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A physicochemically inspired approach to flocking control of multiagent system

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Abstract

Theoretical studies suggest that dispersion and repulsion are two important interactions that occur within non-polar particles. Enlightened by this, we propose a simple model for flocking of autonomous agents interacting by physicochemically inspired dispersion and repulsion interactions. This interdisciplinary effort provides a generic framework for design and analysis of distributed flocking by introducing virtual electrons (VEs). We innovatively utilize the functional theory to construct the energy functional with the distribution density of VEs as the basic variable and then solve the Lagrangian equation to derive the control law of multiagent flocking. Theoretical analysis reveals that the proposed protocol can ensure that autonomous agents asymptotically converge to an equilibrium configuration from chaotic movement and meanwhile all agents tend in time to a common velocity. Numerical simulations are presented to verify the effectiveness of theoretical results. We also give a comparison with the collective potential method and found that the proposed approach can realize the rapid transition of autonomous agents from disordered to ordered movement. This implies that the proposed framework can effectively avoid the limitation of constructing a complicated empirical field and thus may have broad application prospects.

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References

  1. Ariel, G., Be’er, A., Reynolds, A.: Chaotic model for Lévy walks in swarming bacteria. Phys. Rev. Lett. 118(22), 228102 (2017)

    Google Scholar 

  2. Rashid, M.T., Frasca, M., Ali, A.A., Ali, R.S., Fortuna, L., Xibilia, M.G.: Artemia swarm dynamics and path tracking. Nonlinear Dyn. 68(4), 555–563 (2012)

    Google Scholar 

  3. Katz, Y., Tunstrøm, K., Ioannou, C.C., Huepe, C., Couzin, I.D.: Inferring the structure and dynamics of interactions in schooling fish. Proc. Natl. Acad. Sci. U.S.A. 108(46), 18720–18725 (2011)

    Google Scholar 

  4. Ling, H., Mclvor, G.E., van der Vaart, K., Vaughan, R.T., Thornton, A., Ouellette, N.T.: Costs and benefits of social relationships in the collective motion of bird flocks. Nat. Ecol. Evol. 3(6), 943–948 (2019)

    Google Scholar 

  5. Ginelli, F., Peruani, F., Pillot, M.H., Chaté, H., Theraulaz, G., Bon, R.: Intermittent collective dynamics emerge from conflicting imperatives in sheep herds. Proc. Natl. Acad. Sci. U.S.A. 112(41), 12729–12734 (2015)

    Google Scholar 

  6. Morin, A., Desreumaux, N., Caussin, J.B., Bartolo, D.: Distortion and destruction of colloidal flocks in disordered environments. Nat. Phys. 13(1), 63–67 (2017)

    Google Scholar 

  7. Miguel, M.C., Parley, J.T., Pastor-Satorras, R.: Effects of heterogeneous social interactions on flocking dynamics. Phys. Rev. Lett. 120(6), 068303 (2018)

    Google Scholar 

  8. Reynolds, C.W.: Flocks, herds, and schools: a distributed behavioral model. Comput. Graph. 21(4), 25–34 (1987)

    Google Scholar 

  9. Czirók, A., Vicsek, T.: Collective behavior of interacting self-propelled particles. Phys. A 281(1–4), 17–29 (2000)

    Google Scholar 

  10. Paranjape, A.A., Chung, S.J., Kim, K., Shim, D.H.: Robotic herding of a flock of birds using an unmanned aerial vehicle. IEEE Trans. Robot. 34(4), 901–915 (2018)

    Google Scholar 

  11. Ibuki, T., Wilson, S., Yamauchi, J., Fujita, M., Egerstedt, M.: Optimization-based distributed flocking control for multiple rigid bodies. IEEE Robot. Autom. Lett. 5(2), 1891–1898 (2020)

    Google Scholar 

  12. 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), 1226–1229 (1995)

    MathSciNet  Google Scholar 

  13. Toner, J., Tu, Y.: Long-range order in a two-dimensional dynamical xy model: how birds fly together. Phys. Rev. Lett. 75(23), 4326–4329 (1995)

    Google Scholar 

  14. Toner, J., Tu, Y.: Flocks, herds, and schools: a quantitative theory of flocking. Phys. Rev. E 58(4), 4828–4858 (1998)

    MathSciNet  Google Scholar 

  15. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48(6), 988–1001 (2003)

    MathSciNet  MATH  Google Scholar 

  16. Cucker, F., Smale, S.: Emergent behavior in flocks. IEEE Trans. Automat. Control 52(5), 852–862 (2007)

    MathSciNet  MATH  Google Scholar 

  17. Zafeiris, A., Vicsek, T.: Group performance is maximized by hierarchical competence distribution. Nat. Commun. 4(9), 2484 (2013)

    Google Scholar 

  18. Komareji, M., Shang, Y., Bouffanais, R.: Consensus in topologically interacting swarms under communication constraints and time-delays. Nonlinear Dyn. 93(3), 1287–1300 (2018)

    MATH  Google Scholar 

  19. Zhang, X., Jia, S., Li, X.: Improving the synchronization speed of self-propelled particles with restricted vision via randomly changing the line of sight. Nonlinear Dyn. 90(1), 43–51 (2019)

    Google Scholar 

  20. Vásárhelyi, G., Virágh, C., Somorjai, G., Nepusz, T., Eiben, A.E., Vicsek, T.: Optimized flocking of autonomous drones in confined environments. Sci. Robot. 3(20), eaat3536 (2018)

    Google Scholar 

  21. Couzin, I.D., Krause, J., James, R., Ruxton, G.D., Franks, N.R.: Collective memory and spatial sorting in animal groups. J. Theor. Biol. 218(1), 1–11 (2002)

    MathSciNet  Google Scholar 

  22. Romanczuk, P., Couzin, I.D., Schimansky-Geier, L.: Collective motion due to individual escape and pursuit response. Phys. Rev. Lett. 102(1), 010602 (2009)

    Google Scholar 

  23. Couzin, I.D., Krause, J., Franks, N.R., Levin, S.A.: Effective leadership and decision-making in animal groups on the move. Nature 433(7025), 513–516 (2005)

    Google Scholar 

  24. Hildenbrandt, H., Carere, C., Hemelrijk, C.: Self-organized aerial displays of thousands of starlings: a model. Behav. Ecol. 21(6), 6 (2010)

    Google Scholar 

  25. Luo, Q., Duan, H.: Distributed uav flocking control based on homing pigeon hierarchical strategies. Aerosp. Sci. Technol. 70, 257–264 (2017)

    Google Scholar 

  26. Levine, H., Rappel, W.J., Cohen, I.: Self-organization in systems of self-propelled particles. Phys. Rev. E 63(1), 017101 (2000)

    Google Scholar 

  27. Do, K.D.: Flocking for multiple elliptical agents with limited communication ranges. IEEE Trans. Robot. 27(5), 931–942 (2011)

    Google Scholar 

  28. Ge, F., Zhen, W., Lu, Y., Tian, Y., Li, L.: Decentralized coordination of autonomous swarms inspired by chaotic behavior of ants. Nonlinear Dyn. 70(1), 571–584 (2012)

    MathSciNet  Google Scholar 

  29. Jain, A., Ghose, D.: Synchronization of multi-agent systems with heterogeneous controllers. Nonlinear Dyn. 89(2), 1433–1451 (2017)

    MATH  Google Scholar 

  30. Sahu, B.K., Subudhi, B.: Flocking control of multiple auvs based on fuzzy potential functions. IEEE Trans. Fuzzy Syst. 26(5), 2539–2551 (2018)

    Google Scholar 

  31. Jing, G., Wang, L.: Multiagent flocking with angle-based formation shape control. IEEE Trans. Autom. Control 65(2), 817–823 (2020)

    MATH  Google Scholar 

  32. Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51(3), 401–420 (2006)

    MathSciNet  MATH  Google Scholar 

  33. Su, H., Wang, X., Lin, Z.: Flocking of multi-agents with a virtual leader. IEEE Trans. Autom. Control 54(2), 293–307 (2009)

    MathSciNet  MATH  Google Scholar 

  34. Semnani, S.H., Basir, O.A.: Semi-flocking algorithm for motion control of mobile sensors in large-scale surveillance systems. IEEE Trans. Cybern. 45(1), 129–137 (2015)

    Google Scholar 

  35. La, H.M., Lim, R., Sheng, W.: Multirobot cooperative learning for predator avoidance. IEEE Trans. Control Syst. Technol. 23(1), 52–63 (2015)

    Google Scholar 

  36. Saif, O., Fantoni, I., Zavala-Río, A.: Distributed integral control of multiple uavs: precise flocking and navigation. IET Control Theory Appl. 13(13), 2008–2017 (2019)

    Google Scholar 

  37. Maitland, G.C., Rigby, M., Smith, E.B., Wakeham, W.A.: Intermolecular forces: their origin and determination (1983)

  38. Atkins, P., Paula, J.: Atkins’ Physical Chemistry. Oxford University, New York (2006)

    Google Scholar 

  39. Born, M., Oppenheimer, R.: Zur quantentheorie der molekeln. Annalen der Physik 389(20), 2008–2017 (1927)

    MATH  Google Scholar 

  40. Wu, J.: Classical Density Functional Theory for Molecular Systems, pp. 65–99. Springer, Singapore (2017)

    Google Scholar 

  41. Dong, J.G., Qiu, L.: Flocking of the cucker-smale model on general digraphs. IEEE Trans. Autom. Control 62(10), 5234–5239 (2017)

    MathSciNet  MATH  Google Scholar 

  42. Wang, R., Dong, X., Li, Q., Ren, Z.: Distributed time-varying output formation control for general linear multiagent systems with directed topology. IEEE Trans. Control Netw. Syst. 6(2), 609–620 (2019)

    MathSciNet  MATH  Google Scholar 

  43. Godsil, C., Royle, G.: Algebraic Graph Theory, Vol. 207 of Graduate Texts in Mathematics. Springer, New York (2001)

  44. Hu, Y., Liu, H.: Density Functional Theory. Science Press, Beijing (2016)

    Google Scholar 

  45. Olfati-Saber, R.: Flocking for multi-agent dynamic systems: Algorithms and theory. Tech. Rep. 2004-005, California Inst. Technol., Control Dyna. Syst., Pasadena, CA (2004)

  46. Olfati-Saber, R.: Flocking with obstacle avoidance. Tech. Rep. 2003-006, California Inst. Technol., Control Dyna. Syst., Pasadena, CA (2003)

  47. Nicolis, G., Prigogine, I.: Self-Organization in Nonequilibrium Systems. Wiley, New York, NY (1972)

    MATH  Google Scholar 

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Acknowledgements

The authors would like to thank Dr. Xu (Jing Xu, Institute of Zoology) of the Chinese Academy of Sciences for the novel ideas and interdisciplinary concepts introduced for this article. This work was cosupported by the National Natural Science Foundation of China under Grant 61773031, and the Graduate Innovation Practice Fund of Beihang University under Grant YCSJ-01-201915.

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Authors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100083, China

    Guibin Sun & Rui Zhou

  2. National Innovation Institute of Defense Technology, Academy of Military Sciences, Beijing, 100071, China

    Bin Di

  3. Key Laboratory of Aerospace Information Applications, China Electronics Technology Group Corporation, Shijiazhuang, 050081, China

    Yan Hu

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  1. Guibin Sun
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Correspondence to Bin Di.

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Sun, G., Zhou, R., Di, B. et al. A physicochemically inspired approach to flocking control of multiagent system. Nonlinear Dyn 102, 2627–2648 (2020). https://doi.org/10.1007/s11071-020-06062-y

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