Swarm Intelligence

, Volume 13, Issue 3–4, pp 321–345 | Cite as

Coherent collective behaviour emerging from decentralised balancing of social feedback and noise

  • Ilja RauschEmail author
  • Andreagiovanni Reina
  • Pieter Simoens
  • Yara Khaluf


Decentralised systems composed of a large number of locally interacting agents often rely on coherent behaviour to execute coordinated tasks. Agents cooperate to reach a coherent collective behaviour by aligning their individual behaviour to the one of their neighbours. However, system noise, determined by factors such as individual exploration or errors, hampers and reduces collective coherence. The possibility to overcome noise and reach collective coherence is determined by the strength of social feedback, i.e. the number of communication links. On the one hand, scarce social feedback may lead to a noise-driven system and consequently incoherent behaviour within the group. On the other hand, excessively strong social feedback may require unnecessary computing by individual agents and/or may nullify the possible benefits of noise. In this study, we investigate the delicate balance between social feedback and noise, and its relationship with collective coherence. We perform our analysis through a locust-inspired case study of coherently marching agents, modelling the binary collective decision-making problem of symmetry breaking. For this case study, we analytically approximate the minimal number of communication links necessary to attain maximum collective coherence. To validate our findings, we simulate a 500-robot swarm and obtain good agreement between theoretical results and physics-based simulations. We illustrate through simulation experiments how the robot swarm, using a decentralised algorithm, can adaptively reach coherence for various noise levels by regulating the number of communication links. Moreover, we show that when the system is disrupted by increasing and decreasing the robot density, the robot swarm adaptively responds to these changes in real time. This decentralised adaptive behaviour indicates that the derived relationship between social feedback, noise and coherence is robust and swarm size independent.


Collective decision-making Group coherence Social feedback Marching locusts Noise Physics-based simulations Swarm robotics 


Supplementary material

11721_2019_173_MOESM1_ESM.pdf (3.2 mb)
Supplementary material 1 (pdf 3249 KB)


  1. Ariel, G., & Ayali, A. (2015). Locust collective motion and its modeling. PLoS Computational Biology, 11(12), e1004522.Google Scholar
  2. Baronchelli, A. (2018). The emergence of consensus: A primer. Royal Society Open Science, 5(2), 172189.MathSciNetGoogle Scholar
  3. Bayındır, L. (2016). A review of swarm robotics tasks. Neurocomputing, 172(C), 292–321.Google Scholar
  4. Berman, S., Halász, Á., Hsieh, M. A., & Kumar, V. (2009). Optimized stochastic policies for task allocation in swarms of robots. IEEE Transactions on Robotics, 25(4), 927–937.Google Scholar
  5. Böhme, G. A., & Gross, T. (2012). Fragmentation transitions in multistate voter models. Physical Review E, 85, 066117.Google Scholar
  6. Bonabeau, E., Dorigo, M., & Theraulaz, G. (1999). Swarm intelligence: From natural to artificial systems. New York: Oxford University Press.zbMATHGoogle Scholar
  7. Bonani, M., Longchamp, V., Magnenat, S., Rétornaz, P., Burnier, D., Roulet, G., Vaussard, F., Bleuler, H., & Mondada, F. (2010). The marXbot, a miniature mobile robot opening new perspectives for the collective-robotic research. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS 2010) (pp. 4187–4193). IEEE Press.Google Scholar
  8. Bose, T., Reina, A., & Marshall, J. A. R. (2017). Collective decision-making. Current Opinion in Behavioral Sciences, 6, 30–34.Google Scholar
  9. Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41.Google Scholar
  10. Buhl, J., Sumpter, D. J., Couzin, I. D., Hale, J. J., Despland, E., Miller, E. R., et al. (2006). From disorder to order in marching locusts. Science, 312(5778), 1402–1406.Google Scholar
  11. Camazine, S., Deneubourg, J.-L., Franks, N. R., Sneyd, J., Bonabeau, E., & Theraulaz, G. (2003). Self-organization in biological systems (Vol. 7). Princeton: Princeton University Press.zbMATHGoogle Scholar
  12. Castellano, C., Fortunato, S., & Loreto, V. (2009). Statistical physics of social dynamics. Reviews of Modern Physics, 81(2), 591–646.Google Scholar
  13. Chen, L., Huepe, C., & Gross, T. (2016). Adaptive network models of collective decision making in swarming systems. Physical Review E, 94(2), 022415.Google Scholar
  14. Czirók, A., Barabási, A.-L., & Vicsek, T. (1999). Collective motion of self-propelled particles: Kinetic phase transition in one dimension. Physical Review Letters, 82, 209–212.Google Scholar
  15. Danon, L., Ford, A. P., House, T., Jewell, C. P., Keeling, M. J., Roberts, G. O., et al. (2011). Networks and the epidemiology of infectious disease. Interdisciplinary Perspectives on Infectious Diseases, 2011, 284909. Google Scholar
  16. Dussutour, A., Beekman, M., Nicolis, S. C., & Meyer, B. (2009). Noise improves collective decision-making by ants in dynamic environments. Proceedings of the Royal Society of London B: Biological Sciences, 276(1677), 4353–4361.Google Scholar
  17. Gross, T., D’Lima, C. J. D., & Blasius, B. (2006). Epidemic dynamics on an adaptive network. Physical Review Letters, 96, 208701.Google Scholar
  18. Hamann, H. (2018). The role of largest connected components in collective motion. In M. Dorigo, M. Birattari, C. Blum, A. L. Christensen, A. Reina, & V. Trianni (Eds.), Swarm intelligence: 11th International conference, ANTS 2018, volume 11172 of LNCS (pp. 290–301). Cham: Springer.Google Scholar
  19. Hamann, H., Valentini, G., Khaluf, Y., & Dorigo, M. (2014). Derivation of a micro-macro link for collective decision-making systems. In T. Bartz-Beielstein, J. Branke, B. Filipič, & J. Smith (Eds.), International conference on parallel problem solving from nature—PPSN XIII, PPSN 2014, volume 8672 of LNCS (pp. 181–190). Cham: Springer.Google Scholar
  20. Hamann, H., & Wörn, H. (2008). A framework of space–time continuous models for algorithm design in swarm robotics. Swarm Intelligence, 2(2), 209–239.Google Scholar
  21. House, T., Davies, G., Danon, L., & Keeling, M. J. (2009). A motif-based approach to network epidemics. Bulletin of Mathematical Biology, 71(7), 1693–1706.MathSciNetzbMATHGoogle Scholar
  22. Huepe, C., Zschaler, G., Do, A.-L., & Gross, T. (2011). Adaptive-network models of swarm dynamics. New Journal of Physics, 13(7), 073022.Google Scholar
  23. Keeling, M. J., & Eames, K. T. (2005). Networks and epidemic models. Journal of The Royal Society Interface, 2(4), 295–307.Google Scholar
  24. Keeling, M. J., House, T., Cooper, A. J., & Pellis, L. (2016). Systematic approximations to susceptible-infectious-susceptible dynamics on networks. PLoS Computational Biology, 12(12), e1005296.Google Scholar
  25. Khaluf, Y., Birattari, M., & Rammig, F. (2016). Analysis of long-term swarm performance based on short-term experiments. Soft Computing, 20(1), 37–48.Google Scholar
  26. Khaluf, Y., Ferrante, E., Simoens, P., & Huepe, C. (2017a). Scale invariance in natural and artificial collective systems: A review. Journal of The Royal Society Interface, 14(136), 20170662.Google Scholar
  27. Khaluf, Y., & Hamann, H. (2016). On the definition of self-organizing systems: Relevance of positive/negative feedback and fluctuations. In M. Dorigo, M. Birattari, X. Li, M. López-Ibáñez, K. Ohkura, C. Pinciroli, & T. Stützle (Eds.), Swarm intelligence: 10th International conference, ANTS 2016, volume 9882 of LNCS (p. 298). Cham: Springer. (extended abstract).Google Scholar
  28. Khaluf, Y., Pinciroli, C., Valentini, G., & Hamann, H. (2017b). The impact of agent density on scalability in collective systems: Noise-induced versus majority-based bistability. Swarm Intelligence, 11(2), 155–179.Google Scholar
  29. Khaluf, Y., Rausch, I., & Simoens, P. (2018). The impact of interaction models on the coherence of collective decision-making: A case study with simulated locusts. In M. Dorigo, M. Birattari, C. Blum, A. L. Christensen, A. Reina, & V. Trianni (Eds.), Swarm intelligence: 11th International conference, ANTS 2018, volume 11172 of LNCS (pp. 252–263). Cham: Springer.Google Scholar
  30. Kimura, D., & Hayakawa, Y. (2008). Coevolutionary networks with homophily and heterophily. Physical Review E, 78, 016103.Google Scholar
  31. Lerman, K., Martinoli, A., & Galstyan, A. (2004). A review of probabilistic macroscopic models for swarm robotic systems. In E. Şahin & W. M. Spears (Eds.), International workshop on swarm robotics (pp. 143–152). Berlin, Heidelberg: Springer. Google Scholar
  32. Liang, Y., An, K. N., Yang, G., & Huang, J. P. (2013). Contrarian behavior in a complex adaptive system. Physical Review E, 87, 012809.Google Scholar
  33. Mateo, D., Horsevad, N., Hassani, V., Chamanbaz, M., & Bouffanais, R. (2019). Optimal network topology for responsive collective behavior. Science Advances, 5(4), eaau0999.Google Scholar
  34. Mateo, D., Kuan, Y. K., & Bouffanais, R. (2017). Effect of correlations in swarms on collective response. Scientific Reports, 7(1), 10388.Google Scholar
  35. Mayya, S., Pierpaoli, P., & Egerstedt, M. (2019). Voluntary retreat for decentralized interference reduction in robot swarms. In ICRA 2019. IEEE Press. (in press).Google Scholar
  36. Pagliara, R., Gordon, D. M., & Leonard, N. E. (2018). Regulation of harvester ant foraging as a closed-loop excitable system. PLoS Computational Biology, 14(12), e1006200.Google Scholar
  37. Pinciroli, C., Trianni, V., O’Grady, R., Pini, G., Brutschy, A., Brambilla, M., et al. (2012). ARGoS: A modular, parallel, multi-engine simulator for multi-robot systems. Swarm Intelligence, 6(4), 271–295.Google Scholar
  38. Pinero, J., & Sole, R. (2019). Statistical physics of liquid brains. Philosophical Transactions of the Royal Society B, 374(1774), 20180376.Google Scholar
  39. Pitonakova, L., Crowder, R., & Bullock, S. (2018). The Information-Cost-Reward framework for understanding robot swarm foraging. Swarm Intelligence, 12(1), 71–96.Google Scholar
  40. Rausch, I., Khaluf, Y., & Simoens, P. (2019). Scale-free features in collective robot foraging. Applied Sciences, 9(13), 2667.Google Scholar
  41. Reina, A., Miletitch, R., Dorigo, M., & Trianni, V. (2015a). A quantitative micro-macro link for collective decisions: The shortest path discovery/selection example. Swarm Intelligence, 9(2–3), 75–102.Google Scholar
  42. Reina, A., Valentini, G., Fernández-Oto, C., Dorigo, M., & Trianni, V. (2015b). A design pattern for decentralised decision making. PLoS ONE, 10(10), e0140950.Google Scholar
  43. Roberts, J. F., Stirling, T. S., Zufferey, J.-C., & Floreano, D. (2009). 2.5D infrared range and bearing system for collective robotics. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS 2009) (pp. 3659–3664). IEEE Press.Google Scholar
  44. Saldaña, D., Prorok, A., Sundaram, S., Campos, M. F., & Kumar, V. (2017). Resilient consensus for time-varying networks of dynamic agents. In 2017 American control conference (ACC) (pp. 252–258).Google Scholar
  45. Saulnier, K., Saldaña, D., Prorok, A., Pappas, G. J., & Kumar, V. (2017). Resilient flocking for mobile robot teams. IEEE Robotics and Automation Letters, 2(2), 1039–1046.Google Scholar
  46. Shang, Y., & Bouffanais, R. (2014). Influence of the number of topologically interacting neighbors on swarm dynamics. Scientific Reports, 4, 4184.Google Scholar
  47. Shklarsh, A., Ariel, G., Schneidman, E., & Ben-Jacob, E. (2011). Smart swarms of bacteria-inspired agents with performance adaptable interactions. PLoS Computational Biology, 7(9), e1002177.MathSciNetGoogle Scholar
  48. Talamali, M. S., Bose, T., Haire, M., Xu, X., Marshall, J. A. R., & Reina, A. (2019a). Sophisticated collective foraging with minimalist agents: A swarm robotics test. Swarm Intelligence. (in press). Google Scholar
  49. Talamali, M. S., Bose, T., James, M. A., & Reina, A. (2019b). Improving collective decision accuracy via time-varying cross-inhibition. In ICRA 2019. IEEE Press. (in press).Google Scholar
  50. Torney, C. J., Neufeld, Z., & Couzin, I. D. (2009). Context-dependent interaction leads to emergent search behavior in social aggregates. Proceedings of the National Academy of Sciences, 106(52), 22055–22060.Google Scholar
  51. Tsimring, L. S. (2014). Noise in biology. Reports on Progress in Physics, 77(2), 026601.Google Scholar
  52. 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.Google Scholar
  53. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., & Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75, 1226–1229.MathSciNetGoogle Scholar
  54. Wahby, M., Petzold, J., Eschke, C., Schmickl, T., & Hamann, H. (2019). Collective change detection: Adaptivity to dynamic swarm densities and light conditions in robot swarms. In The 2018 conference on artificial life: A hybrid of the European conference on artificial life (ECAL) and the international conference on the synthesis and simulation of living systems (ALIFE) (pp. 642–649). MIT Press.Google Scholar
  55. Yates, C. A., Erban, R., Escudero, C., Couzin, I. D., Buhl, J., Kevrekidis, I. G., et al. (2009). Inherent noise can facilitate coherence in collective swarm motion. Proceedings of the National Academy of Sciences, 106(14), 5464–5469.Google Scholar
  56. Zhong, L.-X., Zheng, D.-F., Zheng, B., & Hui, P. M. (2005). Effects of contrarians in the minority game. Physical Review E, 72, 026134.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.IDLab - Department of Information TechnologyGhent University - imecGhentBelgium
  2. 2.Department of Computer ScienceUniversity of SheffieldSheffieldUK

Personalised recommendations