Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Multi-leader multi-follower coordination with cohesion, dispersion, and containment control via proximity graphs

  • 161 Accesses

  • 15 Citations

Abstract

This paper studies the problem of multi-leader multi-follower coordination with proximity-based network topologies. The particular interest is to drive all the followers towards the convex hull formed by the moving leaders while producing cohesion behavior and keeping group dispersion. First, in the case of stationary leaders, we design a gradient-based continuous control algorithm. We show that with this continuous algorithm the control objective can be achieved, and the tracking error bound can be controlled by tuning some control parameters. We apply the continuous control algorithm to the moving leaders case and show that the tracking error bound is related to the velocities of the leaders. However, in this case, the algorithm has one restriction that the velocities of the leaders should depend on neighboring followers’ velocities, which might not be desirable in some scenarios. Therefore, we propose a nonsmooth algorithm for moving leaders which works under the mild assumption of boundedness of leaders’ velocities. Finally, we present numerical examples to show the validity of the proposed algorithms.

This is a preview of subscription content, log in to check access.

References

  1. 1

    Qu Z. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Berlin: Springer, 2009

  2. 2

    Bullo F, Cortés J, Martínez S. Distributed Control of Robotic Networks. Princeton: Princeton University Press, 2009

  3. 3

    Yu W, Wen G, Chen G, et al. Distributed Cooperative Control of Multi-agent Systems. Hoboken: John Wiley & Sons, 2016

  4. 4

    Chen F, Ren W. Distributed Consensus in Networks. Hoboken: John Wiley & Sons, 2016

  5. 5

    Ji M, Ferrari-Trecate G, Egerstedt M, et al. Containment control in mobile networks. IEEE Trans Autom Control, 2008, 53: 1972–1975

  6. 6

    Rui L, Shi Y, Teo K. Coordination arrival control for multi-agent systems. Int J Robust Nonlinear Control, 2016, 26: 1456–1474

  7. 7

    Engelberger J F. Robotics in Practice: Management and Applications of Industrial Robots. Berlin: Springer, 2012

  8. 8

    Iyengar S, Brooks R. Distributed Sensor Networks: Sensor Networking and Applications. Boca Raton: CRC Press, 2016

  9. 9

    Cao Y, Ren W, Egerstedt M. Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica, 2012, 48: 1586–1597

  10. 10

    Li J, Ren W, Xu S. Distributed containment control with multiple dynamic leaders for double-integrator dynamics using only position measurements. IEEE Trans Autom Control, 2012, 57: 1553–1559

  11. 11

    Wang X, Li S, Shi P. Distributed finite-time containment control for double-integrator multiagent systems. IEEE Trans Cyber, 2014, 44: 1518–1528

  12. 12

    Mei J, Ren W, Ma G. Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph. Automatica, 2012, 48: 653–659

  13. 13

    Meng Z, Lin Z, Ren W. Leader-follower swarm tracking for networked Lagrange systems. Syst Control Lett, 2012, 61: 117–126

  14. 14

    Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica, 2008, 44: 846–850

  15. 15

    Chen F, Xiang L, Lan W, et al. Coordinated tracking in mean square for a multi-agent system with noisy channels and switching directed network topologies. IEEE Trans Circ Syst II Express Briefs, 2012, 59: 835–839

  16. 16

    Chen F, Ren W, Cao Y. Surrounding control in cooperative agent networks. Syst Control Lett, 2010, 59: 704–712

  17. 17

    Shi Y J, Li R, Teo K L. Cooperative enclosing control for multiple moving targets by a group of agents. Int J Control, 2015, 88: 80–89

  18. 18

    Chen F, Ren W, Lin Z L. Multi-agent coordination with cohesion, dispersion, and containment control. In: Proceedings of American Control Conference, Baltimore, 2010

  19. 19

    Lalish E, Morgansen K A, Tsukamaki T. Decentralized reactive collision avoidance for multiple unicycle-type vehicles. In: Proceedings of American Control Conference, Seattle, 2008

  20. 20

    Su H, Wang X, Chen G. A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements. Int J Control, 2009, 82: 1334–1343

  21. 21

    Ji M, Egerstedt E. Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Robot, 2007, 23: 693–703

  22. 22

    Sabattini L, Secchi C, Chopra N. Distributed control of multirobot systems with global connectivity maintenance. IEEE Trans Robot, 2013, 29: 1326–1332

  23. 23

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

  24. 24

    Tanner H G, Jadbabaie A, Pappas G J. Flocking in fixed and switching networks. IEEE Trans Autom Control, 2007, 52: 863–868

  25. 25

    Zavlanos M M, Pappas G J. Distributed connectivity control of mobile networks. IEEE Trans Robot, 2008, 24: 1416–1428

  26. 26

    Zhan J, Li X. Flocking of multi-agent systems via model predictive control based on position-only measurements. IEEE Trans Ind Inf, 2013, 9: 377–385

  27. 27

    Zhang H, Cheng Z, Chen G, et al. Model predictive flocking control for second-order multi-agent systems with input constraints. IEEE Trans Circuit Syst I Regul Pap, 2015, 62: 1599–1606

Download references

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61473240, 61528301), National Natural Science Foundation of Fujian Province (Grant No. 2017J01119), 111 Project (Grant No. B17048), and State Key Laboratory of Intelligent Control and Decision of Complex Systems.

Author information

Correspondence to Fei Chen.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, F., Ren, W. & Lin, Z. Multi-leader multi-follower coordination with cohesion, dispersion, and containment control via proximity graphs. Sci. China Inf. Sci. 60, 110204 (2017). https://doi.org/10.1007/s11432-017-9146-1

Download citation

Keywords

  • cooperative control
  • multi-agent system
  • containment control
  • cohesion
  • dispersion
  • collision-free movement