Autonomous Agents and Multi-Agent Systems

, Volume 30, Issue 3, pp 553–580 | Cite as

Collective decision with 100 Kilobots: speed versus accuracy in binary discrimination problems

  • Gabriele Valentini
  • Eliseo Ferrante
  • Heiko Hamann
  • Marco Dorigo


Achieving fast and accurate collective decisions with a large number of simple agents without relying on a central planning unit or on global communication is essential for developing complex collective behaviors. In this paper, we investigate the speed versus accuracy trade-off in collective decision-making in the context of a binary discrimination problem—i.e., how a swarm can collectively determine the best of two options. We describe a novel, fully distributed collective decision-making strategy that only requires agents with minimal capabilities and is faster than previous approaches. We evaluate our strategy experimentally, using a swarm of 100 Kilobots, and we study it theoretically, using both continuum and finite-size models. We find that the main factor affecting the speed versus accuracy trade-off of our strategy is the agents’ neighborhood size—i.e., the number of agents with whom the current opinion of each agent is shared. The proposed strategy and the associated theoretical framework can be used to design swarms that take collective decisions at a given level of speed and/or accuracy.


Collective decision-making Swarm robotics Majority rule Voter model Self-organization Ordinary differential equations Chemical reaction network Gillespie algorithm Kilobot 



This work has been partially supported by the European Research Council through the ERC Advanced Grant “E-SWARM: Engineering Swarm Intelligence Systems” (Contract 246939) and by the EU-H2020-FET Project ‘flora robotica’, No. 640959. Marco Dorigo acknowledges support from the Belgian F.R.S.–FNRS. Eliseo Ferrante acknowledges support from the Fund for Scientific Research (FWO), Flanders, Belgium.


  1. 1.
    Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41.CrossRefGoogle Scholar
  2. 2.
    Brutschy, A., Scheidler, A., Ferrante, E., Dorigo, M., & Birattari, M. (2012). Can ants inspire robots? Self-organized decision making in robotic swarms. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 4272–4273). IEEE Press.Google Scholar
  3. 3.
    Campo, A., Garnier, S., Dédriche, O., Zekkri, M., & Dorigo, M. (2010). Self-organized discrimination of resources. PLoS One, 6(5), e19,888.CrossRefGoogle Scholar
  4. 4.
    Clifford, P., & Sudbury, A. (1973). A model for spatial conflict. Biometrika, 60(3), 581–588.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Deffuant, G., Neau, D., Amblard, F., & Weisbuch, G. (2000). Mixing beliefs among interacting agents. Advances in Complex Systems, 3(01–04), 87–98.CrossRefGoogle Scholar
  6. 6.
    Franks, N. R., Dornhaus, A., Fitzsimmons, J. P., & Stevens, M. (2003). Speed versus accuracy in collective decision making. Proceedings of the Royal Society of London B, 270, 2457–2463.CrossRefGoogle Scholar
  7. 7.
    Franks, N. R., Pratt, S. C., Mallon, E. B., Britton, N. F., & Sumpter, D. J. T. (2002). Information flow, opinion polling and collective intelligence in house-hunting social insects. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 357(1427), 1567–1583.CrossRefGoogle Scholar
  8. 8.
    Galam, S. (1986). Majority rule, hierarchical structures, and democratic totalitarianism: A statistical approach. Journal of Mathematical Psychology, 30(4), 426–434.CrossRefzbMATHGoogle Scholar
  9. 9.
    Garnier, S., Gautrais, J., Asadpour, M., Jost, C., & Theraulaz, G. (2009). Self-organized aggregation triggers collective decision making in a group of cockroach-like robots. Adaptive Behavior, 17(2), 109–133.CrossRefGoogle Scholar
  10. 10.
    Garnier, S., Gautrais, J., & Theraulaz, G. (2007). The biological principles of swarm intelligence. Swarm Intelligence, 1(1), 3–31.CrossRefGoogle Scholar
  11. 11.
    Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25), 2340–2361.CrossRefGoogle Scholar
  12. 12.
    Hamann, H. (2013). Towards swarm calculus: Urn models of collective decisions and universal properties of swarm performance. Swarm Intelligence, 7(2–3), 145–172.CrossRefGoogle Scholar
  13. 13.
    Hatano, Y., & Mesbahi, M. (2005). Agreement over random networks. IEEE Transactions on Automatic Control, 50(11), 1867–1872.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Jøsang, A., Ismail, R., & Boyd, C. (2007). A survey of trust and reputation systems for online service provision. Decision Support Systems, 43(2), 618–644.CrossRefGoogle Scholar
  15. 15.
    Kernbach, S., Thenius, R., Kernbach, O., & Schmickl, T. (2009). Re-embodiment of honeybee aggregation behavior in an artificial micro-robotic system. Adaptive Behavior, 17(3), 237–259.CrossRefGoogle Scholar
  16. 16.
    Lerman, K., Martinoli, A., & Galstyan, A. (2005). A review of probabilistic macroscopic models for swarm robotic systems. In Swarm robotics, LNCS (Vol. 3342, pp. 143–152). Berlin: Springer.Google Scholar
  17. 17.
    Liggett, T. M. (1999). Stochastic interacting systems: Contact, voter and exclusion processes. In Grundlehren der mathematischen Wissenschaften (Vol. 324). Berlin: Springer.Google Scholar
  18. 18.
    List, C. (2004). Democracy in animal groups: A political science perspective. Trends in Ecology & Evolution, 19(4), 168–169.CrossRefGoogle Scholar
  19. 19.
    Marshall, J. A., Bogacz, R., Dornhaus, A., \({\tilde{\rm P}}\)lanqué, R., Kovacs, T., & Franks, N. R. (2009). On optimal decision-making in brains and social insect colonies. Journal of the Royal Society Interface, 6(40), 1065–1074.Google Scholar
  20. 20.
    Martinoli, A., Easton, K., & Agassounon, W. (2004). Modeling swarm robotic systems: A case study in collaborative distributed manipulation. The International Journal of Robotics Research, 23(4–5), 415–436.CrossRefGoogle Scholar
  21. 21.
    Martinoli, A., Ijspeert, A., & Mondada, F. (1999). Understanding collective aggregation mechanisms: From probabilistic modelling to experiments with real robots. Robotics and Autonomous Systems, 29(1), 51–63.CrossRefGoogle Scholar
  22. 22.
    Mathews, N., Valentini, G., Christensen, A. L., O’Grady, R., Brutschy, A., & Dorigo, M. (2015). Spatially targeted communication in decentralized multirobot systems. Autonomous Robots, 38(4), 439–457.CrossRefGoogle Scholar
  23. 23.
    Mesbahi, M., & Egerstedt, M. (2010). Graph theoretic methods in multiagent networks. Princeton, NJ: Princeton University Press.CrossRefzbMATHGoogle Scholar
  24. 24.
    Montes de Oca, M., Ferrante, E., Scheidler, A., Pinciroli, C., Birattari, M., & Dorigo, M., (2011). Majority-rule opinion dynamics with differential latency: A mechanism for self-organized collective decision-making. Swarm Intelligence, 5, 305–327.Google Scholar
  25. 25.
    Parker, C. A. C., & Zhang, H. (2009). Cooperative decision-making in decentralized multiple-robot systems: The best-of-n problem. IEEE/ASME Transactions on Mechatronics, 14(2), 240–251.CrossRefGoogle Scholar
  26. 26.
    Parker, C. A. C., & Zhang, H. (2010). Collective unary decision-making by decentralized multiple-robot systems applied to the task-sequencing problem. Swarm Intelligence, 4, 199–220.CrossRefGoogle Scholar
  27. 27.
    Passino, K. M., & Seeley, T. D. (2006). Modeling and analysis of nest-site selection by honeybee swarms: The speed and accuracy trade-off. Behavioral Ecology and Sociobiology, 59(3), 427–442.CrossRefGoogle Scholar
  28. 28.
    Reina, A., Miletitch, R., Dorigo, M., & Trianni, V. (2015). A quantitative micro-macro link for collective decisions: The shortest path discovery/selection example. Swarm Intelligence, 9(2–3), 75–102.CrossRefGoogle Scholar
  29. 29.
    Reina, A., Valentini, G., Fernández-Oto, C., Dorigo, M., & Trianni, V. (2015). A design pattern for decentralized decision making. PLoS One, 10(10), e0140950.CrossRefGoogle Scholar
  30. 30.
    Ren, W., Beard, R., & Atkins, E. (2005) A survey of consensus problems in multi-agent coordination. In Proceedings of the 2005 American Control Conference (Vol. 3, pp. 1859–1864). IEEE Press.Google Scholar
  31. 31.
    Ren, W., & Beard, R. W. (2008). Distributed consensus in multi-vehicle cooperative control: Theory and applications, communications and control engineering. Berlin: Springer.CrossRefzbMATHGoogle Scholar
  32. 32.
    Rubenstein, M., Ahler, C., Hoff, N., Cabrera, A., & Nagpal, R. (2014). Kilobot: A low cost robot with scalable operations designed for collective behaviors. Robotics and Autonomous Systems, 62(7), 966–975.CrossRefGoogle Scholar
  33. 33.
    Rubenstein, M., Cabrera, A., Werfel, J., Habibi, G., McLurkin, J., & Nagpal, R. (2013). Collective transport of complex objects by simple robots: Theory and experiments. In T. Ito, C. Jonker, M. Gini, & O. Shehory (Eds.), Proceedings of the 12th international conference on autonomous agents and multiagent systems, AAMAS ’13 (pp. 47–54). IFAAMAS.Google Scholar
  34. 34.
    Rubenstein, M., Cornejo, A., & Nagpal, R. (2014). Programmable self-assembly in a thousand-robot swarm. Science, 345(6198), 795–799.CrossRefGoogle Scholar
  35. 35.
    Sartoretti, G., Hongler, M. O., de Oliveira, M., & Mondada, F. (2014). Decentralized self-selection of swarm trajectories: From dynamical systems theory to robotic implementation. Swarm Intelligence, 8(4), 329–351.CrossRefGoogle Scholar
  36. 36.
    Scheidler, A. (2011). Dynamics of majority rule with differential latencies. Physical Review E, 83(031), 116.Google Scholar
  37. 37.
    Scheidler, A., Brutschy, A., Ferrante, E., & Dorigo, M. (2015). The k-unanimity rule for self-organized decision-making in swarms of robots. IEEE Transactions on Cybernetics, PP(99), 1.Google Scholar
  38. 38.
    Seeley, T. D. (2010). Honeybee democracy. Princeton, NJ: Princeton University Press.Google Scholar
  39. 39.
    Soysal, O., & Şahin, E. (2007). A macroscopic model for self-organized aggregation in swarm robotic systems. In E. Şahin, W. M. Spears, & A. F. Winfield (Eds.), Swarm robotics, LNCS (Vol. 4433, pp. 27–42). Berlin: Springer.CrossRefGoogle Scholar
  40. 40.
    Sumpter, D. J. (2010). Collective animal behavior. Princeton, NJ: Princeton University Press.CrossRefzbMATHGoogle Scholar
  41. 41.
    Toral, R., & Tessone, C. J. (2007). Finite size effects in the dynamics of opinion formation. Communications in Computational Physics, 2(2), 177–195.MathSciNetGoogle Scholar
  42. 42.
    van Kampen, N. G. (1992). Stochastic processes in physics and chemistry. Amsterdam, NL: Elsevier.zbMATHGoogle Scholar
  43. 43.
    von Frisch, K. (1967). The dance language and orientation of bees. Cambridge, MA: Harvard University Press.Google Scholar
  44. 44.
    Valentini, G., Birattari, M., & Dorigo, M. (2013) Majority rule with differential latency: An absorbing Markov chain to model consensus. In Proceedings of the European conference on complex systems 2012, Proceedings in complexity (pp. 651–658). Berlin: Springer.Google Scholar
  45. 45.
    Valentini, G., Ferrante, E., Hamann, H., & Dorigo, M. (2015). Collective decision with 100 kilobots: Speed vs accuracy in binary discrimination problems. Supplementary material.
  46. 46.
    Valentini, G., & Hamann, H. (2015). Time-variant feedback processes in collective decision-making systems: Influence and effect of dynamic neighborhood sizes. Swarm Intelligence, 9(2–3), 153–176.CrossRefGoogle Scholar
  47. 47.
    Valentini, G., Hamann, H., & Dorigo, M. (2014). Self-organized collective decision making: The weighted voter model. In A. Lomuscio, P. Scerri, A. Bazzan, & M. Huhns (Eds.), Proceedings of the 13th international conference on autonomous agents and multiagent systems, AAMAS ’14 (pp. 45–52). IFAAMAS.Google Scholar
  48. 48.
    Valentini, G., Hamann, H., & Dorigo, M. (2015). Efficient decision-making in a self-organizing robot swarm: On the speed versus accuracy trade-off. In Proceedings of the 14th International conference on autonomous agents and multiagent systems, AAMAS ’15 (pp. 1305–1314). IFAAMAS.Google Scholar
  49. 49.
    Valentini, G., Hamann, H., & Dorigo, M. (2015). Self-organized collective decisions in a robot swarm. In Proceedings of the 29th AAAI conference on artificial intelligence, AI Video Competition. AAAI Press.
  50. 50.
    Vigelius, M., Meyer, B., & Pascoe, G. (2014). Multiscale modelling and analysis of collective decision making in swarm robotics. PLoS One, 9(11), e111542.CrossRefGoogle Scholar
  51. 51.
    Wang, Y., & Vassileva, J. (2003). Trust and reputation model in peer-to-peer networks. In Proceedings of the third international conference on peer-to-peer computing (P2P 2003) (pp. 150–157). IEEE Press.Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Gabriele Valentini
    • 1
  • Eliseo Ferrante
    • 2
  • Heiko Hamann
    • 3
  • Marco Dorigo
    • 1
  1. 1.IRIDIAUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Laboratory of Socioecology and Social EvolutionKU LeuvenLeuvenBelgium
  3. 3.Department of Computer Science, Heinz Nixdorf InstituteUniversity of PaderbornPaderbornGermany

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