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.
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References
Qu Z. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Berlin: Springer, 2009
Bullo F, Cortés J, Martínez S. Distributed Control of Robotic Networks. Princeton: Princeton University Press, 2009
Yu W, Wen G, Chen G, et al. Distributed Cooperative Control of Multi-agent Systems. Hoboken: John Wiley & Sons, 2016
Chen F, Ren W. Distributed Consensus in Networks. Hoboken: John Wiley & Sons, 2016
Ji M, Ferrari-Trecate G, Egerstedt M, et al. Containment control in mobile networks. IEEE Trans Autom Control, 2008, 53: 1972–1975
Rui L, Shi Y, Teo K. Coordination arrival control for multi-agent systems. Int J Robust Nonlinear Control, 2016, 26: 1456–1474
Engelberger J F. Robotics in Practice: Management and Applications of Industrial Robots. Berlin: Springer, 2012
Iyengar S, Brooks R. Distributed Sensor Networks: Sensor Networking and Applications. Boca Raton: CRC Press, 2016
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
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
Wang X, Li S, Shi P. Distributed finite-time containment control for double-integrator multiagent systems. IEEE Trans Cyber, 2014, 44: 1518–1528
Mei J, Ren W, Ma G. Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph. Automatica, 2012, 48: 653–659
Meng Z, Lin Z, Ren W. Leader-follower swarm tracking for networked Lagrange systems. Syst Control Lett, 2012, 61: 117–126
Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica, 2008, 44: 846–850
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
Chen F, Ren W, Cao Y. Surrounding control in cooperative agent networks. Syst Control Lett, 2010, 59: 704–712
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
Chen F, Ren W, Lin Z L. Multi-agent coordination with cohesion, dispersion, and containment control. In: Proceedings of American Control Conference, Baltimore, 2010
Lalish E, Morgansen K A, Tsukamaki T. Decentralized reactive collision avoidance for multiple unicycle-type vehicles. In: Proceedings of American Control Conference, Seattle, 2008
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
Ji M, Egerstedt E. Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Robot, 2007, 23: 693–703
Sabattini L, Secchi C, Chopra N. Distributed control of multirobot systems with global connectivity maintenance. IEEE Trans Robot, 2013, 29: 1326–1332
Olfati-Saber R. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Control, 2006, 51: 401–420
Tanner H G, Jadbabaie A, Pappas G J. Flocking in fixed and switching networks. IEEE Trans Autom Control, 2007, 52: 863–868
Zavlanos M M, Pappas G J. Distributed connectivity control of mobile networks. IEEE Trans Robot, 2008, 24: 1416–1428
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
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
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.
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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
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DOI: https://doi.org/10.1007/s11432-017-9146-1