Path-tracking control of underactuated ships under tracking error constraints

Abstract

This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the distance from the ship to the reference path always be within a specified value. The control design is based on a global exponential disturbance observer, a transformation of the ship dynamics to an almost spherical form, an interpretation of the tracking errors in an earth-fixed frame, an introduction of dynamic variables to compensate for relaxation of the reference path generation, p-times differentiable step functions, and backstepping and Lyapunov’s direct methods. The effectiveness of the proposed results is illustrated through simulations.

Keywords

underactuated ship / path-tracking / error constraint / Lyapunov method / backstepping method

References

[1] Aguiar AP, Pascoal AM. Regulation of a nonholonomic autonomous underwater vehicle with parametric modeling uncertainty using Lyapunov functions. Proceedings of 40th IEEE Conference on Decision and Control, 2001, 5: 4178-4183

[2] Aicardi M, Casalino G, Indiveri G, Aguiar A, Encarnação P, Pascoal A. A planar path following controller for underactuated marine vehicles. Proceedings of the Ninth IEEE Mediterranean Conference on Control and Automation, 2001, 1-6

[3] Brockett RW. Brockett RW, Millman RS, Sussmann HJ. Asymptotic stability and feedback stabilization. Differential Geometric Control Theory, 1983, 181-191

[4] Chwa D. Global tracking control of underactuated ships with input and velocity constraints using dynamic surface control method. IEEE Transactions on Control Systems Technology, 2011, 19(6): 1357-1370

[5] Do KD. Control of nonlinear systems with output tracking error constraints and its application to magnetic bearings. International Journal of Control, 2010, 83(6): 1199-1216

[6] Do KD. Practical control of underactuated ships. Ocean Engineering, 2010, 37(13): 1111-1119

[7] Do KD. Global inverse optimal tracking control of underactuated omni-directional intelligent navigators (ODINs). Journal of Marine Science and Application, 2015, 14(1): 1-13

[8] Do KD, Jiang ZP, Pan J. Underactuated ship global tracking under relaxed conditions. IEEE Transactions on Automatic Control, 2002, 47(9): 1529-1536

[9] Do KD, Jiang ZP, Pan J. Universal controllers for stabilization and tracking of underactuated ships. Systems & Control Letters, 2002, 47(4): 299-317

[10] Do KD, Jiang ZP, Pan J. On global tracking control of a VTOL aircraft without velocity measurements. IEEE Transactions on Automatic Control, 2003, 48(12): 2212-2217

[11] Do KD, Jiang ZP, Pan J. Robust adaptive path following of underactuated ships. Automatica, 2004, 40(6): 929-944

[12] Do KD, Pan J. State- and output-feedback robust path-following controllers for underactuated ships using Serret-Frenet frame. Ocean Engineering, 2004, 31(5–6): 587-613

[13] Do KD, Pan J. Global tracking control of underactuated ships with nonzero off-diagonal terms in their system matrices. Automatica, 2005, 41(1): 87-95

[14] Do KD, Pan J. Underactuated ships follow smooth paths with integral actions and without velocity measurements for feedback: Theory and experiments. IEEE Transactions on Control Systems Technology, 2006, 14(2): 308-322

[15] Encarnação P, Pascoal A, Arcak M. Path following for autonomous marine craft. Proceedings of the 5th IFAC Conference on Manoeuvring and Control of Marine Craft, 2000, 117-122

[16] Fossen TI. Handbook of marine craft hydrodynamics and motion control, 2011, West Sussex, England: John Wiley & Sons, 133-183

[17] Fredriksen E, Pettersen KY. Global Kappa-exponential way-point maneuvering of ships: Theory and experiments. Automatica, 2006, 42(4): 677-687

[18] Ghommam J, Mnif F, Benali A, Derbel N. Nonsingular Serret-Frenet based path following control for an underactuated surface vessel. Journal of Dynamic Systems, Measurement, and Control, 2008, 131(2): 021006

[19] Godhavn JM, Fossen TI, Berge SP. Non-linear and adaptive backstepping designs for tracking control of ships. International Journal of Adaptive Control and Signal Processing, 1998, 12(8): 649-670

[20] Jiang ZP. Global tracking control of underactuated ships by Lyapunov’s direct method. Automatica, 2002, 38(2): 301-309

[21] Jiang ZP, Nijmeijer H. A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Transactions on Automatic Control, 1999, 44(2): 265-279

[22] Khalil HK. Nonlinear Systems, 2002, 323-325

[23] Krstic M, Kanellakopoulos I, Kokotović PV. Nonlinear and adaptive control design, 1995, New York, USA: Wiley

[24] Lapierre L, Jouvencel B. Robust nonlinear path-following control of an AUV. IEEE Journal of Oceanic Engineering, 2008, 33(2): 89-102

[25] Lee TC, Jiang ZP. New cascade approach for global κ-exponential tracking of underactuated ships. IEEE Transactions on Automatic Control, 2004, 49(12): 2297-2303

[26] Lefeber E, Pettersen KY, Nijmeijer H. Tracking control of an underactuated ship. IEEE Transactions on Control Systems Technology, 2003, 11(1): 52-61

[27] Li A, Sun J, Oh S. Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels. Automatica, 2009, 45(7): 1649-1658

[28] Li JH, Lee PM, Jun BH, Lim YK. Point-to-point navigation of underactuated ships. Automatica, 2008, 44(12): 3201-3205

[29] Martin P, Devasia S, Paden B. A different look at output tracking: control of a vtol aircraft. Automatica, 1996, 32(1): 101-107

[30] Mazenc F, Pettersen K, Nijmeijer H. Global uniform asymptotic stabilization of an underactuated surface vessel. IEEE Transactions on Automatic Control, 2002, 47(10): 1759-1762

[31] Moreira L, Fossen TI, Soares CG. Path following control system for a tanker ship model. Ocean Engineering, 2007, 34(14–15): 2074-2085

[32] Pettersen KY, Egeland O. Exponential stabilization of an underactuated surface vessel. Proceedings of 35th IEEE Conference on Decision and Control, 1996, 967-971

[33] Pettersen KY, Lefeber E. Way-point tracking control of ships. Proceedings of the 40th IEEE Conference on Decision and Control, 2001, 940-945

[34] Pettersen KY, Nijmeijer H. Underactuated ship tracking control: theory and experiments. International Journal of Control, 2001, 74(14): 1435-1446

[35] Reyhanoglu M. Exponential stabilization of an underactuated autonomous surface vessel. Automatica, 1997, 33(12): 2249-2254

[36] Skjetne R, Fossen TI. Nonlinear maneuvering and control of ships. Proceedings of OCEANS 2001 MTS/IEEE Conference and Exhibition, 2001, 1808-1815