An Improved Dynamic Surface Sliding Mode Method for Autonomous Cooperative Formation Control of Underactuated USVS with Complex Marine Environment Disturbances

Dong, Zaopeng; Qi, Shijie; Yu, Min; Zhang, Zhengqi; Zhang, Haisheng; Li, Jiakang; Liu, Yang

doi:10.2478/pomr-2022-0025

Abstract

In this paper, a novel dynamic surface sliding mode control (DSSMC) method, combined with a lateral velocity tracking differentiator (LVTD), is proposed for the cooperative formation control of underactuated unmanned surface vehicles (USVs) exposed to complex marine environment disturbances. Firstly, in view of the kinematic and dynamic models of USVs and the design idea of a virtual control law in a backstepping approach, the trajectory tracking control problem of USVs’ cooperative formation is transformed into a stabilisation problem of the virtual control law of longitudinal and lateral velocities. Then, aiming at the problem of differential explosion caused by repeated derivation in the process of backstepping design, the first-order low-pass filter about the virtual longitudinal velocity and intermediate state quantity of position is constructed to replace differential calculations during the design of the control law, respectively. In order to reduce the steady-state error when stabilising the virtual lateral velocity control law, the integral term is introduced into the design of the sliding mode surface with a lateral velocity error, and then the second-order sliding mode surface with an integral is structured. In addition, due to the problem of controller oscillation and the role of the tracking differentiator (TD) in active disturbance rejection control (ADRC), the LVTD is designed to smooth the state quantity of lateral velocity. Subsequently, based on the dynamic model of USV under complex marine environment disturbances, the nonlinear disturbance observer is designed to observe the disturbances and compensate the control law. Finally, the whole cooperative formation system is proved to be uniformly and ultimately bounded, according to the Lyapunov stability theory, and the stability and validity of the method is also verified by the simulation results.

References

1. P.N.N. Thanh, P.M. Tom and H.P.H. Anh, ‘A new approach for three-dimensional trajectory tracking control of under-actuated AUVs with model uncertainties,’ Ocean Engineering, vol. 228, pp. 1-17, May. 2021. doi:10.1016/j.oceaneng.2021.108951.
Open DOI Search in Google Scholar Back to article
2. P.J.B. Sanchez, F.P.G. Marquez, S. Govindara, A. But, B. Sportich, S. Marini, V. Jantara and M. Papaelias, ‘Use of UIoT for offshore surveys through autonomous vehicles,’ Polish Maritime Research, vol. 28, no. 3, pp. 175-189, Oct. 2021. doi:10.2478/pomr-2021-0044.
Open DOI Search in Google Scholar Back to article
3. X.Y. Zhou, P. Wu, H.F. Zhang, W.H. Guo and Y.C. Liu, ‘Learn to Navigate: Cooperative path planning for unmanned surface vehicles using deep reinforcement learning,’ IEEE Access, vol. 7, pp. 165262-165278, Feb. 2019. doi:10.1109/ACCESS.2019.2953326.
Open DOI Search in Google Scholar Back to article
4. H.B. Huang, M. Gong, Y.F. Zhuang, S. Sharma and D.G. Xu, ‘A new guidance law for trajectory tracking of an underactuated unmanned surface vehicle with parameter perturbations,’ Ocean Engineering, vol. 175, pp. 217-222, Mar. 2019. doi:10.1016/j.oceaneng. 2019.02.042.
Open DOI Search in Google Scholar Back to article
5. L.G. Li, Z.Y. Pei, J.C. Jin and Y.S. Dai, ‘Control of unmanned surface vehicle along the desired trajectory using improved line of sight and estimated sideslip angle,’ Polish Maritime Research, vol. 28, no. 2, pp. 18-26, Jul. 2021. doi:10.2478/pomr-2021-0017.
Open DOI Search in Google Scholar Back to article
6. S.S. Wang and Y.L. Tuo, ‘Robust trajectory tracking control of underactuated surface vehicles with prescribed performance,’ Polish Maritime Research, vol. 17, no. 4, pp. 148-156, Dec. 2020. doi:10.2478/pomr-2020-0075.
Open DOI Search in Google Scholar Back to article
7. A. Stateczny and P. Burdziakowski, ‘Universal autonomous control and management system for multipurpose unmanned surface vessel,’ Polish Maritime Research, vol. 26, no. 1, pp. 30-39, Apr. 2019. doi:10.2478/pomr-2019-0004.
Open DOI Search in Google Scholar Back to article
8. Z.P. Dong, Y. Liu, H. Wang and T. Qin, ‘Method of cooperative formation control for underactuated USVs based on nonlinear backstepping and cascade system theory,’ Polish Maritime Research, vol. 28, no. 1, pp. 149-162, Mar. 2021. doi:10.2478/pomr-2021-0014.
Open DOI Search in Google Scholar Back to article
9. J.A. Gonzalez-Prieto, C. Perez-Collazo and Y. Singh, ‘Adaptive integral sliding mode based course keeping control of unmanned surface vehicle,’ Journal of Marine Science and Engineering, vol. 10, no. 1, pp. 1-20, Jan. 2022. doi:10.3390/jmse10010068.
Open DOI Search in Google Scholar Back to article
10. J.Y. Zhuang, L. Zhang, Z.H. Qin, H.B. Sun, B. Wang and J. Cao, ‘Motion control and collision avoidance algorithm for unmanned surface vehicle swarm in practical maritime environment,’ Polish Maritime Research, vol. 26, no. 1, pp.107−116, Apr. 2019. doi:10.2478/pomr-2019-0012.
Open DOI Search in Google Scholar Back to article
11. R.L. Miao, L.X. Wang and S. Pang, ‘Coordination of distributed unmanned surface vehicles via model-based reinforcement learning methods,’ Applied Ocean Research, vol. 122, pp. 1-15, May. 2022. doi:10.1016/j.apor.2022.103106.
Open DOI Search in Google Scholar Back to article
12. L. Rowinski and M. Kaczmarczyk, ‘Evaluation of effectiveness of waterjet propulsor for a small underwater vehicle,’ Polish Maritime Research, vol. 28, no. 4, pp. 30-41, Jan. 2022. doi: 10.2478/pomr-2021-0047.
Open DOI Search in Google Scholar Back to article
13. G.G. Tan, J. Zou, J.Y. Zhuang, L. Wan, H.B. Sun and Z.Y. Sun, ‘Fast marching square method based intelligent navigation of the unmanned surface vehicle swarm in restricted waters,’ Applied Ocean Research, vol. 95, pp. 1-15, Feb. 2020. doi:10.1016/j.apor.2019.102018.
Open DOI Search in Google Scholar Back to article
14. H.N. Esfahani and R. Szlapczynski, ‘Model predictive super-twisting sliding mode control for an autonomous surface vehicle,’ Polish Maritime Research, vol. 26, no. 3, pp. 163−171, Sept. 2019. doi:10.2478/pomr-2019-0057.
Open DOI Search in Google Scholar Back to article
15. X.L. Jiang and G.H. Xia, ‘Sliding mode formation control of leaderless unmanned surface vehicles with environmental disturbances,’ Ocean Engineering, vol. 244, pp. 1-9, Jan. 2022. doi:10.1016/j.oceaneng.2021.110301.
Open DOI Search in Google Scholar Back to article
16. K. Shojaei, ‘Observer-based neural adaptive formation control of autonomous surface vessels with limited torque,’ Robotics and Autonomous Systems, vol. 78, pp. 83-96, Apr. 2016. doi: 10.1016/j.robot.2016.01.005.
Open DOI Search in Google Scholar Back to article
17. J. Ghommam and M. Saad, ‘Adaptive leader-follower formation control of underactuated surface vessels under asymmetric range and bearing constraints,’ IEEE Transactions on Vehicular Technology, vol. 67, no. 2, pp. 852-865, Feb. 2018. doi:10.1109/TVT.2017.2760367.
Open DOI Search in Google Scholar Back to article
18. D.S. Wang and M.Y. Fu, ‘Adaptive formation control for waterjet USV with input and output constraints based on bioinspired neurodynamics,’ IEEE Access, vol. 7, pp. 165852-165861, Dec. 2019. doi:10.1109/ACCESS.2019.2953563.
Open DOI Search in Google Scholar Back to article
19. S.W. Wang, F. Ma, X.P. Yan, P. Wu and Y.C. Liu, ‘Adaptive and extendable control of unmanned surface vehicle formations using distributed deep reinforcement learning,’ Applied Ocean Research, vol. 110, pp. 1-28, May. 2021. doi:10.1016/j.apor.2021.102590.
Open DOI Search in Google Scholar Back to article
20. L.Y. Chen, H. Hopman and R.R. Negenborn, ‘Distributed model predictive control for vessel train formations of cooperative multi-vessel systems,’ Transportation Research Part C-Emerging Technologies, vol. 92, pp. 101-118, Jul. 2018. doi:10.1016/j.trc.2018.04.013.
Open DOI Search in Google Scholar Back to article
21. M.Y. Fu and L.L. Yu, ‘Finite-time extended state observer-based distributed formation control for marine surface vehicles with input saturation and disturbances,’ Ocean Engineering, vol. 159, pp. 219-227, Jul. 2018. doi:10.1016/j.oceaneng.2018.04.016.
Open DOI Search in Google Scholar Back to article
22. B. Huang, S. Song, C. Zhu, J. Li and B. Zhou, ‘Finite-time distributed formation control for multiple unmanned surface vehicles with input saturation,’ Ocean Engineering, vol. 233, pp. 1-14, Aug. 2021. doi:10.1016/j.oceaneng.2021.109158.
Open DOI Search in Google Scholar Back to article
23. S.L. Dai, S.D. He, H. Lin and C. Wang, ‘Platoon formation control with prescribed performance guarantees for USVs,’ IEEE Transactions on Industrial Electronics, vol. 65, no. 5, pp. 4237-4246, May. 2018. doi:10.1109/TIE.2017.2758743.
Open DOI Search in Google Scholar Back to article
24. J. Ghommam, M. Saad, F. Mnif and Q.M. Zhu, ‘Guaranteed performance design for formation tracking and collision avoidance of multiple USVs with disturbances and unmodeled dynamics,’ IEEE Systems Journal, vol. 15, no. 3, pp. 4346-4357, Sep. 2021. doi:10.1109/JSYST.2020.3019169.
Open DOI Search in Google Scholar Back to article
25. X. Jin, ‘Fault tolerant finite-time leader–follower formation control for autonomous surface vessels with LOS range and angle constraints,’ Automatica, vol. 68, pp. 228-236, Jun. 2016. doi:10.1016/j.automatica.2016.01.064.
Open DOI Search in Google Scholar Back to article
26. Y. Lu, G.Q. Zhang, Z.J. Sun and W.D. Zhang, ‘Robust adaptive formation control of underactuated autonomous surface vessels based on MLP and DOB,’ Nonlinear Dynamics, vol. 94, no. 1, pp. 503-519, Oct. 2018. doi:10.1007/s11071-018-4374-z.
Open DOI Search in Google Scholar Back to article
27. B.S. Park and S.J. Yoo, ‘Adaptive-observer-based formation tracking of networked uncertain underactuated surface vessels with connectivity preservation and collision avoidance,’ Journal of The Franklin Institute-Engineering and Applied Mathematics, vol. 356, no. 15, pp. 7947-7966, Oct. 2019. doi:10.1016/j.jfranklin.2019.04.017.
Open DOI Search in Google Scholar Back to article
28. H.N. Esfahani, R. Szlapczynski and H. Ghaemi, ‘High performance super-twisting sliding mode control for a maritime autonomous surface ship (MASS) using ADP-Based adaptive gains and time delay estimation,’ Ocean Engineering, vol. 191, pp. 1-19, Nov. 2019. doi: 10.1016/j.oceaneng.2019.106526.
Open DOI Search in Google Scholar Back to article
29. K. Xue and T.Y. Wu, ‘Distributed consensus of USVs under heterogeneous UAV-USV multi-agent systems cooperative control scheme,’ Journal of Marine Science and Engineering, vol. 9, no. 11, pp. 1-20, Nov. 2021. doi:10.3390/jmse9111314.
Open DOI Search in Google Scholar Back to article
30. S.J. Yoo and B.S. Park, ‘Guaranteed-connectivity-based distributed robust event-triggered tracking of multiple underactuated surface vessels with uncertain nonlinear dynamics,’ Nonlinear Dynamics, vol. 99, no. 3, pp. 2233-2249, Feb. 2020. doi:10.1007/s11071-019-05432-5.
Open DOI Search in Google Scholar Back to article
31. B.S. Park and S.J. Yoo, ‘Connectivity-maintaining and collision-avoiding performance function approach for robust leader–follower formation control of multiple uncertain underactuated surface vessels,’ Automatica, vol. 127, pp. 1-10, May. 2021. doi:10.1016/j.automatica.2021.109501.
Open DOI Search in Google Scholar Back to article
32. H.C. Lamraoui and Q.D. Zhu, ‘Path following control of fully actuated Autonomous underwater vehicle based on LADRC,’ Polish Maritime Research, vol. 25, no. 4, pp. 39-48, Dec. 2018. doi:10.2478/pomr-2018-0130.
Open DOI Search in Google Scholar Back to article
33. M. Tomera and K. Podgorski, ‘Control of dynamic positioning system with disturbance observer for autonomous marine surface vessels,’ Sensors, vol. 21, no. 20, pp. 1-24, Oct. 2021. doi.org/10.3390/s21206723.
Open DOI Search in Google Scholar Back to article
34. T. Perez and T.I. Fossen, ‘Kinematic models for maneuvering and sea keeping of marine vessels,’ Modeling, Identification and Control, vol. 28, no. 1, pp. 19-30, Jan. 2007. doi: 10.4173/mic.2007.1.3.
Open DOI Search in Google Scholar Back to article
35. W.H. Chen, ‘Disturbance observer based control for nonlinear systems,’ IEEE-ASME Transactions on Mechatronics, vol. 9, no. 4, pp. 706-710, Dec. 2004. doi:10.1109/TMECH.2004.839034.
Open DOI Search in Google Scholar Back to article
36. J.Q. Han, ‘From PID to active disturbance rejection control,’ IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900-906, Mar. 2009. doi:10.1109/TIE.2008.2011621.
Open DOI Search in Google Scholar Back to article
37. K.D. Do and J. Pan, ‘Global robust adaptive path following of underactuated ships,’ Automatic, vol. 42, no. 10, pp. 1713-1722, Oct. 2006. doi:10.1016/j.automatica.2006.04.026.
Open DOI Search in Google Scholar Back to article

An Improved Dynamic Surface Sliding Mode Method for Autonomous Cooperative Formation Control of Underactuated USVS with Complex Marine Environment Disturbances

Abstract

Paradigm

My account