bifurcation
- Swarm Size
- Interference Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
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)
Bjerknes, J.D., Winfield, A.: On fault-tolerance and scalability of swarm robotic systems. In: Proc. Distributed Auton. Robotic Syst, DARS 2010 (2010)
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)
Breder, C.M.: Equations descriptive of fish schools and other animal aggregations. Ecology 35(3), 361–370 (1954)
Camazine, S., Deneubourg, J.L., Franks, N.R., Sneyd, J., Theraulaz, G., Bonabeau, E.: Self-Organizing Biological Systems. Princeton Univ. Press (2001)
Edelstein-Keshet, L.: Mathematical models of swarming and social aggregation. Robotica 24(3), 315–324 (2006)
Ehrenfest, P., Ehrenfest, T.: Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem. Physikalische Zeitschrift 8, 311–314 (1907)
Eigen, M., Winkler, R.: Laws of the game: how the principles of nature govern chance. Princeton University Press (1993)
Hamann, H.: Modeling and Investigation of Robot Swarms. Master’s thesis, University of Stuttgart, Germany (2006)
Hamann, H.: Space-Time Continuous Models of Swarm Robotics Systems: Supporting Global-to-Local Programming. Springer (2010)
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)
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)
Hamann, H., Wörn, H.: Embodied computation. Parallel Processing Letters 17(3), 287–298 (2007)
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)
Lerman, K., Galstyan, A.: Mathematical model of foraging in a group of robots: Effect of interference. Autonomous Robots 13, 127–141 (2002)
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)
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)
Milutinovic, D., Lima, P.: Cells and Robots: Modeling and Control of Large-Size Agent Populations. Springer (2007)
Miramontes, O.: Order-disorder transitions in the behavior of ant societies. Complexity 1(1), 56–60 (1995)
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)
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)
Okubo, A.: Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds. Advances in Biophysics 22, 1–94 (1986)
Okubo, A., Levin, S.A.: Diffusion and Ecological Problems: Modern Perspectives. Springer, Berlin (2001)
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)
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)
Strogatz, S.H.: Exploring complex networks. Nature 410(6825), 268–276 (2001)
Vicsek, T., Zafiris, A.: Collective motion. arXiv:1010.5017v1 (2010)
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)
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Hamann, H. (2012). Towards Swarm Calculus: Universal Properties of Swarm Performance and Collective Decisions. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2012. Lecture Notes in Computer Science, vol 7461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32650-9_15
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DOI: https://doi.org/10.1007/978-3-642-32650-9_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32649-3
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