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Adaptive Fuzzy Trajectory Tracking Control of an Under-Actuated Autonomous Underwater Vehicle Subject to Actuator Saturation

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Abstract

This paper focuses on vertical-plane trajectory tracking of an under-actuated autonomous underwater vehicle (AUV) subject to actuator saturation and external disturbances. A successive guidance and control frame is designed to avoid the cascade analysis between the kinematics guidance and the dynamics control, and the complete Lyapunov function is chosen to analyze the asymptotic stability of trajectory tracking system. In the guidance loop, the line-of-sight guidance law is applied to trajectory tracking of AUVs, which transforms the depth tracking error into the elevation angle tracking error and solves the problem of the under-actuated configuration in heave. In the control loop, direct adaptive fuzzy control is adopted to compensate for the effect of actuator saturation, which guarantees the system stability of trajectory tracking in the presence of actuator saturation. Finally, comparative numerical simulations are provided to illustrate the robust and bounded performance of the designed trajectory tracking control system.

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References

  1. Huang, H.C., Chiang, C.H.: Backstepping holonomic tracking control of wheeled robots using an evolutionary fuzzy system with qualified ant colony optimization. Int. J. Fuzzy Syst. 18(1), 28–40 (2016)

    Article  MathSciNet  Google Scholar 

  2. Ju, Z., Liu, H.: A unified fuzzy framework for human-hand motion recognition. IEEE Trans. Fuzzy Syst. 19(5), 901–913 (2011)

    Article  Google Scholar 

  3. Lu, X.G., Liu, M., Liu, J.X.: Design and optimization of interval type-2 fuzzy logic controller for delta parallel robot trajectory control. Int. J. Fuzzy Syst. 19(1), 190–206 (2017)

    Article  Google Scholar 

  4. Wang, N., Er, M.J.: Direct adaptive fuzzy tracking control of marine vehicles with fully unknown parametric dynamics and uncertainties. IEEE Trans. Control Syst. Technol. 24(5), 1845–1852 (2016)

    Article  Google Scholar 

  5. Xiang, X., Yu, C., Zhang, Q.: On intelligent risk analysis and critical decision of underwater robotic vehicle. Ocean Eng. 140, 453–465 (2017)

    Article  Google Scholar 

  6. Yu, C., Xiang, X., Lapierre, L., Zhang, Q.: Nonlinear guidance and fuzzy control for three-dimensional path following of an underactuated autonomous underwater vehicle. Ocean Eng. (2017)

  7. Hussain, N.A.A., Arshad, M.R., Mohd-Mokhtar, R.: Underwater glider modelling and analysis for net buoyancy, depth and pitch angle control. Ocean Eng. 38(16), 1782–1791 (2011)

    Article  Google Scholar 

  8. Mišković, N., Bibuli, M., Birk, A., Caccia, M., Egi, M., Grammer, K., Marroni, A., Neasham, J., Pascoal, A., Vasilijević, A., et al.: Caddy-cognitive autonomous diving buddy: two years of underwater human–robot interaction. Mar. Technol. Soc. J. 50(4), 54–66 (2016)

    Article  Google Scholar 

  9. Sun, B., Zhu, D., Yang, S.X.: A bioinspired filtered backstepping tracking control of 7000-m manned submarine vehicle. IEEE Trans. Ind. Electron. 61(7), 3682–3693 (2014)

    Article  Google Scholar 

  10. Xiang, X., Jouvencel, B., Parodi, O.: Coordinated formation control of multiple autonomous underwater vehicles for pipeline inspection. Int. J. Adv. Rob. Syst. 7(1), 75–84 (2010)

    Google Scholar 

  11. Xiang, X., Yu, C., Niu, Z., Zhang, Q.: Subsea cable tracking by autonomous underwater vehicle with magnetic sensing guidance. Sensors 16(8), 1335 (2016)

    Article  Google Scholar 

  12. Xiang, X., Yu, C., Zheng, J., Xu, G.: Motion forecast of intelligent underwater sampling apparatus-part i: design and algorithm. Indian J. Geo Mar. Sci. 44(12), 1962–1970 (2015)

    Google Scholar 

  13. Zhang, L., Jouvencel, B., Fang, Z., Xiang, X.: 3d reconstruction of seabed surface through sonar data of AUVs. Indian J. Geo Mar. Sci. 41(6), 509–515 (2012)

    Google Scholar 

  14. Wang, N., Lv, S., Er, M.J., Chen, W.H.: Fast and accurate trajectory tracking control of an autonomous surface vehicle with unmodelled dynamics and disturbances. IEEE Trans. Intell. Veh. 1(3), 230–243 (2016)

    Article  Google Scholar 

  15. Wang, N., Qian, C., Sun, J.C., Liu, Y.C.: Adaptive robust finite-time trajectory tracking control of fully actuated marine surface vehicles. IEEE Trans. Control Syst. Technol. 24(4), 1454–1462 (2016)

    Article  Google Scholar 

  16. Xia, Y., Xu, G., Xu, K., Chen, Y., Xiang, X., Ji, Z.: Dynamics and control of underwater tension leg platform for diving and leveling. Ocean Eng. 109, 454–478 (2015)

    Article  Google Scholar 

  17. Zhu, D., Huang, H., Yang, S.X.: Dynamic task assignment and path planning of multi-auv system based on an improved self-organizing map and velocity synthesis method in three-dimensional underwater workspace. IEEE Trans. Cybern. 43(2), 504–514 (2013)

    Article  Google Scholar 

  18. Wang, N., Er, M.J., Sun, J.C., Liu, Y.C.: Adaptive robust online constructive fuzzy control of a complex surface vehicle system. IEEE Trans. Cybern. 46(7), 1511–1523 (2016)

    Article  Google Scholar 

  19. Xiang, X., Lapierre, L., Jouvencel, B.: Smooth transition of auv motion control: from fully-actuated to under-actuated configuration. Rob. Auton. Syst. 67, 14–22 (2015)

    Article  Google Scholar 

  20. Fischer, N., Hughes, D., Walters, P., Schwartz, E.M., Dixon, W.E.: Nonlinear rise-based control of an autonomous underwater vehicle. IEEE Trans. Rob. 30(4), 845–852 (2014)

    Article  Google Scholar 

  21. Maalouf, D., Chemori, A., Creuze, V.: L1 adaptive depth and pitch control of an underwater vehicle with real-time experiments. Ocean Eng. 98, 66–77 (2015)

    Article  Google Scholar 

  22. Gao, J., An, X., Proctor, A., Bradley, C.: Sliding mode adaptive neural network control for hybrid visual servoing of underwater vehicles. Ocean Eng. 142, 666–675 (2017)

    Article  Google Scholar 

  23. Chu, Z., Zhu, D., Jan, G.E.: Observer-based adaptive neural network control for a class of remotely operated vehicles. Ocean Eng. 127, 82–89 (2016)

    Article  Google Scholar 

  24. Cui, R., Yang, C., Li, Y., Sharma, S.: Adaptive neural network control of auvs with control input nonlinearities using reinforcement learning. IEEE Trans. Syst. Man Cybern. Syst. 47(6), 1019–1029 (2017)

    Article  Google Scholar 

  25. Peng, Z., Wang, J., Wang, D.: Containment maneuvering of marine surface vehicles with multiple parameterized paths via spatial-temporal decoupling. IEEE/ASME Trans. Mechatron. 22(2), 1026–1036 (2017)

    Article  Google Scholar 

  26. Peng, Z., Wang, J., Wang, D.: Distributed containment maneuvering of multiple marine vessels via neurodynamics-based output feedback. IEEE Trans. Ind. Electron. 64(5), 3831–3839 (2017)

    Article  Google Scholar 

  27. Zhang, G., Cai, Y., Zhang, W.: Robust neural control for dynamic positioning ships with the optimum-seeking guidance. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1500–1509 (2017)

    Article  MathSciNet  Google Scholar 

  28. Zhang, Q., Liu, R., Chen, W., Xiong, C.: Simultaneous and continuous estimation of shoulder and elbow kinematics from surface emg signals. Front. Neurosci. 11, 1–12 (2017). doi:10.3389/fnins.2017.00280

    Google Scholar 

  29. Do, K.D.: Global robust adaptive path-tracking control of underactuated ships under stochastic disturbances. Ocean Eng. 111, 267–278 (2016)

    Article  Google Scholar 

  30. Li, J.H., Lee, P.M., Jun, B.H., Lim, Y.K.: Point-to-point navigation of underactuated ships. Automatica 44(12), 3201–3205 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Peng, Z., Wang, J. (2017) Output-feedback path-following control of autonomous underwater vehicles based on an extended state observer and projection neural networks. IEEE Trans. Syst. Man Cybern. Syst. doi:10.1109/TSMC.2017.2697447

  32. Xiang, X., Yu, C., Zhang, Q., Xu, G.: Path-following control of an auv: fully actuated versus under-actuated configuration. Mar. Technol. Soc. J. 50(1), 34–47 (2016)

    Article  Google Scholar 

  33. Lapierre, L., Soetanto, D.: Nonlinear path-following control of an auv. Ocean Eng. 34(11–12), 1734–1744 (2007)

    Article  Google Scholar 

  34. Fossen, T.I., Pettersen, K.Y., Galeazzi, R.: Line-of-sight path following for dubins paths with adaptive sideslip compensation of drift forces. IEEE Trans. Control Syst. Technol. 23(2), 820–827 (2015)

    Article  Google Scholar 

  35. Caharija, W., Pettersen, K.Y., Bibuli, M., Calado, P., Zereik, E., Braga, J., Gravdahl, J.T., Sorensen, A.J., Milovanovic, M., Bruzzone, G.: Integral line-of-sight guidance and control of underactuated marine vehicles: theory, simulations, and experiments. IEEE Trans. Control Syst. Technol. 24(5), 1623–1642 (2016)

    Article  Google Scholar 

  36. Bechlioulis, C.P., Karras, G.C., Heshmati-Alamdari, S., Kyriakopoulos, K.J.: Trajectory tracking with prescribed performance for underactuated underwater vehicles under model uncertainties and external disturbances. IEEE Trans. Control Syst. Technol. 25(2), 429–440 (2017)

    Article  Google Scholar 

  37. Xiang, X., Yu, C., Zhang, Q.: Robust fuzzy 3d path following for autonomous underwater vehicle subject to uncertainties. Comput. Oper. Res. 84, 165–177 (2017)

    Article  MathSciNet  Google Scholar 

  38. Su, H., Qiu, Y., Wang, L.: Semi-global output consensus of discrete-time multi-agent systems with input saturation and external disturbances. ISA Trans. 67, 131–139 (2017)

    Article  Google Scholar 

  39. Wang, X., Su, H., Wang, X., Chen, G.: Fully distributed event-triggered semiglobal consensus of multi-agent systems with input saturation. IEEE Trans. Ind. Electron. 64(6), 5055–5064 (2017)

    Article  Google Scholar 

  40. Zheng, Z., Sun, L., Xie, L.: Error-constrained los path following of a surface vessel with actuator saturation and faults. IEEE Trans. Syst. Man Cybern. Syst. (2017). doi:10.1109/TSMC.2017.2717850

  41. Chen, M., Jiang, B.: Adaptive control and constrained control allocation for overactuated ocean surface vessels. Int. J. Syst. Sci. 44(12), 2295–2309 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  42. Harmouche, M., Laghrouche, S., Chitour, Y.: Global tracking for underactuated ships with bounded feedback controllers. Int. J. Control 87(10), 2035–2043 (2014)

    MathSciNet  MATH  Google Scholar 

  43. Naik, M.S., Singh, S.N.: State-dependent riccati equation-based robust dive plane control of AUV with control constraints. Ocean Eng. 34(11), 1711–1723 (2007)

    Article  Google Scholar 

  44. Ju, Z., Liu, H.: Fuzzy gaussian mixture models. Pattern Recogn. 45(3), 1146–1158 (2012)

    Article  MATH  Google Scholar 

  45. Wai, R.J., Lin, C.M., Hsu, C.F.: Adaptive fuzzy sliding-mode control for electrical servo drive. Fuzzy Sets Syst. 143(2), 295–310 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  46. Wang, L.X., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans. Neural Netw. 3(5), 807–814 (1992)

    Article  Google Scholar 

  47. Lefeber, A.A.J.: Tracking control of nonlinear mechanical systems. Ph.D. thesis, University of Twente (2000)

  48. Slotime, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)

    Google Scholar 

  49. Prestero, T.: Verification of a six-degree of freedom simulation model for the REMUS autonomous underwater vehicle. Master’s thesis, Massachusetts Institute of Technology (2001)

  50. Liang, X., Qu, X., Hou, Y., Zhang, J.: Three-dimensional path following control of underactuated autonomous underwater vehicle based on damping backstepping. Int. J. Adv. Rob. Syst. 14(4), 1–9 (2017)

    Google Scholar 

  51. Wang, N., Qian, C., Sun, Z.Y.: Global asymptotic output tracking of nonlinear second-order systems with power integrators. Automatica 80, 156–161 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  52. Zheng, Z., Huang, Y., Xie, L., Zhu, B.: Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output. IEEE Trans. Control Syst. Technol. (2017). doi:10.1109/TCST.2017.2728518

    Google Scholar 

  53. Qiao, L., Yi, B., Wu, D., Zhang, W.: Design of three exponentially convergent robust controllers for the trajectory tracking of autonomous underwater vehicles. Ocean Eng. 134, 157–172 (2017)

    Article  Google Scholar 

  54. Wang, N., Su, S.F., Yin, J., Zheng, Z., Er, M.J.: Global asymptotic model-free trajectory-independent tracking control of an uncertain marine vehicle: an adaptive universe-based fuzzy control approach. IEEE Trans. Fuzzy Syst. (2017). doi:10.1109/TFUZZ.2017.2737405

    Google Scholar 

  55. Xiang, X., Liu, C., Su, H., Zhang, Q.: On decentralized adaptive full-order sliding mode control of multiple uavs. ISA Trans. (2017). doi:10.1016/j.isatra.2017.09.008

    Google Scholar 

  56. Zhang, Q., Lapierre, L., Xiang, X.: Distributed control of coordinated path tracking for networked nonholonomic mobile vehicles. IEEE Trans. Ind. Inform. 9(1), 472–484 (2013)

    Article  Google Scholar 

  57. Wang, N., Sun, J.C., Er, M.J.: Tracking-error-based universal adaptive fuzzy control for output tracking of nonlinear systems with completely unknown dynamics. IEEE Trans. Fuzzy Syst. (2017). doi:10.1109/TFUZZ.2017.2697399

    Google Scholar 

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Acknowledgements

This work is supported by National Natural Science Foundation of China (under Grant 51579111 and 51209100), the Fundamental Research Funds for the Central Universities (under Grant 2017KFYXJJ005), State Key Laboratory of Ocean Engineering (under Grant 1504) and International Exchanges of the UK Royal Society (under Grant IE161588).

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Correspondence to Xianbo Xiang.

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Yu, C., Xiang, X., Zhang, Q. et al. Adaptive Fuzzy Trajectory Tracking Control of an Under-Actuated Autonomous Underwater Vehicle Subject to Actuator Saturation. Int. J. Fuzzy Syst. 20, 269–279 (2018). https://doi.org/10.1007/s40815-017-0396-9

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