This paper studies the complete state tracking control of an underactuated ship with only two controls, namely, surge force and yaw moment. A novel finite-time switching controller is developed guaranteeing that the ship can track a reference trajectory generated by a virtual ship. The solution is based on the inherent cascaded interconnected structure of the ship dynamics. As opposed to the previous works, the assumptions used in this work are more relaxed in the sense that the reference surge and yaw velocities are allowed to be zero at the same time. Simulation results are given to serve the purpose of demonstrating and validating the proposed tracking methodology.
Issue Section:
Technical Brief
References
1.
Reyhanoglu
, M.
, 1997
, “Exponential Stabilization of an Underactuated Autonomous Surface Vessel
,” Automatica
, 33
(12
), pp. 2249
–2254
.10.1016/S0005-1098(97)00141-62.
Murray
, R. M.
, and Sastry
, S. S.
, 1993
, “Nonholonomic Motion Planning: Steering Using Sinusoids
,” IEEE Trans. Autom. Control
, 38
(5
), pp. 700
–716
.10.1109/9.2772353.
Pettersen
, K. Y.
, 1996
, “Exponential Stabilization of Underactuated Vehicles
,” Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway.4.
Ghommam
, J.
, Mnif
, F.
, Benali
, A.
, and Derbel
, N.
, 2006
, “Asymptotic Backstepping Stabilization of an Underactuated Surface Vessel
,” IEEE Trans. Control Syst. Technol.
, 14
(6
), pp. 1150
–1157
.10.1109/TCST.2006.8802205.
Ding
, F. G.
, Wu
, J.
, and Wang
, Y. H.
, 2013
, “Stabilization of an Underactuated Surface Vessel Based on Adaptive Sliding Mode and Backstepping Control
,” Math. Probl. Eng.
, 2013
, p. 324954
.10.1155/2013/3249546.
Pettersen
, K. Y.
, and Nijmeijer
, H.
, 2001
, “Underactuated Ship Tracking Control: Theory and Experiments
,” Int. J. Control
, 74
(14
), pp. 1435
–1446
.10.1080/002071701100720397.
Jiang
, Z. P.
, and Nijmeijer
, H.
, 1999
, “A Recursive Technique for Tracking Control of Nonholonomic Systems in Chained Form
,” IEEE Trans. Autom. Control
, 44
(2
), pp. 265
–279
.10.1109/9.7462538.
Godhavn
, J. M.
, Fossen
, T. I.
, and Berge
, S. P.
, 1998
, “Nonlinear and Adaptive Backstepping Designs for Tracking Control of Ships
,” Int. J. Adapt. Control Signal Process.
, 12
(8
), pp. 239
–248
.10.1002/(SICI)1099-1115(199812)12:8<649::AID-ACS515>3.0.CO;2-P9.
Jiang
, Z. P.
, 2002
, “Global Tracking Control of Underactuated Ships by Lyapunov's Direct Method
,” Automatica
, 38
(2
), pp. 301
–309
.10.1016/S0005-1098(01)00199-610.
Do
, K. D.
, Jiang
, Z. P.
, and Pan
, J.
, 2002
, “Underactuated Ship Global Tracking Under Relaxed Conditions
,” IEEE Trans. Autom. Control
, 47
(9
), pp. 1529
–1536
.10.1109/TAC.2002.80275511.
Chwa
, D.
, 2011
, “Global Tracking Control of Underactuated Ships With Input and Velocity Constraints Using Dynamic Surface Control Method
,” IEEE Trans. Control Syst. Technol.
, 19
(6
), pp. 1357
–1370
.10.1109/TCST.2010.209052612.
Meng
, W.
, Guo
, C.
, Liu
, Y.
, and Shen
, Z. P.
, 2012
, “Sliding Mode Trajectory Tracking Control of Underactuated Surface Vessels
,” Proceedings of the International Conference on Automatic Control and Artificial Intelligence
, Xiamen, China
, Mar. 3–5, pp. 1866
–1870
.13.
Ghommam
, J.
, Mnif
, F.
, Benali
, A.
, and Derbel
, N.
, 2009
, “Nonsingular Serret–Frenet Based Path Following Control for an Underactuated Surface Vessel
,” ASME J. Dyn. Syst., Meas., Control
, 131
(2
), p. 021006
.10.1115/1.302313914.
Liu
, Y.
, Guo
, C.
, Shen
, Z. P.
, Liu
, Y.
, and Guo
, D.
, 2010
, “Stable Adaptive Neural Network Control of Path Following for Underactuated Ships
,” J. Control Theory Appl.
, 27
(2
), pp. 169
–174
.15.
Oh
, S. R.
, and Sun
, J.
, 2010
, “Path Following of Underactuated Marine Surface Vessels Using Line-of-Sight Based Model Predictive Control
,” Ocean Eng.
, 37
(2–3
), pp. 289
–295
.10.1016/j.oceaneng.2009.10.00416.
Meng
, W.
, Guo
, C.
, and Liu
, Y.
, 2012
, “Robust Adaptive Path Following for Underactuated Surface Vessels With Uncertain Dynamics
,” J. Mar. Sci. Appl.
, 11
(2
), pp. 244
–250
.10.1007/s11804-012-1129-y17.
Aguiar
, A. P.
, and Hespanha
, J. P.
, 2007
, “Trajectory-Tracking and Path-Following of Underactuated Autonomous Vehicles With Parametric Modeling Uncertainty
,” IEEE Trans. Autom. Control
, 52
(8
), pp. 1362
–1379
.10.1109/TAC.2007.90273118.
Lefeber
, E.
, 2000
, “Tracking Control of Nonlinear Mechanical Systems
,” Ph.D. thesis, University of Twente, Twente, The Netherlands.19.
Do
, K. D.
, and Pan
, J.
, 2005
, “Global Tracking Control of Underactuated Ships With Nonzero Off-Diagonal Terms in Their System Matrices
,” Automatica
, 41
(1
), pp. 87
–95
.10.1016/j.automatica.2004.08.00520.
Huang
, X. Q.
, Lin
, W.
, and Yang
, B.
, 2005
, “Global Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems
,” Automatica
, 41
(5
), pp. 881
–888
.10.1016/j.automatica.2004.11.03621.
Qian
, C. J.
, and Lin
, W.
, 2001
, “Non-Lipschitz Continuous Stabilizers for Nonlinear Systems With Uncontrollable Unstable Linearization
,” Syst. Control Lett.
, 42
(3
), pp. 185
–200
.10.1016/S0167-6911(00)00089-XCopyright © 2014 by ASME
You do not currently have access to this content.
