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Leader-follower swarm tracking for networked Lagrange systems. (English) Zbl 1250.93014
Summary: In this paper, swarm tracking problems with group dispersion and cohesion behaviors are discussed for a group of Lagrange systems. The agent group is separated into two subgroups. One is called the leader group, whose members are encapsulated with the desired generalized coordinates and generalized coordinate derivatives. The other one, referred to as the follower group, is guided by the leader group. The objective is to guarantee distributed tracking of generalized coordinate derivatives for the followers and to drive the generalized coordinates of the followers close to the convex hull formed by those of the leaders. Both the case of constant leaders’ generalized coordinate derivatives and the case of time-varying leaders’ generalized coordinate derivatives are considered. The proposed control algorithms are shown to achieve velocity matching, connectivity maintenance and collision avoidance. In addition, the sum of the steady-state distances between the followers and the convex hull formed by the leaders is shown to be bounded and the bound is explicitly given. Simulation results are presented to validate the effectiveness of theoretical conclusions.

MSC:
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
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[1] Ren, W.; Beard, R.W.; Atkins, E.M., Information consensus in multivehicle cooperative control: collective group behavior through local interaction, IEEE control systems magazine, 27, 2, 71-82, (2007)
[2] Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138
[3] Wang, P.K.C.; Hadaegh, F.Y., Coordination and control of multiple microspacecraft moving in formation, Journal of the astronautical sciences, 44, 3, 315-355, (1996)
[4] Smith, R.S.; Hadaegh, F.Y., Distributed estimation, communication and control for deep space formations, IET control theory & applications, 1, 2, 445-451, (2007)
[5] Meng, Z.; Ren, W.; You, Z., Decentralised cooperative attitude tracking using modified rodriguez parameters based on relative attitude information, International journal of control, 83, 12, 2427-2439, (2010) · Zbl 1205.93009
[6] Ren, W., Distributed cooperative attitude synchronization and tracking for multiple rigid bodies, IEEE transactions on control systems technology, 18, 2, 383-392, (2010)
[7] Chung, S.-J.; Ahsun, U.; Slotine, J.-J.E., Application of synchronization to formation flying spacecraft: Lgrangian approach, Journal of guidance, control, and dynamics, 32, 2, 512-526, (2009)
[8] Chung, S.-J.; Slotine, J.-J.E., Cooperative robot control and concurrent synchronization of Lagrangian systems, IEEE transations on robotics, 25, 3, 686-700, (2009)
[9] Ren, W., Distributed leaderless consensus algorithms for networked euler – lagrange systems, International journal of control, 82, 11, 2137-2149, (2009) · Zbl 1175.93074
[10] N. Chopra, D.M. Stipanovi, M.W. Spong, On synchronization and collision avoidance for mechanical systems, in: 2008 American Control Conference,Westin Seattle Hotel, Seattle, Washington, USA, 2008, pp. 3713-3718.
[11] Min, H.; Sun, F.; Wang, S.; Li, H., Distributed adaptive consensus algorithm for networked euler – lagrange systems, IET control theory and applications, 5, 1, 145-154, (2011)
[12] Hokayem, P.F.; Stipanovic, D.M.; Spong, M.W., Semiautonomous control of multiple networked Lagrangian systems, International journal of robust and nonlinear control, 19, 18, 2040-2055, (2008) · Zbl 1192.93012
[13] Gazi, V., Swarm aggregations using artificial potentials and sliding-mode control, IEEE transactions on robotics, 21, 6, 1208-1214, (2005)
[14] J. Yao, R. Ordonez, V. Gazi, Swarm tracking using artificial potentials and sliding mode control, in: Proceedings of the IEEE Conference on Decision and Control, San Diego, CA, USA, 2006, pp. 4670-4675.
[15] Li, W., Stability analysis of swarms with general topology, IEEE transactions on systems, man and cybernetics, part B: (cybernetics), 38, 4, 1084-1097, (2008)
[16] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[17] M.M. Zavlanos, A. Jadbabaie, G.J. Pappas, Flocking while preserving network connectivity, in: Proceedings of the IEEE Conference on Decision and Control, New Orleans, LA, USA, 2007, pp. 2919-2924.
[18] Amir Ajorlou, A.M.; Aghdam, A.G., A class of bounded distributed control strategies for connectivity preservation in multi-agent systems, IEEE transactions on automatic control, 55, 12, 2828-2833, (2010) · Zbl 1368.93418
[19] Y. Cao, W. Ren, Distributed coordinated tracking via a variable structure approach - part ii: Swarm tracking in: Proceedings of the American Control Conference, Marriott Waterfront, Baltimore, MD, USA, 2010, pp. 4750-4755.
[20] Hokayem, P.F.; Stipanovic, D.M.; Spong, M.W., Coordination and collision avoidance for Lagrangian systems, Applied mathematics and computation, 217, 3, 1085-1094, (2010) · Zbl 1201.93008
[21] Cheah, C.C.; How, S.P.; Slotine, J.J.E., Region-based shape control for a swarm of robots, Automatica, 45, 10, 2406-2411, (2009) · Zbl 1179.93024
[22] Ji, M.; Ferrari-Trecate, G.; Egerstedt, M.; Buffa, A., Containment control in mobile networks, IEEE transactions on automatic control, 53, 8, 1972-1975, (2008) · Zbl 1367.93398
[23] Y. Cao, W. Ren, Containment control with multiple stationary or dynamic leaders under a directed interaction graph, in: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, PR China, 2009, pp. 3014-3019.
[24] Notarstefano, G.; Egerstedt, M.; Haque, M., Containment in leader-follower networks with switching communication topologies, Automatica, 47, 5, 1035-1040, (2011) · Zbl 1233.93009
[25] Dimarogonas, D.V.; Tsiotras, P.; Kyriakopoulos, K.J., Leader-follower cooperative attitude control of multiple rigid bodies, Systems and control letters, 58, 6, 429-435, (2009) · Zbl 1161.93002
[26] Meng, Z.; Ren, W.; You, Z., Distributed finite-time attitude containment control for multiple rigid bodies, Automatica, 46, 12, 2092-2099, (2010) · Zbl 1205.93010
[27] Tanner, H.G.; Jadbabaie, A.; Pappas, G.J., Flocking in fixed and switching networks, IEEE transactions on automatic control, 52, 5, 863-868, (2007) · Zbl 1366.93414
[28] Slotine, J.-J.E.; Li, W., Applied nonlinear control, (1991), Prentice Hall Englewood Cliffs, New Jersey
[29] Bai, H.; Arcak, M.; Wen, J.T.-Y., Rigid body attitude coordination without inertial frame information, Automatica, 44, 12, 3170-3175, (2008) · Zbl 1153.93422
[30] Shi, H.; Wang, L.; Chu, T., Flocking of multi-agent systems with a dynamic virtual leader, International journal of control, 82, 1, 43-58, (2009) · Zbl 1154.93371
[31] Su, H.; Wang, X.; Lin, Z., Flocking of multi-agents with a virtual leader, IEEE transactions on automatic control, 54, 2, 293-307, (2009) · Zbl 1367.37059
[32] A.R. Pereira, L. Hsu, R. Ortega, Globally stable adaptive formation control of Euler-Lagrange agents via potential functions, in: Proceedings of the American Control Conference, Hyatt Regency Riverfront, St. Louis, MO, USA, 2009, pp. 2606-2611.
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