Research Papers

Global Path-Following Control of Stochastic Underactuated Ships: A Level Curve Approach

[+] Author and Article Information
K. D. Do

Department of Mechanical Engineering,
Curtin University,
Kent Street,
Bentley, WA 6102, Australia
e-mail: duc@curtin.edu.au

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 15, 2014; final manuscript received February 17, 2015; published online March 26, 2015. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 137(7), 071010 (Jul 01, 2015) (10 pages) Paper No: DS-14-1335; doi: 10.1115/1.4029885 History: Received August 15, 2014; Revised February 17, 2015; Online March 26, 2015

A level curve approach is introduced to design global path-following controllers for an underactuated surface ship. The approach is based on the observation: if the position of the ship satisfies the equation of the reference path, then the ship will be on the path. Thus, the controllers are designed based on Lyapunov's direct and backstepping methods to force the position of the ship to satisfy the equation of the path and to move along the path tangentially. The approach does not require computation of the position from the ship to the path. Weak and strong nonlinear Lyapunov functions are introduced in the control design to overcome difficulties caused by underactuation and to guarantee boundedness of the sway velocity. Simulations are included to illustrate the effectiveness of the proposed results.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Fossen, T. I., 2011, Handbook of Marine Craft Hydrodynamics and Motion Control, Wiley, West Sussex, UK. [CrossRef]
Do, K. D., and Pan, J., 2009, Control of Ships and Underwater Vehicles: Design for Underactuated and Nonlinear Marine Systems, Springer, London.
Fossen, T. I., 2002, Marine Control Systems, Marine Cybernetics, Trondheim, Norway.
Wichlund, K. Y., Sordalen, O. J., and Egeland, O., 1995, “Control Properties of Underactuated Vehicles,” IEEE International Conference on Robotics and Automation, Nagoya, May 21–27, pp. 2009–2014. [CrossRef]
Brockett, R. W., 1983, “Asymptotic Stability and Feedback Stabilization,” Differential Geometric Control Theory, R. W.Brockett, R. S.Millman, and H. J.Sussmann, eds. Birkhauser, Boston, MA, pp. 181–191.
Reyhanoglu, M., 1997, “Exponential Stabilization of an Underactuated Autonomous Surface Vessel,” Automatica, 33(12), pp. 2249–2254. [CrossRef]
Pettersen, K. Y., and Egeland, O., 1996, “Exponential Stabilization of an Underactuated Autonomous Surface Vessel,” 35th IEEE Conference on Decision and Control, pp. 967–971.
Olfati-Saber, R., 2006, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory,” IEEE Trans. Autom. Control, 51(3), pp. 401–420. [CrossRef]
Aguiar, A. P., and Pascoal, A. M., 2001, “Regulation of a Nonholonomic Autonomous Underwater Vehicle With Parametric Modeling Uncertainty Using Lyapunov Functions,” 40th IEEE Conference on Decision and Control, Orlando, FL, Vol. 40, pp. 4178–4183. [CrossRef]
Mazenc, F., Pettersen, K., and Nijmeijer, H., 2002, “Global Uniform Asymptotic Stabilization of an Underactuated Surface Vessel,” IEEE Trans. Autom. Control, 47(10), pp. 1759–1762. [CrossRef]
Do, K. D., Jiang, Z. P., and Pan, J., 2002, “Universal Controllers for Stabilization and Tracking of Underactuated Ships,” Syst. Control Lett., 47(4), pp. 299–317. [CrossRef]
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. [CrossRef]
Lefeber, E., Pettersen, K. Y., and Nijmeijer, H., 2003, “Tracking Control of an Underactuated Ship,” IEEE Trans. Control Syst. Technol., 11(1), pp. 52–61. [CrossRef]
Do, K. D., and Pan, J., 2005, “Global Tracking of Underactuated Ships With Nonzero Off-Diagonal Terms,” Automatica, 41(1), pp. 87–95. [CrossRef]
Skjetne, R., and Fossen, T. I., 2001, “Nonlinear Maneuvering and Control of Ships,” OCEANS 2001 MTS/IEEE Conference and Exhibition, Honolulu, HI, pp. 1808–1815. [CrossRef]
Encarnacao, P., Pacoal, A., and Arcak, M., 2000, “Path Following for Autonomous Marine Craft,” 5th IFAC Conference on Manoeuvring and Control of Marine Craft, pp. 117–122.
Do, K. D., and Pan, J., 2004, “State- and Output-Feedback Robust Path-Following Controllers for Underactuated Ships Using Serret–Frenet Frame,” Ocean Eng., 31(5–6), pp. 587–613. [CrossRef]
Li, A., Sun, J., and Oh, S., 2009, “Design, Analysis and Experimental Validation of a Robust Nonlinear Path Following Controller for Marine Surface Vessels,” Automatica, 45(7), pp. 1649–1658. [CrossRef]
Pettersen, K. Y., and Lefeber, E., 2001, “Way-Point Tracking Control of Ships,” 40th IEEE Conference on Decision and Control, Orlando, FL, pp. 940–945. [CrossRef]
Do, K. D., Jiang, Z. P., and Pan, J., 2003, “Robust Global Stabilization of Underactuated Ships on a Linear Course: State and Output Feedback,” Int. J. Control, 76(1), pp. 1–17. [CrossRef]
Fredriksen, E., and Pettersen, K. Y., 2006, “Global K-Exponential Way-Point Maneuvering of Ships: Theory and Experiments,” Automatica, 42(4), pp. 677–687. [CrossRef]
Moreira, L., Fossen, T. I., and Soares, C. G., 2007, “Path Following Control System for a Tanker Ship Model,” Ocean Eng., 34(14–15), pp. 2074–2085. [CrossRef]
Krstic, M., Kanellakopoulos, I., and Kokotovic, P., 1995, Nonlinear and Adaptive Control Design, Wiley, New York.
Aicardi, M., Casalino, G., Indiveri, G., Aguiar, A., Encarnacao, P., and Pascoal, A., 2001, “A Planar Path Following Controller for Underactuated Marine Vehicles,” Ninth IEEE Mediterranean Conference on Control and Automation, Dubrovnik, Croatia.
Do, K. D., Jiang, Z. P., and Pan, J., 2004, “Robust and Adaptive Path Following for Underactuated Ships,” Automatica, 40(6), pp. 929–944. [CrossRef]
Li, J. H., Lee, P. M., Jun, B. H., and Lim, Y. K., 2008, “Point-to-Point Navigation of Underactuated Ships,” Automatica, 44(12), pp. 3201–3205. [CrossRef]
Lapierre, L., and Jouvencel, B., 2008, “Robust Nonlinear Path-Following Control of an AUV,” IEEE J. Oceanic Eng., 33(2), pp. 89–102. [CrossRef]
Do, K. D., and Pan, J., 2006, “Underactuated Ships Follow Smooth Paths With Integral Actions and Without Velocity Measurements for Feedback: Theory and Experiments,” IEEE Trans. Control Syst. Technol., 14(2), pp. 308–322. [CrossRef]
Ghommam, J., Mnif, F., Benali, A., and Derbel, N., 2008, “Nonsingular Serret–Frenet Based Path Following Control for an Underactuated Surface Vessel,” ASME J. Dyn. Syst. Meas. Control, 131(2), p. 021006. [CrossRef]
Fahimi, F., Rineesh, S. V. S., and Nataraj, C., 2008, “Formation Controllers for Underactuated Surface Vessels and Zero Dynamics Stability,” Control Intell. Syst., 36(3), pp. 277–287.
Fahimi, F., and Kleeck, C. V., 2013, “Alternative Trajectory-Tracking Control Approach for Marine Surface Vessels With Experimental Verification,” Robotica, 31(1), pp. 25–33. [CrossRef]
Lawton, J. R. T., Beard, R. W., and Young, B. J., 2003, “A Decentralized Approach to Formation Maneuvers,” IEEE Trans. Rob. Autom., 19(6), pp. 933–941. [CrossRef]
Godhavn, J. M., Fossen, T. I., and Berge, S., 1998, “Nonlinear and Adaptive Backstepping Designs for Tracking Control of Ships,” Int. J. Adapt. Control Signal Process., 12(8), pp. 649–670. [CrossRef]
Ashrafiuon, H., Muske, K. R., McNinch, L. C., and Soltan, R. A., 2008, “Sliding-Mode Tracking Control of Surface Vessels,” IEEE Trans. Ind. Electron., 55(11), pp. 4004–4012. [CrossRef]
Mahini, F., DiWilliams, L., Burke, K., and Ashrafiuon, H., 2013, “An Experimental Setup for Autonomous Operation of Surface Vessels in Rough Seas,” Robotica, 31(5), pp. 703–715. [CrossRef]
Naess, A., and Moan, T., 2013, Stochastic Dynamics of Marine Structures, Cambridge University Press, New York.
Khasminskii, R., 1980, Stochastic Stability of Differential Equations, S & N International, Rockville, MD.
Krstic, M., and Deng, H., 1998, Stabilization of Nonlinear Uncertain Systems, Springer, London.
Hardy, G., Littlewood, J. E., and Polya, G., 1989, Inequalities, 2nd ed., Cambridge University Press, Cambridge, MA.
Karatzas, I., and Shreve, S. E., 1991, Brownian Motion and Stochastic Calculus, 2nd ed., Springer, New York.
Pomet, J. B., and Praly, L., 1992, “Adaptive Nonlinear Regulation: Estimation From the Lyapunov Equation,” IEEE Trans. Autom. Control, 37(6), pp. 729–740. [CrossRef]


Grahic Jump Location
Fig. 1

Coordinate systems

Grahic Jump Location
Fig. 2

Illustration of the level curve approach

Grahic Jump Location
Fig. 3

Simulation results with accurate system parameters

Grahic Jump Location
Fig. 4

Simulation results with system parameter uncertainties



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In