Flock Diameter Control in a Collision-Avoiding Cucker-Smale Flocking Model

  • Jing MaEmail author
  • Edmund M-K Lai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10385)


Both the original Cucker-Smale flocking model and a more recent version with collision avoidance do not have any control over how tightly the system of agents flock, which is measured by the flock diameter. In this paper, a cohesive force is introduced to potentially reduce the flock diameter. This cohesive force is similar to the repelling force used for collision avoidance. Simulation results show that this cohesive force can reduce or control the flock diameter. Furthermore, we show that for any set of model parameters, the cohesive force coefficient is the single determining factor of this diameter. The ability of this modified collision-avoiding Cucker-Smale model to provide control of the flock diameter could have significance when applied to robotic flocks.


Flock diameter control Flocking Cucker-Smale model Collision avoidance 


  1. 1.
    Cucker, F., Dong, J.G.: Avoiding collisions in flocks. IEEE Trans. Autom. Control 55(5), 1238–1243 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cucker, F., Dong, J.G.: A general collision-avoiding flocking framework. IEEE Trans. Autom. Control 56(5), 1124–1129 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cucker, F., Smale, S.: Emergent behaviour in flocks. IEEE Trans. Autom. Control 52(5), 852–862 (2007)CrossRefGoogle Scholar
  4. 4.
    Elkawkagy, M.: Improving the performance of hybrid planning. Int. J. Artif. Intell. 14(2), 98–116 (2016)Google Scholar
  5. 5.
    Ha, S.Y., Liu, J.G., et al.: A simple proof of the cucker-smale flocking dynamics and mean-field limit. Commun. Math. Sci. 7(2), 297–325 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ha, S.Y., Tadmor, E.: From particle to kinetic and hydrodynamic descriptions of flocking. Kinet. Relat. Models 1(3), 415–435 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Okubo, A.: Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Adv. Biophys. 22, 1–94 (1986)CrossRefGoogle Scholar
  8. 8.
    Park, J., Kim, H.J., Ha, S.Y.: Cucker-Smale flocking with inter-particle bonding forces. IEEE Trans. Autom. Control 55(11), 2617–2623 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Precup, R.E., Angelov, P., Costa, B.S.J., Sayed-Mouchaweh, M.: An overview on fault diagnosis and nature-inspired optimal control of industrial process applications. Comput. Ind. 74, 75–94 (2015)CrossRefGoogle Scholar
  10. 10.
    Qin, Q., Cheng, S., Zhang, Q., Li, L., Shi, Y.: Biomimicry of parasitic behavior in a coevolutionary particle swarm optimization algorithm for global optimization. Appl. Soft Comput. 32, 224–240 (2015)CrossRefGoogle Scholar
  11. 11.
    Reynolds, C.W.: Flocks, herds and schools: a distributed behavioural model. SIGGRAPH Comput. Graph. 21(4), 25–34 (1987)CrossRefGoogle Scholar
  12. 12.
    Tan, Y., Dai, H.H., Huang, D., Xu, J.X.: Unified iterative learning control schemes for nonlinear dynamic systems with nonlinear input uncertainties. Automatica 48(12), 3173–3182 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Ton, T.V., Linh, N.T.H., Yagi, A.: Flocking and non-flocking behavior in a stochastic Cucker-Smale system. Anal. Appl. 12(01), 63–73 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226 (1995)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Vicsek, T., Zafeiris, A.: Collective motion. Phys. Rep. 517(3), 71–140 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Information Technology and Software EngineeringAuckland University of TechnologyAucklandNew Zealand

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