Skip to main content
SpringerLink
Log in

Bottom-following control for an underactuated unmanned undersea vehicle using integral-terminal sliding mode control

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

The bottom-following problem of an underactuated unmanned undersea vehicle (UUV) is addressed. A robust nonlinear controller is developed by using integral-terminal sliding mode control (ITSMC), which can exponentially drive an UUV onto a predefined path at a constant forward speed. The kinematic error equations are first derived in the Serret-Frenet frame. Using the line of sight (LOS) method, Lyapunov’s direct technique and tracking differentiator, the guidance law is established. Then, the kinematic controller, the guidance law, is expanded to cope with vehicle dynamics by resorting to introduce two integral-terminal sliding surfaces. Robustness to parameter perturbation is addressed by incorporating the reaching laws associated with the upper bound of the parameter perturbation. The proposed control law can guarantee that all error signals globally exponentially converge to the origin. Finally, a series of numerical simulation results are presented and discussed. In these simulations, wave, constant unknown ocean currents (for the purposes of the controller) and the parameter perturbation are added to illustrate the robustness and effectiveness of the bottom-following control scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. CHEN Qiang. Unmanned underwater vehicle [M]. Beijing: National Defense Industry Press, 2014: 29–31. (in Chinese)

    Google Scholar 

  2. YUH J. Design and control of autonomous underwater robots: A survey [J]. Autonomous Robots, 2000, 8(1): 7–24.

    Article  Google Scholar 

  3. BROCKETT R W. Asymptotic stability and feedback stabilization [J]. Differential Geometric Control Theory, 1983, 27(1): 181–191.

    Google Scholar 

  4. POMET J B. Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift [J]. System and Control Letters, 1992, 18(2): 147–158.

    Article  MathSciNet  MATH  Google Scholar 

  5. FOSSEN T I. Handbook of marine craft hydrodynamics and motion control [M]. New York: John Wiley and Sons Ltd, 2011: 187–225.

    Book  Google Scholar 

  6. YAN Zhe-ping, YU Hao-miao, LI Ben-yin, ZHOU Jia-jia. Sliding mode trajectory tracking of underactuated UUV on dive plane [C]// Proceedings of the 33rd Chinese Control Conference. Nanjing, China, 2014: 7909–7914.

    Google Scholar 

  7. CACCIA M, BRUZZONE G, VERUGGIO G. Active sonar-based bottom-following for unmanned underwater vehicles [J]. Control Engineering Practice, 1999, 7(4): 459–468.

    Article  Google Scholar 

  8. PAULINO N, SILVESTRE C, CUNHA R, PASCOAL A. A bottom-following preview controller for autonomous underwater vehicles [C]// Proceedings of the 45th IEEE Conference on Decision & Control. San Diego, CA, USA, 2006: 715–720.

    Book  Google Scholar 

  9. SILVESTRE C, CUNHA R, PAULINO N, PASCOAL A. A bottom-following preview controller for autonomous underwater vehicles [J]. IEEE Transactions on Control Systems Technology, 2009, 17(2): 257–266.

    Article  Google Scholar 

  10. BIAN Xin-qian, ZHOU Jia-jia, JIA He-ming, ZHAO Xiao-yi. Adaptive neural network control system of bottom following for an underactuated AUV [C]// OCEANS 2010. Seattle, WA, USA: IEE, 2010: 1–6.

    Google Scholar 

  11. BIAN Xin-qian, CHENG Xiang-qin, JIA He-ming, YAN Zhe-ping, ZHANG Li-jun. A bottom-following controller for underactuated AUV based on iterative sliding and increment feedback [J]. Control and Decision, 2011, 26(2): 289–292, 296. (in Chinese)

    MathSciNet  Google Scholar 

  12. DUAN Hai-qing, JIA He-ming, ZHOU Jia-jia, YANG Xin. Bottom following control for underactuated AUV based on neural network [J]. Journal of Southeast University, 2012, 42(9): 203–207. (in Chinese)

    MathSciNet  Google Scholar 

  13. JIA He-ming, SONG Wen-long, ZHOU Jia-jia. Bottom following control for an underactuated AUV based on nonlinear backstepping method [J]. Journal of Beijing University of Technology, 2012, 38(12): 1780–1785. (in Chinese)

    MathSciNet  Google Scholar 

  14. JIA He-ming, ZHANG Li-jun, BIAN Xin-qian, YAN Zhe-ping, CHENG Xiang-qin, ZHOU Jia-jia. A nonlinear bottom-following controller for underactuated autonomous underactuated vehicles [J]. Journal of Central South University, 2012, 19(5): 1240–1248.

    Article  Google Scholar 

  15. ARAS A M, MOHAMMAS J Y, AGUIAR A P. Automatic bottom-following for underwater robotic vehicles [J]. Automatica, 2014, 50(8): 2155–2162.

    Article  MathSciNet  MATH  Google Scholar 

  16. ZHANG Li-jun, QI Xue, PANG Yong-jie. Adaptive output feedback control based on DRFNN for AUV [J]. Ocean Engineering, 2009, 36 (9/10): 716–722.

    Article  Google Scholar 

  17. LAPIERRE L, SOETANTO D. Nonlinear path-following control of an AUV [J]. Ocean Engineering, 2007, 34(11): 1734–1744.

    Article  Google Scholar 

  18. LAPIERRE L, JOUVENCEL B. Robust nonlinear path-following control of an AUV [J]. IEEE Journal of Ocean Engineering, 2008, 33(2): 89–102.

    Article  Google Scholar 

  19. YAN Zhe-ping, CHI Dong-nan, HOU Shu-ping, ZHENG Ya-lin. Underwater environment SDAP method using multi single-beam sonars [J/OL]. Mathematical Problems in Engineering, 2013: 1–17.

    Google Scholar 

  20. YAN Zhe-ping, LIU Yi-bo, ZHOU Jia-jia, WU Di. Path following control of an AUV under the current using the SVR-ADRC [J/OL]. Journal of Applied Mathematics, 2014: 1–12.

    Google Scholar 

  21. LI Juan, GAO Hai-tao, ZHOU Jia-jia, YAN Zhe-ping. Dynamic surface and active disturbance rejection control for path following of an underactuated UUV [J/OL]. Journal of Applied Mathematics, 2014: 1–9.

    Google Scholar 

  22. XIANG Xian-bo. Research on path following and coordinated control for second-order nonholonomic AUVs [D]. Wuhan: Huazhong University of Science and Technology, 2010. (in Chinese)

    Google Scholar 

  23. UTKIN V I. Sliding mode control design principles and applications to electric drives [J]. IEEE Transactions on Industrial Electronics, 1993, 40(1): 23–36.

    Article  Google Scholar 

  24. ZAK M. Terminal attractors for addressable memory in neural networks [J]. Physics Letters A, 1988, 133(1/2): 18–22.

    Article  Google Scholar 

  25. VENKATARAMAN S T, GULATI S. Control of Nonlinear Systems Using Terminal Sliding Modes [C]// American Control Conference 1992. Chicago, IL, USA: IEEE, 1992: 891–893.

    Google Scholar 

  26. YANG Jun, LI Shi-hua, SU Jin-ya, YU Xing-huo. Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances [J]. Automatica, 2013, 49(7): 2287–2291.

    Article  MathSciNet  Google Scholar 

  27. ZHANG Niao-na. Terminal sliding mode control theory and applications [M]. Beijing: Science Press, 2011: 1–15. (in Chinese)

    Google Scholar 

  28. KHOO S, XIE Li-Hua, MAN Zhi-hong. Integral terminal sliding mode cooperative control of multi-robot networks [C]// Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Singapore, 2009: 969–973.

    Google Scholar 

  29. CHIU Chian-Song. Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems [J]. Automatica, 2012, 48(2): 316–326.

    Article  MathSciNet  MATH  Google Scholar 

  30. YANG Jun, LI Shi-hua, YU Xing-huo. Sliding-mode control for systems with mismatched uncertainties via a disturbance observer [J]. IEEE Transactions on Industrial Electronics, 2013, 60(1): 160–169.

    Article  Google Scholar 

  31. YANG Jun, SU Jin-ya, LI Shi-hua, YU Xing-huo. High-order mismatched disturbance compensation for motion control systems via a continuous dynamic sliding-mode approach [J]. IEEE Transactions on Industrial Informatics, 2014, 10(1): 604–614.

    Article  Google Scholar 

  32. LICEAGA-CASTRO E, VAN DER MOLEN G M. Submarine H8 depth control under wave disturbances [J]. IEEE Transactions on Control Systems Technology, 1995, 3(3): 338–346.

    Article  Google Scholar 

  33. MOREIA L, SOARES C G. H 2 and H ∞ designs for diving and course control of an autonomous underwater vehicle in presence of waves [J]. IEEE Journal of Oceanic Engineering, 2008, 33(2): 69–88.

    Article  Google Scholar 

  34. HAN Jing-qing. Active disturbance rejection control technique-the technique for estimating and compensating the uncertainties [M]. Beijing: National Defense Industry Press, 2008: 46–72. (in Chinese)

    Google Scholar 

  35. HAN Jing-qing. From PID to active disturbance rejection control [J]. IEEE Transactions on Industrial Electronics, 2009, 56(3): 900–906.

    Article  Google Scholar 

  36. ZHAO Zhi-liang. Convergence of nonlinear active disturbance rejection control [D]. Hefei: University of Science and Technology of China, 2012. (in Chinese)

    Google Scholar 

  37. MARQUEZ H J. Nonlinear control systems analysis and design [M]. New Jersey: John Wiley and Sons Inc, 2003: 82–83.

    Google Scholar 

  38. PETTERSEN K Y, EGELAND O. Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle [J]. IEEE Transactions on Automatic Control, 1999, 44(1): 112–115.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Automation, Harbin Engineering University, Harbin, 150001, China

    Zhe-ping Yan  (严浙平), Hao-miao Yu  (于浩淼) & Ben-yin Li  (李本银)

Authors
  1. Zhe-ping Yan  (严浙平)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao-miao Yu  (于浩淼)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ben-yin Li  (李本银)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hao-miao Yu  (于浩淼).

Additional information

Foundation item: Projects(51179038, 51309067) supported by the National Natural Science Foundation of China; Project(HEUCFX41402) supported by the Fundamental Research Funds for the Central Universities, China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, Zp., Yu, Hm. & Li, By. Bottom-following control for an underactuated unmanned undersea vehicle using integral-terminal sliding mode control. J. Cent. South Univ. 22, 4193–4204 (2015). https://doi.org/10.1007/s11771-015-2967-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-015-2967-y

Key words

Search

Navigation