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Finite-time formation control for multi-agent systems. (English) Zbl 1180.93006

Summary: We develop a new finite-time formation control framework for multi-agent systems with a large population of members. In this framework, we divide the formation information into two independent parts, namely, the global information and the local information. The global formation information decides the geometric pattern of the desired formation. Furthermore, it is assumed that only a small number of agents, which are responsible for the navigation of the whole team, can obtain the global formation information, and the other agents regulate their positions by the local information in a distributed manner. This approach can greatly reduce the data exchange and can easily realize various kinds of complex formations. As a theoretical preparation, we first propose a class of nonlinear consensus protocols, which ensures that the related states of all agents will reach an agreement in a finite time under suitable conditions. And then we apply these consensus protocols to the formation control, including time-invariant formation, time-varying formation and trajectory tracking, respectively. It is shown that all agents will maintain the expected formation in a finite time. Finally, several simulations are worked out to illustrate the effectiveness of our theoretical results.

MSC:

93A14 Decentralized systems
93B50 Synthesis problems
94C15 Applications of graph theory to circuits and networks
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[1] Arkin, R.C., Behavior-based robotics, (1998), MIT Press Cambridge, MA
[2] Balch, T.; Arkin, R.C., Behavior-based formation control for multirobot teams, IEEE transactions on robotics and automatation, 14, 6, 926-939, (1998)
[3] Bhat, S.P.; Bernstein, D.S., Finite-time stability of continuous autonomous systems, SIAM journal on control and optimization, 38, 3, 751-766, (2000) · Zbl 0945.34039
[4] Cortés, J., Finite-time convergent gradient flows with applications to network consensus, Automatica, 42, 11, 1993-2000, (2006) · Zbl 1261.93058
[5] Couzin, I.D.; Krause, J.; Franks, N.R.; Levin, S.A., Effective leadership and decision-making in animal groups on themove, Nature, 433, 3, 513-516, (2005)
[6] Egerstedt, M.; Hu, X., Formation constrained multi-agent control, IEEE transactions on robotics and automation, 17, 6, 947-951, (2001)
[7] Egerstedt, M.; Hu, X.; Stotsky, A., Control of mobile platforms using a virtual vehicle approach, IEEE transactions on automatic control, 46, 11, 1777-1782, (2001) · Zbl 1015.93040
[8] Fax, J.A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control, 49, 9, 1465-1476, (2004) · Zbl 1365.90056
[9] Haimo, V.T., Finite time controllers, SIAM journal control and optimization, 24, 4, 760-770, (1986) · Zbl 0603.93005
[10] Hartman, P., Ordinary differential equations, (1982), Birkhäuser · Zbl 0125.32102
[11] Johansson, B.; Speranzon, A.; Johansson, M.; Johansson, K.H., On decentralized negotiation of optimal consensus, Automatica, 44, 4, 1175-1179, (2008) · Zbl 1283.93021
[12] Keviczky, T., & Johansson, K. H. (2008). A study on distributed model predictive consensus. In Proceedings of the 17th world congress, the international federation of automatic control (pp. 1516-1521)
[13] Lafferriere, G.; Williams, A.; Caughman, J.; Veerman, J.J.P., Decentralized control of vehicle formations, Systems & control letters, 54, 899-910, (2005) · Zbl 1129.93303
[14] Leonard, N. E., & Fiorelli, E. (2001). Virtual leaders, artificial potentials and coordinated control of groups. In Proceedings of the 40th IEEE conference on decision and control (pp. 2968-2973)
[15] Lewis, M.A.; Tan, K.-H., High precision formation control of mobile robots using virtual structures, Autonomous robots, 4, 387-403, (1997)
[16] Lumelsky, V.J.; Harinarayan, K.R., Decentralized motion planning for multiple mobile robots: the cocktail party model, Autonomous robots, 4, 1, 121-135, (1997)
[17] Martínez, S.; Cortés, J.; Bullo, F., Motion coordination with distributed information, IEEE control systems magazine, 27, 4, (2007)
[18] 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
[19] Olfati-Saber, R.; Murray, R.M., Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301
[20] Ren, W. (2006). Consensus based formation control strategies for multi-vehicle systems. In Proceedings of the 2006 american control conference (pp. 4237-4242)
[21] Ren, W., Multi-vehicle consensus with a time-varying reference state, Systems & control letters, 56, 474-483, (2007) · Zbl 1157.90459
[22] Ren, W.; Beard, R.W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control, 50, 5, 655-661, (2005) · Zbl 1365.93302
[23] Ren, W.; Beard, R.W.; Atkins, E.M., Information consensus in multi-vehicle cooperative control, IEEE control systems magazine, 27, 2, 71-82, (2007)
[24] Shao, J.; Xie, G.; Wang, L., Leader-following formation control of multiple mobile vehicles, IET control theory and applications, 1, 2, 545-552, (2007)
[25] Sundaram, S., & Hadjicostis, C. N. (2007). Finite-time distributed consensus in graphs with time-invariant topologies. In Proceedings of the american control conference (pp. 711-716)
[26] Wang, X., & Hong, Y. (2008). Finite-time consensus for multi-agent networks with second-order agent dynamics. In Proceedings of the 17th world congress, the international federation of automatic control (pp. 15185-15190)
[27] Xiao, F. (2008). Consensus problems in networks of multiple autonomous agents, Ph.D. thesis, Peking University
[28] Xiao, F., & Wang, L. (2007). Reaching agreement in finite time via continuous local state feedback. In Proceedings of the 26th chinese control conference(pp. 711-715)
[29] Xiao, F.; Wang, L., Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE transactions on automatic control, 53, 8, 1804-1816, (2008) · Zbl 1367.93255
[30] Xiao, F.; Wang, L., Consensus protocols for discrete-time multi-agent systems with time-varying delays, Automatica, 44, 2577-2582, (2008) · Zbl 1155.93312
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