SCIENCE CHINA Information Sciences, Volume 60, Issue 11: 110204(2017) https://doi.org/10.1007/s11432-017-9146-1

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

More info
  • ReceivedApr 11, 2017
  • AcceptedJun 23, 2017
  • PublishedOct 10, 2017


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 showthe validity of the proposed algorithms.


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.


[1] Qu Z. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Berlin: Springer, 2009. Google Scholar

[2] Bullo F, Cortés J, Mart'ınez S. Distributed Control of Robotic Networks. Princeton: Princeton University Press, 2009. Google Scholar

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

[4] Chen F, Ren W. Distributed Consensus in Networks. Hoboken: John Wiley & Sons, 2016. Google Scholar

[5] Ji M, Ferrari-Trecate G, Egerstedt M. Containment control in mobile networks. IEEE Trans Automat Contr, 2008, 53: 1972-1975 CrossRef Google Scholar

[6] Li R, Shi Y J, Teo K L. Coordination arrival control for multi-agent systems. Int J Robust NOnlinear Control, 2016, 26: 1456-1474 CrossRef Google Scholar

[7] Engelberger J F. Robotics in Practice: Management and Applications of Industrial Robots. Berlin: Springer, 2012. Google Scholar

[8] Iyengar S, Brooks R. Distributed Sensor Networks: Sensor Networking and Applications. Boca Raton: CRC Press, 2016. Google Scholar

[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 CrossRef Google Scholar

[10] Li J, Ren W, Xu S. Distributed Containment Control with Multiple Dynamic Leaders for Double-Integrator Dynamics Using Only Position Measurements. IEEE Trans Automat Contr, 2012, 57: 1553-1559 CrossRef Google Scholar

[11] Wang X, Li S, Shi P. Distributed finite-time containment control for double-integrator multiagent systems.. IEEE Trans Cybern, 2014, 44: 1518-1528 CrossRef PubMed Google Scholar

[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 CrossRef Google Scholar

[13] Meng Z, Lin Z, Ren W. Leader-follower swarm tracking for networked Lagrange systems. Syst Control Lett, 2012, 61: 117-126 CrossRef Google Scholar

[14] Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica, 2008, 44: 846-850 CrossRef Google Scholar

[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. Google Scholar

[16] Chen F, Ren W, Cao Y. Surrounding control in cooperative agent networks. Syst Control Lett, 2010, 59: 704-712 CrossRef Google Scholar

[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 CrossRef Google Scholar

[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. Google Scholar

[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. Google Scholar

[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 CrossRef Google Scholar

[21] Ji M, Egerstedt M. Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Robot, 2007, 23: 693-703 CrossRef Google Scholar

[22] Sabattini L, Secchi C, Chopra N. Distributed control of multirobot systems with global connectivity maintenance. IEEE Trans Robot, 2013, 29: 1326-1332 CrossRef Google Scholar

[23] Olfati-Saber R. Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory. IEEE Trans Automat Contr, 2006, 51: 401-420 CrossRef Google Scholar

[24] Tanner H G, Jadbabaie A, Pappas G J. Flocking in fixed and switching networks. IEEE Trans Automat Contr, 2007, 52: 863-868 CrossRef Google Scholar

[25] Zavlanos M M, Pappas G J. Distributed connectivity control of mobile networks. IEEE Trans Robot, 2008, 24: 1416-1428 CrossRef Google Scholar

[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 CrossRef Google Scholar

[27] Zhang H T, Cheng Z, Chen G. Model predictive flocking control for second-order multi-agent systems with input constraints. IEEE Trans Circuits Syst I, 2015, 62: 1599-1606 CrossRef Google Scholar

  • Figure 1

    An illustration of the function $r_{ij}$ with the parameters: $r_{\rm~F}=1$, $d_2=0.4$, $a_1=0.84$, $a_2=-1$.

  • Figure 2

    Snapshots for the stationary leaders case. The leaders are denoted by “$\diamond$”, while the followers are denoted by “*”. The parameters are specified as follows: $r_{\rm~L}=5$, $r_{\rm~F}=1$, $d_1=0.8$, $d_2=0.4$, $a_2=-1$, $a_1=a_2(d_2^2-r_{\rm~F}^2)$, $b_{ik}=1$ for all $i~\in~\mathcal{V}_{\rm~F}$ and $k~\in~\left(\mathcal{N}_i~\cap~\mathcal{V}_{\rm~L}\right)$. (a) $t=0~{\rm~s}$; (b) $t=0.25~{\rm~s}$; (c) $t=0.75~{\rm~s}$; (d) $t=1~{\rm~s}$.

  • Figure 3

    (Color online) Stationary leaders: the trajectory of $\|x_i-x_j\|$ for $(i,j)~\in~\mathcal{E}(0)$, $i~\in~\mathcal{V}_{\rm~F}$ and $j~\in~\mathcal{V}_{\rm~F}$ with the dashed line $\|x_i-x_j\|=d_1$.

  • Figure 4

    (Color online) Stationary leaders: the trajectory of $\|x_i-x_j\|$ for $(i,j)~\in~\mathcal{E}(0)$, $i~\in~\mathcal{V}_{\rm~L}$, and $j~\in~\mathcal{V}_{\rm~F}$ with the dashed line $\|x_i-x_j\|=r_{\rm~L}$.

  • Figure 5

    Snapshots for the moving leaders case. (a) $t=0~{\rm~s}$; (b) $t=0.25~{\rm~s}$; (c) $t=0.75~{\rm~s}$; (d) $t=1~{\rm~s}$.

  • Figure 7

    (Color online) Moving leaders: the trajectory of $\|x_i-x_j\|$ for $(i,j)~\in~\mathcal{E}(0)$, $i~\in~\mathcal{V}_{\rm~L}$, and $j~\in~\mathcal{V}_{\rm~F}$ with the dashed line $\|x_i-x_j\|=r_{\rm~L}$.

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号