Leader-following coordination of multiple UUVs formation under two independent topologies and time-varying delays

Abstract

The new method which uses the consensus algorithm to solve the coordinate control problems of multiple unmanned underwater vehicles (multi-UUVs) formation in the case of leader-following is adapted. As the communication between the UUVs is difficult and it is easy to be interfered under the water, time delay is assumed to be time-varying during the members communicate with each other. Meanwhile, the state feedback linearization method is used to transfer the nonlinear and coupling model of UUV into double-integrator dynamic. With this simplified double-integrator math model, the UUV formation coordinate control is regarded as consensus problem with time-varying communication delays. In addition, the position and velocity topologies are adapted to reduce the data volume in each data packet which is sent between members in formation. With two independent topologies designed, two cases of communication delay which are same and different are considered and the sufficient conditions are proposed and analyzed. The stability of the multi-UUVs formation is proven by using Lyapunov-Razumikhin theorem. Finally, the simulation results are presented to confirm and illustrate the theoretical results.

Keywords

multiple unmanned underwater vehicles formation / consensus algorithm / Lyapunov-Razumikhin theory / time-varying delay / state feedback linearization method

References

[1] ChenQiangUnmanned underwater vehicle [M]., 2014Beijing, ChinaNational Defense Industry Press

[2] YuhJ. Design and control of autonomous underwater robots: A survey [J]. Autonomous Robots, 2000, 8(1): 7-24

[3] YanZ-p, LiuY-b, ZhouJ-j, WuDi. Path following control of an AUV under the current using the SVR-ADRC [J/OL]. Journal of Applied Mathematics, 2014, 2014: 1-12

[4] PengZ-h, WangD, ShiY, WangH, WangWei. Containment control of networked autonomous underwater vehicles with model uncertainty and ocean disturbances guided by multiple leaders [J]. Information Sciences, 2015, 316: 163-179

[5] LapierreL, SoetantoD. Nonlinear path-following control of an AUV [J]. Ocean engineering, 2007, 34(11): 1734-1744

[6] ZhuD-q, HuaX, SunBing. A neurodynamics control strategy for real-time tracking control of autonomous underwater vehicles [J]. Journal of Navigation, 2014, 67(1): 113-127

[7] JiaH-m, ZhangL-j, BianX-q, YanZ-p, ChengX-q, ZhouJ-jia. A nonlinear bottom-following controller for underactuated autonomous underwater vehicles [J]. Journal of Central South University, 2012, 19(5): 1240-1248

[8] ZhuD-q, SunBing. The bio-inspired model based hybrid sliding-mode tracking control for unmanned underwater vehicles [J]. Engineering Applications of Artificial Intelligence, 2013, 26(10): 2260-2269

[9] ZhangL-j, QiX, PangY-jie. Adaptive output feedback control based on DRFNN for AUV [J]. Ocean Engineering, 2009, 36(9): 716-722

[10] ZhangL-j, ZhaoJ-m, QiX, JiaH-ming. NN-adaptive output feedback tracking control for a class of discrete-time non-affine systems with a dynamic compensator [J]. International Journal of Control, 2013, 86(6): 1008-1017

[11] LiS-h, WangX-y, ZhangL-jun. Finite-time output feedback tracking control for autonomous underwater vehicles [J]. IEEE Journal of Oceanic Engineering, 2015, 40(3): 727-751

[12] CuiR-x, GeS S, HowB V E, ChooY S. Leader–follower formation control of underactuated autonomous underwater vehicles [J]. Ocean Engineering, 2010, 37(17): 1491-1502

[13] PengZ-h, WangD, WangH, WangWei. Distributed coordinated tracking of multiple autonomous underwater vehicles [J]. Nonlinear Dynamics, 2014, 78(2): 1261-1276

[14] LinP, JiaY-min. Average consensus in networks of multi-agents with both switching topology and coupling time-delay [J]. Physica A: Statistical Mechanics and its Applications, 2008, 387(1): 303-313

[15] HuJ-p, LinY S. Consensus control for multi-agent systems with double-integrator dynamics and time delays [J]. IET Control Theory & Applications, 2010, 4(1): 109-118

[16] PengZ-h, WangD, ZhangH-w, LinY-jin. Cooperative output feedback adaptive control of uncertain nonlinear multi-agent systems with a dynamic leader [J]. Neurocomputing, 2015, 149: 132-141

[17] YangH-z, WangC-f, ZhangF-min. A decoupled controller design approach for formation control of autonomous underwater vehicles with time delays [J]. IET Control Theory & Applications, 2013, 7(15): 1950-1958

[18] LiS-h, WangX-yu. Finite-time consensus and collision avoidance control algorithms for multiple AUVs [J]. Automatica, 2013, 49(11): 3359-3367

[19] HuZ-l, MaC, ZhangL-x, AarneH, TasawarH, BashirA. Formation control of impulsive networked autonomous underwater vehicles under fixed and switching topologies [J]. Neurocomputing, 2015, 147: 291-298

[20] OlfatiS R, MurrayR M. Consensus problems in networks of agents with switching topology and time-delays [J]. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533

[21] RenW, BeardR W. Consensus seeking in multiagent systems under dynamically changing interaction topologies [J]. IEEE Transactions on Automatic Control, 2005, 50(5): 655-661

[22] LiuK-e, XieG-m, WangLong. Containment control for second-order multi-agent systems with time-varying delays [J]. Systems & Control Letters, 2014, 67: 24-31

[23] HuJ-p, HongY-guang. Leader-following coordination of multi-agent systems with coupling time delays [J]. Physica A: Statistical Mechanics and Its Applications, 2007, 374(2): 853-863

[24] FaxJ A, MurrayR M. Information flow and cooperative control of vehicle formations [J]. IEEE Transactions on Automatic Control, 2004, 49(9): 1465-1476

[25] RenW, BeardR W. Consensus seeking in multiagent systems under dynamically changing interaction topologies [J]. IEEE Transactions on Automatic Control, 2005, 50(5): 655-661

[26] FossenT IHandbook of marine craft hydrodynamics and motion control [M], 2011

[27] HaleJ K, LunelS M VIntroduction to functional differential equations [M], 2013

[28] MoonY S, ParkP, KwonW H, LeeY S. Delay-dependent robust stabilization of uncertain state-delayed systems [J]. International Journal of Control, 2001, 74(14): 1447-1455

[29] BodyS, GhaouiL E, FeronE, BalakrishnanVLinear matrix inequalities in system and control theory [M]., 1994

[30] YanZ-p, YuH-m, LiB-yin. Bottom-following control for an underactuated unmanned undersea vehicle using integralterminal sliding mode control [J]. Journal of Central South University, 2015, 22(11): 4193-4204