Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T16:46:27.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Global path-following control of underactuated ships under deterministic and stochastic sea loads

Published online by Cambridge University Press:  20 March 2015

K. D. Do
K. D. Do*
Affiliation:
Department of Mechanical Engineering, Curtin University, Kent Street, Bentley, WA 6102, Australia
*
*Corresponding author. E-mail: duc@@curtin.edu.au
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents a new method to design global path-following controllers for underactuated ships under both deterministic and stochastic sea loads. The path-following errors are first interpreted in a moving frame attached to the path. These errors are then to be stabilized at the origin by a design of controllers based on backstepping and Lyapunov's direct methods. Weak and strong nonlinear Lyapunov functions are introduced to overcome difficulties caused by underactuation and Hessian terms induced by stochastic differentiation rule, and to guarantee boundedness of the sway velocity. Potential projection functions are introduced to design update laws that provide bounded estimates of the mean values and covariances of the disturbances. Simulations are included to illustrate the effectiveness of the proposed approach.

Keywords

Underactuated shipPath-followingStochastic loadsGlobal stabilityPotential projection functions
Type
Articles
Information
Robotica , Volume 34 , Issue 11 , November 2016 , pp. 2566 - 2591
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Fossen, T. I., Handbook of Marine Craft Hydrodynamics and Motion Control (John Wiley & Sons, West Sussex, UK, 2011).Google Scholar
2. Do, K. D. and Pan, J., Control of Ships and Underwater Vehicles: Design for Underactuated and Nonlinear Marine Systems (Springer, London, UK, 2009).Google Scholar
3. Paull, L., Saeedi, S., Seto, M. and Li, H., “AUV navigation and localization: A review,” IEEE J. Ocean. Eng. 39 (1), 131–149 (2014).Google Scholar
4. Ashrafiuon, H., Muske, K. R. and McNinch, L. C., “Review of Nonlinear Tracking and Setpoint Control Approaches for Autonomous Underactuated Marine Vehicles,” Proceedings of American Control Conference, Baltimore, Maryland, USA (2010) pp. 5203–5211.Google Scholar
5. Jiang, Z. P., “Global tracking control of underactuated ships by Lyapunov's direct method,” Automatica 38 (2), 301–309 (2002).Google Scholar
6. Lefeber, E., Pettersen, K. Y. and Nijmeijer, H., “Tracking control of an underactuated ship,” IEEE Trans. Control Syst. Technol. 11 (1), 52–61 (2003).Google Scholar
7. Do, K. D. and Pan, J., “Global tracking of underactuated ships with nonzero off-diagonal terms,” Automatica 41 (1), 87–95 (2005).Google Scholar
8. Skjetne, R. and Fossen, T. I., “Nonlinear Maneuvering and Control of Ships,” Proceedings of OCEANS 2001 MTS/IEEE Conference and Exhibition, Honolulu, USA (2001) pp. 1808–1815.Google Scholar
9. Encarnacao, P., Pacoal, A. and Arcak, M., “Path Following for Autonomous Marine Craft,” Proceedings of the 5th IFAC Conference on Manoeuvring and Control of Marine Craft, Aalborg, Denmark (2000) pp. 117–122.Google Scholar
10. Do, K. D., Jiang, Z. P. and Pan, J., “State and output feedback controllers for path following of underactuated ships,” Ocean Eng., 31 (5–6), 587–613 (2004).Google Scholar
11. Li, A., Sun, J. and Oh, S., “Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels,” Automatica 45 (7), 1649–1658 (2009).Google Scholar
12. Pettersen, K. Y. and Lefeber, E., “Way-Point Tracking Control of Ships,” Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, USA (2001) pp. 940–945.Google Scholar
13. Do, K. D., Jiang, Z. P. and Pan, J., “Robust global stabilization of underactuated ships on a linear course: State and output feedback,” Int. J. Control 76 (1), 1–17 (2003).Google Scholar
14. Fredriksen, E. and Pettersen, K. Y., “Global K-exponential way-point maneuvering of ships: theory and experiments,” Automatica 42 (4), 677–687 (2006).Google Scholar
15. Moreira, T. I. F., , L. and Soares, C. G., “Path following control system for a tanker ship model,” Ocean Eng. 34 (14–15), 2074–2085 (2007).Google Scholar
16. Krstic, M., Kanellakopoulos, I. and Kokotovic, P., Nonlinear and Adaptive Control Design (Wiley, New York, 1995).Google Scholar
17. Aicardi, M., Casalino, G., Indiveri, G., Aguiar, A., Encarnacao, P. and Pascoal, A., “A Planar Path Following Controller for Underactuated Marine Vehicles,” Proceedings of the Ninth IEEE Mediterranean Conference on Control and Automation, Dubrovnik, Croatia (2001), pp. 1–6.Google Scholar
18. Do, K. D., Jiang, Z. P. and Pan, J., “Robust and adaptive path following for underactuated ships,” Automatica 40 (6), 929–944 (2004).Google Scholar
19. Li, J. H., Lee, P. M., Jun, B. H. and Lim, Y. K., “Point-to-point navigation of underactuated ships,” Automatica 44 (12), 3201–3205 (2008).Google Scholar
20. Naess, A. and Moan, T., Stochastic Dynamics of Marine Structures (Cambridge University Press, New York, USA, 2013).Google Scholar
21. Khalil, H., Nonlinear Systems (Prentice Hall, New Jersey, USA, 2002).Google Scholar
22. Do, K. D., “Practical control of underactuated ships,” Ocean Eng. 37 (13), 1111–1119 (2010).Google Scholar
23. Martin, P., Devasia, S. and Paden, B., “A different look at output tracking control of a VTOL aircraft,” Automatica 32 (1), 101–107 (1996).Google Scholar
24. Do, K. D., Jiang, Z. P., and Pan, J., “Global tracking control of a VTOL aircraft without velocity measurements,” IEEE Trans. Autom. Control 48 (12), 2212–2217 (2003).Google Scholar
25. Pomet, J. B. and Praly, L., “Adaptive nonlinear regulation: Estimation from the Lyapunov equation,” IEEE Trans. Autom. Control 37 (6), 729–740 (1992).Google Scholar
26. Fossen, T. I., Guidance and Control of Ocean Vehicles (John Wiley and Sons Ltd., New York, USA, 1994).Google Scholar
27. Hardy, G., Littlewood, J. E. and Polya, G., Inequalities, 2nd ed. (Cambridge University Press, Cambridge, 1989).Google Scholar
28. Karatzas, I. and Shreve, S. E., Brownian Motion and Stochastic Caculus, 2nd ed. (Springer, New York, 1991).Google Scholar
29. Khasminskii, R., Stochastic Stability of Differential Equations (S&N International, Rockville MD, 1980).CrossRefGoogle Scholar
30. Krstic, M. and Deng, H., Stabilization of Nonlinear Uncertain Systems, (Springer, London, 1998).Google Scholar