Global inverse optimal tracking control of underactuated omni-directional intelligent navigators (ODINs)

Abstract

This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator (ODIN) under unknown constant environmental loads to track a reference trajectory in two-dimensional space. Motivated by the vehicle’s steering practice, the yaw angle regarded as a virtual control plus the surge thrust force are used to force the position of the vehicle to globally track its reference trajectory. The control design is based on several recent results developed for inverse optimal control and stability analysis of nonlinear systems, a new design of bounded disturbance observers, and backstepping and Lyapunov’s direct methods. Both state- and output-feedback control designs are addressed. Simulations are included to illustrate the effectiveness of the proposed results.

Keywords

inverse optimality / optimal controller / global tracking / underactuated omni-directional intelligent navigator (ODIN) / Lyapunov’s direct method / backstepping method

References

[1] Antonelli G. Underwater robots: Motion and force control of vehicle-manipulator systems, 2006, 2nd ed., Berlin, Germany: Springer, 15-77

[2] Antonelli G, Chiaverini S, Sarkar N, West M. Adaptive control of an autonomous underwater vehicle: Experimental results on ODIN. IEEE Transactions on Control Systems Technology, 2001, 9(5): 756-765

[3] Behal A, Dawson DM, Dixon WE, Yang F. Tracking and regulation control of an underactuated surface vessel with nonintegrable dynamics. IEEE Transactions on Automatic Control, 2002, 47(3): 495-500

[4] Chen WH, Balance DJ, Gawthrop PJ, OReilly J. A nonlinear disturbance observer for robotic manipulators. IEEE Transactions on Industrial Electronics, 2000, 47(4): 932-938

[5] Do KD. Global tracking control of underactuated ODINs in three dimensional space. International Journal of Control, 2013, 86(2): 183-196

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

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

[8] Do KD, Jiang ZP, Pan J, Nijmeijer H. A global output-feedback controller for stabilization and tracking of underactuated ODIN: A spherical underwater vehicle. Automatica, 2004, 40(1): 117-124

[9] Do KD, Jiang ZP, Pan J. Robust and adaptive path following for underactuated autonomous underwater vehicle. Ocean Engineering, 2004, 31(16): 1967-1997

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

[11] Do KD, Pan J. Nonlinear control of an active heave compensation system. Ocean Engineering, 2008, 35(5–6): 558-571

[12] Do KD, Pan J. Control of ships and underwater vehicles: Design for underactuated and nonlinear marine systems, 2009, London, UK: Springer, 89-211

[13] Encarnacao P, Pacoal A, Arcak M. Path following for autonomous marine craft. Proceedings of the 5th IFAC Conference on Manoeuvring and Control of Marine Craft, Girona, Spain, 2000, 117-122

[14] Fossen TI. Guidance and control of ocean vehicles, 1994, West Sussex, England: John Wiley and Sons Ltd., 221-352

[15] Fossen TI (2002). Marine control systems. Marine Cybernetics, Trondheim, Norway, 389-415.

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

[17] Fossen TI. How to incorporate wind, waves and ocean currents in the marine craft equations of motion. Proceedings of the 9th IFAC Conference on Manoeuvring and Control of Marine Craft, Arenzano, Italy, 2012, 9: 126-131

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

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

[20] 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

[21] Krstic M, Tsiotras P. Inverse optimal stabilization of a rigid spacecraft. IEEE Transactions on Automatic Control, 1999, 44(5): 1042-1049

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

[23] Leonard NE. Control synthesis and adaptation for an underactuated autonomous underwater vehicle. IEEE Journal of Oceanic Engineering, 1995, 20(2): 211-220

[24] Leonard NE. Periodic forcing, dynamics and control of underactuated spacecraft and underwater vehicles. Proceedings of the 34th IEEE Conference on Decision and Contro, Kobe, Japan, 1995, 3980-3985

[25] Mohammadi A, Tavakoli M, Marquez HJ, Hashemzadeh F. Nonlinear disturbance observer design for robotic manipulators. Control Engineering Practice, 2013, 21(3): 253-267

[26] Moylan PJ, Anderson BDO. Nonlinear regulator theory and an inverse optimal control problem. IEEE Transactions on Automatic Control, 1973, 18(5): 460-465

[27] Muske H, Ashrafiuon KR, McNinch LC. Review of nonlinear tracking and setpoint control approaches for autonomous underactuated marine vehicles. Proceedings of American Control Conference, Baltimore, USA, 2010, 5203-5211

[28] Paull L, Saeedi S, Seto M, Li H. AUV navigation and localization: A review. IEEE Journal of Oceanic Engineering, 2014, 39(1): 131-149

[29] Pettersen KY. Exponential stabilization of underactuated vehicles, 1996, Trondheim, Norway: Norwegian University of Science Technology

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

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

[32] Sepulchre R, Jankovic M, Kokotovic P. Constructive nonlinear control, 1997, New York, USA: Springer, 71-120

[33] Silvestre C, Pascoal A, Kaminer I. On the design of gain-scheduling trajectory tracking controllers. International Journal of Robust and Nonlinear Control, 2002, 12(9): 797-839

[34] Zhang R, Chen Y, Sun Z, Sun F, Xu H. Path control of a surface ship in restricted waters using sliding mode. IEEE Transactions on Control Systems Technology, 2000, 8(4): 722-732