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Adaptive trajectory tracking control of vector propulsion unmanned surface vehicle with disturbances and input saturation

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Abstract

This paper presents an adaptive trajectory tracking controller with full state feedback for vector propulsion unmanned surface vehicle (USV). The controller solves the problem of strong coupling of control inputs with vector propulsion by virtual control point method. Then, a guidance trajectory is designed to avoid input saturation as much as possible. In order to be closer to the reality of USV system, the tracking controller is also designed for its actuator. When designing the trajectory tracking controller, neural network-minimum learning parameter (NN-MLP) technology and parameter adaptive correction method are used to approximate and compensate the actuator error, model uncertainty and unknown environmental disturbances. By introducing a continuously differentiable approximate saturation function, the oscillation problem caused by the discontinuous signum function in the standard sliding mode control method is avoided. Next, the Lyapunov stability analysis of designed control law shows that the controller is ultimately uniformly bounded stability. Then, the zero-dynamics stability condition of virtual control point is also proved. Finally, compared with standard method, numerical simulation results verify the effectiveness of proposed method.

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References

  1. Liu, Z., Zhang, Y., Yu, X., Yuan, C.: Unmanned surface vehicles: an overview of developments and challenges. Annu. Rev. Control 41, 71–93 (2016)

    Article  Google Scholar 

  2. Yoo, S.J., Park, B.S.: Guaranteed performance design for distributed bounded containment control of networked uncertain underactuated surface vessels. J. Franklin Inst. 354(3), 1584–1602 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Vasilijevic, A., Nad, D., Mandic, F., Miskovic, N., Vukic, Z.: Coordinated navigation of surface and underwater marine robotic vehicles for ocean sampling and environmental monitoring. IEEE/ASME Trans. Mechatron. 22(3), 1174–1184 (2017)

    Article  Google Scholar 

  4. Jorge, V.A.M., Granada, R., Maidana, R.G., Jurak, D.A., Heck, G., Negreiros, A.P.F., dos Santos, D.H., Goncalves, L.M.G., Amory, A.M.: A survey on unmanned surface vehicles for disaster robotics: main challenges and directions. Sensors 19(3), 702 (2019)

    Article  Google Scholar 

  5. Brink, G., Garvelmann, M.: USV-UUV Swarm Vehicle Combo for Deep-Sea Exploration. Mapping. Sea Technol. 59(8), 21–24 (2018)

    Google Scholar 

  6. Zhang, W., Wang, K., Wang, S.A., Laporte, G.: Clustered coverage orienteering problem of unmanned surface vehicles for water sampling. Nav. Res. Logist. 67(5), 353–367 (2020)

    Article  Google Scholar 

  7. Yao, W., Zhang, J., Liu, Y., Zhou, M., Sun, M., Zhang, G.: Improved vector control for marine podded propulsion control system based on wavelet analysis. J. Coast. Res. 73, 54–58 (2015)

    Article  Google Scholar 

  8. Gierusz, W.: Modelling the dynamics of ships with different propulsion systems for control purpose. Pol. Marit. Res. 23(1), 31–36 (2016)

    Article  Google Scholar 

  9. Zhang, G., Zhang, X.: A novel dvs guidance principle and robust adaptive path-following control for underactuated ships using low frequency gain-learning. ISA Trans. 56, 75–85 (2015)

    Article  Google Scholar 

  10. Wang, J., Liu, J.Y., Yi, H., Wu, N.L.: Adaptive non-strict trajectory tracking control scheme for a fully actuated unmanned surface vehicle. Appl. Sci. 8(4), 598 (2018)

    Article  Google Scholar 

  11. Xie, W., Ma, B., Huang, W., Zhao, Y.: Global trajectory tracking control of underactuated surface vessels with non-diagonal inertial and damping matrices. Nonlinear Dyn. 92(4), 1481–1492 (2018)

    Article  MATH  Google Scholar 

  12. Li, J.W.: Robust tracking control and stabilization of underactuated ships. Asian J. Control 20(6), 2143–2153 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, N., Karimi, H.R.: Successive waypoints tracking of an underactuated surface vehicle. IEEE Trans. Ind. Electron. 16(2), 898–908 (2020)

    Google Scholar 

  14. Khooban, M.H., Vafamand, N., Dragicevic, T., Blaabjerg, F.: Polynomial fuzzy model-based approach for underactuated surface vessels. IET Contr. Theory Appl. 12(7), 914–921 (2018)

    Article  MathSciNet  Google Scholar 

  15. Liang, X., Qu, X., Hou, Y., Li, Y., Zhang, R.: Distributed coordinated tracking control of multiple unmanned surface vehicles under complex marine environments. Ocean Eng. 205 (2020)

  16. Dong, C., Ye, Q., Dai, S.L.: Neural-network-based adaptive output-feedback formation tracking control of USVs under collision avoidance and connectivity maintenance constraints. Neurocomputing 401, 101–112 (2020)

    Article  Google Scholar 

  17. Wang, N., Lv, S.L., Gao, Y., Er, M.J.: Disturbance/uncertainty estimation based accurate trajectory tracking control of an unmanned surface vehicle with system uncertainties and external disturbances. Indian J. Geo-marine Sci. 46(12), 2510–2518 (2017)

    Google Scholar 

  18. Wang, N., Gao, Y., Lv, S., Er, M.J.: Integral sliding mode based finite-time trajectory tracking control of unmanned surface vehicles with input saturations. Indian J. Geo-marine Sci. 46(12), 2493–2501 (2017)

    Google Scholar 

  19. Wang, N., Zhu, Z.B., Qin, H.D., Deng, Z.C., Sun, Y.C.: Finite-time extended state observer-based exact tracking control of an unmanned surface vehicle. Int. J. Robust Nonlinear Control 31(5), 1704–1719 (2021)

    Article  MathSciNet  Google Scholar 

  20. Huang, H., Gong, M., Zhuang, Y., Sharma, S., Xu, D.: A new guidance law for trajectory tracking of an underactuated unmanned surface vehicle with parameter perturbations. Ocean Eng. 175, 217–222 (2019)

    Article  Google Scholar 

  21. Yao, Q.J.: Fixed-time trajectory tracking control for unmanned surface vessels in the presence of model uncertainties and external disturbances. Int. J, Control (2020)

  22. Wang, S., Fu, M., Wang, Y., Tuo, Y., Ren, H.: Adaptive online constructive fuzzy tracking control for unmanned surface vessel with unknown time-varying uncertainties. IEEE Access 6, 70444–70455 (2018)

    Article  Google Scholar 

  23. Wang, S.S., Tuo, Y.L.: Robust trajectory tracking control of underactuated surface vehicles with prescribed performance. Pol. Marit. Res. 27(4), 148–156 (2020)

    Article  Google Scholar 

  24. Chen, L., Cui, R., Yang, C., Yan, W.: Adaptive neural network control of underactuated surface vessels with guaranteed transient performance: theory and experimental results. IEEE Trans. Ind. Electron. 67(5), 4024–4035 (2020)

    Article  Google Scholar 

  25. Chen, Z., Zhang, Y., Nie, Y., Tang, J., Zhu, S.: Adaptive sliding mode control design for nonlinear unmanned surface vessel using rbfnn and disturbance-observer. IEEE Access 8, 45457–45467 (2020)

    Article  Google Scholar 

  26. Li, L.L., Dong, K., Guo, G.: Trajectory tracking control of underactuated surface vessel with full state constraints. Asian J, Control (2020)

  27. Park, B.S.: A simple output-feedback control for trajectory tracking of underactuated surface vessels. Ocean Eng. 143, 133–139 (2017)

    Article  Google Scholar 

  28. Akram, A., Hussain, M., us Saqib, N., Rehan, M.: Dynamic anti-windup compensation of nonlinear time-delay systems using lpv approach. Nonlinear Dyn. 90(1), 513–533 (2017)

  29. Rehan, M., Hong, K.S.: Decoupled-architecture-based nonlinear anti-windup design for a class of nonlinear systems. Nonlinear Dyn. 73(3), 1955–1967 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hussain, M., Rehan, M., Ahn, C.K., Zheng, Z.: Static anti-windup compensator design for nonlinear time-delay systems subjected to input saturation. Nonlinear Dyn. 95(3), 1879–1901 (2019)

    Article  Google Scholar 

  31. Qin, H., Li, C., Sun, Y.: Adaptive neural network-based fault-tolerant trajectory-tracking control of unmanned surface vessels with input saturation and error constraints. IET Intell. Transp. Syst. 14(5), 356–363 (2020)

    Article  Google Scholar 

  32. Wang, N., Pan, X.X., Su, S.F.: Finite-time fault-tolerant trajectory tracking control of an autonomous surface vehicle. Journal of the Franklin Institute-engineering and Applied Mathematics 357(16), 11114–11135 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  33. Yasukawa, H., Yoshimura, Y.: Introduction of mmg standard method for ship maneuvering predictions. J. Mar. Sci. Technol. 20(1), 37–52 (2015)

    Article  Google Scholar 

  34. Suzuki, R., Tsukada, Y., Ueno, M.: Estimation of full-scale ship manoeuvrability in adverse weather using free-running model test. Ocean Eng. 213, 107562 (2020)

    Article  Google Scholar 

  35. Dong, W., Guo, Y.: Global time-varying stabilization of underactuated surface vessel. IEEE Trans. Autom. Control 50(6), 859–864 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  36. Fossen, T.I.: Handbook of marine craft hydrodynamics and motion control. Wiley, London (2011)

    Book  Google Scholar 

  37. Gierusz, W.: Simulation model of the lng carrier with podded propulsion part i: forces generated by pods. Ocean Eng. 108, 105–114 (2015)

    Article  Google Scholar 

  38. Consolini, L., Tosques, M.: A minimum phase output in the exact tracking problem for the nonminimum phase underactuated surface ship. IEEE Trans. Autom. Control 57(12), 3174–3180 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang, G.Q., Deng, Y.J., Zhang, W.D., Huang, C.F.: Novel dvs guidance and path-following control for underactuated ships in presence of multiple static and moving obstacles. Ocean Eng. 170, 100–110 (2018)

    Article  Google Scholar 

  40. Sun, X., Wang, G., Fan, Y.: Model identification and trajectory tracking control for vector propulsion unmanned surface vehicles. Electronics 9, 22 (2020)

    Article  Google Scholar 

  41. Wang, R., Zhang, J., Li, X., Liu, Y., Fu, W., Yang, Y.: Simulation study on marine main engine control based on predictive control theory. Ship Eng. 41(S1), 165–169 (2019)

    Google Scholar 

  42. Sun, X., Wang, G., Fan, Y., Mu, D., Qiu, B.: Collision avoidance of podded propulsion unmanned surface vehicle with colregs compliance and its modeling and identification. IEEE Access 6, 55473–55491 (2018)

    Article  Google Scholar 

  43. Teel, Andrew: Windup in control: Its effects and their prevention (by hippe, p.; 2006). IEEE Trans. Autom. Control 53(8), 1976–1977 (2008)

  44. Hippe, P.: Windup in Control: Its Effects and Their Prevention. Springer-Verlag, New York (2006)

    MATH  Google Scholar 

  45. Morel, Y., Leonessa, A.: Indirect adaptive control of a class of marine vehicles. Int. J. Adapt. Control Signal Process. 24(4), 261–274 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  46. Bu, X.W., Wu, X.Y., Huang, J.Q., Ma, Z., Zhang, R.: Minimal-learning-parameter based simplified adaptive neural back-stepping control of flexible air-breathing hypersonic vehicles without virtual controllers. Neurocomputing 175, 816–825 (2016)

    Article  Google Scholar 

  47. Elmokadem, T., Zribi, M., Youcef-Toumi, K.: Trajectory tracking sliding mode control of underactuated auvs. Nonlinear Dyn. 84(2), 1079–1091 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  48. Fetzer, K.L., Nersesov, S., Ashrafiuon, H.: Full-state nonlinear trajectory tracking control of underactuated surface vessels. J. Vib. Control 26(15–16), 1077546319895658 (2020)

    MathSciNet  Google Scholar 

  49. Yu, R., Zhu, Q., Xia, G., Liu, Z.: Sliding mode tracking control of an underactuated surface vessel. IET Contr. Theory Appl. 6(3), 461–466 (2012)

    Article  MathSciNet  Google Scholar 

  50. Pan, C.Z., Lai, X.Z., Yang, S.X., Wu, M.: A biologically inspired approach to tracking control of underactuated surface vessels subject to unknown dynamics. Expert Syst. Appl. 42(4), 2153–2161 (2015)

    Article  Google Scholar 

  51. Hu, X., Du, J.L., Sun, Y.Q.: Robust adaptive control for dynamic positioning of ships. IEEE J. Oceanic. Eng. 42(4), 826–835 (2017)

    Article  Google Scholar 

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Acknowledgements

This paper is partly supported by the Nature Science Foundation of China (Grand Number 51609033), the Nature Science Foundation of Liaoning Province of China (Grand Number 20180520005), the Key Development Guidance Program of Liaoning Province of China (Grand Number 2019JH8/10100100), the Soft Science Research Program of Dalian City of China (Grand Number 2019J11CY014) and the Fundamental Research Funds for the Central Universities (Grand Number 3132019005, 3132019311).

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Correspondence to Xiaojie Sun.

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Sun, X., Wang, G. & Fan, Y. Adaptive trajectory tracking control of vector propulsion unmanned surface vehicle with disturbances and input saturation. Nonlinear Dyn 106, 2277–2291 (2021). https://doi.org/10.1007/s11071-021-06873-7

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