Abstract
This paper investigates the path following control problem for underactuated unmanned surface vehicle (USV) in the presence of unmodeled dynamics, external disturbances and input saturation. A novel adaptive robust path following control scheme is proposed by employing trajectory linearization control (TLC) technology and finite-time disturbance observer, which is composed of a concise yaw rate controller and a surge speed controller. The salient features of the proposed scheme include: a path following guidance law is designed to ensure USV effectively converging to and following the desired path; TLC is introduced into the field of USV motion control as new effective technique, and it is the first time used to design path following controller for underactuated USV; a finite-time nonlinear tracking differentiator is constructed not only to avoid the signal jump caused by derivation, but also to filter noise and high frequency interference. A finite-time disturbance observer (FDO) is devised to exactly observe the uncertain dynamics and unknown external disturbances, which improves the tracking accuracy and precise disturbance rejection of the proposed controller; then, an auxiliary dynamic system that is governed by smooth switching function is developed to compensate for the saturation constraint on actuator. Stability analysis verifies that all signals in the closed-loop system are uniformly ultimately bounded. Finally, simulation results and comparisons illustrate the superiority of the proposed control scheme.
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A. J. Sinisterra, M. R. Dhanak, and K. Von Ellenrieder, “Stereovision-based target tracking system for USV operations,” Ocean Engineering, vol. 133, pp. 197–214, 2017.
Y. H. Qu, B. Xiao, Z. Z. Fu, and D. G. Yuan, “Trajectory exponential tracking control of unmanned surface ships with external disturbance and system uncertainties,” ISA Transactions, vol. 78, pp. 47–55, July 2018.
Y. C. Liu and R. Bucknall, “Efficient multi-task allocation and path planning for unmanned surface vehicle in support of ocean operations,” Neurocomputing, vol. 275, pp. 1550–1566, January 2018.
D. D. Mu, G. F. Wang, and Y. S. Fan, “Tracking control of podded propulsion unmanned surface vehicle with unknown dynamics and disturbance under input saturation”, International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1905–1915, August 2018.
K. D. Do and J. Pan, “State- and output-feedback robust path-following controllers for underactuated ships using Serret-Frenet frame,” Ocean Engineering, vol. 31, no. 5-6, pp. 587–613, April 2004.
J. H. Li, P. M. Lee, B. H. Jun, and Y. K. Lim, “Point-to-point navigation of underactuated ships”, Automatica, vol. 44, no. 12, pp. 3201–3205, December 2008.
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, October 2018.
G. Zhang and X. Zhang, “A novel DVS guidance principle and robust adaptive path-following control for underactu-ated ships using low frequency gain-learning,” ISA Transactions, vol. 56, pp. 75–85, May 2015.
Y. Yu, C. Guo, and H. Yu, “Finite-time predictor line-of-sight-based adaptive neural network path following for unmanned surface vessels with unknown dynamics and input saturation,” International Journal of Advanced Robotic Systems, vol. 15, no. 6, November 2018.
Y. Yu, C. Guo, and H. Yu, “Finite-time PLOS-based integral sliding-mode adaptive neural path following for unmanned surface vessels with unknown dynamics and disturbances,” IEEE Transactions on Automation Science and Engineering, 2019. DOI: 10.1109/TASE.2019.2925657
H. Wang, D. Wang, and Z. Peng, “Neural network based adaptive dynamic surface control for cooperative path following of marine surface vehicles via state and output feedback,” Neurocomputing, vol. 133, pp. 170–178, June 2014.
Z. Zheng and Y. Zou, “Adaptive integral LOS path following for an unmanned airship with uncertainties based on robust RBFNN backstepping,” ISA Transactions, vol. 65, pp. 210–219, November 2016.
Z. Zheng, L. Sun, and L. Xie, “Error-constrained LOS path following of a surface vessel with actuator saturation and faults”, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 10, pp. 1794–1805, October 2018.
L. Liu, D. Wang, Z. Peng and H. Wang, “Predictor-based LOS guidance law for path following of underactuated marine surface vehicles with sideslip compensation,” Ocean Engineering, vol. 124, pp. 340–348, September 2016.
R. Wu and J. Du, “Adaptive robust course-tracking control of time-varying uncertain ships with disturbances”, International Journal of Control, Automation, and Systems, vol. 17, no. 7, pp. 1847–1855, July 2019.
C. Ren and S. He, “Sliding mode control for a class of nonlinear positive Markov jumping systems with uncertainties in a finite-time interval”, International Journal of Control, Automation, and Systems, vol. 17, no. 7, pp. 1634–1641, July 2019.
A. Shourangiz-Haghighi and A. R. Tavakolpour-Saleh, “A neural network-based scheme for predicting critical un-measurable parameters of a free piston Stirling oscillator,” Energy Conversion and Management, vol. 196, pp. 623–639, September 2019.
W. He, Z. Yin, and C. Sun, “Adaptive neural Network control of a marine vessel with constraints using the asymmetric barrier Lyapunov function”, IEEE Transactions on Cybernetics, vol. 47, no. 7, pp. 1641–1651, July 2017.
N. Wang and M. J. Er, “Direct adaptive fuzzy tracking control of marine vehicles with fully unknown parametric dynamics and uncertainties”, IEEE Transactions on Control Systems Technology, vol. 24, no. 5, pp. 1845–1852, September 2016.
Z. Peng, J. Wang, and D. Wang, “Distributed maneuvering of autonomous surface vehicles based on neurodynamic optimization and fuzzy approximation”, IEEE Transactions on Control Systems Technology, vol. 26, no. 3, pp. 1083–1090, May 2018.
Z. Zheng and L. Sun, “Path following control for marine surface vessel with uncertainties and input saturation,” Neurocomputing, vol. 177, pp. 158–167, February 2016.
G. Zhu, J. Du, and Y. Kao, “Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation”, Journal of the Franklin Institute, vol. 355, no. 15, pp. 7548–7569, October 2018.
J. Du, X. Hu, M. Krstic, and Y. Sun, “Robust dynamic positioning of ships with disturbances under input saturation,” Automatica, vol. 73, pp. 207–214, November 2016.
D. Mu, G. Wang, Y. Fan, X. Sun, and B. Qiu, “Adaptive LOS Path Following for Podded Propulsion Unmanned Surface Vehicle with Uncertainty of Model and Actuator Saturation,” Applied Sciences, vol. 12, no. 7, pp. 1232, December 2017.
H. K. Khalil, Nonlinear Systems, Prentice Hall, New York, America, 1996.
N. Wang, Z. Sun, J. Yin, S. Su, and S. Sharma, “Finite-time observer based guidance and control of underactuated surface vehicles with unknown sideslip angles and disturbances,” IEEE Access, vol. 6, pp. 14059–14070, January 2018.
Z. Zheng and M. Feroskhan, “Path following of a surface vessel with prescribed performance in the presence of input saturation and external disturbances”, IEEE/ASME Transactions on Mechatronics, vol. 22, no. 6, pp. 2564–2575, December 2017.
Y. Zou and Z. Zheng, “A robust adaptive RBFNN augmenting backstepping control approach for a model-scaled helicopter,” IEEE Transactions on Control Systems Technology, vol. 23, no. 6, pp. 2344–2352, 2015.
X. Shao and H. Wang, “Back-stepping robust trajectory linearization control for hypersonic reentry vehicle via novel tracking differentiator”, Journal of the Franklin Institute, vol. 353, no. 9, pp. 1957–1984, June 2016.
B. Qiu, G. Wang, Y. Fan, D. Mu, and X. Sun, “Robust adaptive trajectory linearization control for tracking control of surface vessels with modeling uncertainties under input saturation,” IEEE Access, vol. 7, pp. 5057–5070, January 2019.
Y. Liu, J. J. Zhu, R. Williams II, and J. Wu, “Omnidirectional mobile robot controller based on trajectory linearization”, Robotics and Autonomous Systems, vol. 56, no. 5, pp. 461–479, May 2008.
Y. Chen and J. J. Zhu, “Car-like ground vehicle trajectory tracking by using trajectory linearization control,” Proc. of ASME 2017 Dynamic Systems and Control Conference, vol. 2, 2017.
T. I. Fossen and J. P. Strand, “Passive nonlinear observer design for ships using Lyapunov methods: full-scale experiments with a supply vessel”, Automatica, vol. 35, no. 1, pp. 3–16, January 1999.
D. Mu, G. Wang, Y. Fan, X. Sun, and B. Qiu, “Modeling and identification for vector propulsion of an unmanned surface vehicle: Three degrees of freedom model and response model,” Sensors, vol. 18, no. 6, June 2018.
B. Z. Guo and Z. L. Zhao, “Weak convergence of nonlinear high-gain tracking differentiator,” IEEE Transactions on Automatic Control, vol. 58, no. 4, pp. 1074–1080, 2013.
D. Mu, G. Wang, Y. Fan, B. Qiu, and X. Sun, “Adaptive course control based on trajectory linearization control for unmanned surface vehicle with unmodeled dynamics and input saturation,” Neurocomputing, vol. 330, pp. 1–10, February 2019.
S. Zare, A. Tavakolpour-Saleh, A. Shourangiz-Haghighi, and T. Binazadeh, “Assessment of damping coefficients ranges in design of a free piston Stirling engine: Simulation and experiment,” Energy, vol. 185, pp. 633–643, October 2019.
A. Shourangiz-Haghighi, M. A. Haghnegahdar, L. Wang, M. Mussetta, A. Kolios, and M. Lander, “State of the art in the optimisation of wind turbine performance using CFD,” Archives of Computational Methods in Engineering, 2019. DOI: 10.1007/s11831-019-09316-0
R. Faraji and H. Farzanehfard, “Soft-switched nonisolated high step-up three-port DC-DC converter for hybrid energy systems”, IEEE Transactions on Power Electronics, vol. 33, no. 12, pp. 10101–10111, December 2018.
V. Stojanovic, N. Nedic, D. Prsic, and L. Dubonjic, “Optimal experiment design for identification of ARX models with constrained output in non-Gaussian noise,” Applied Mathematical Modelling, vol. 40, no. 13-14, pp. 6676–6689, July 2016.
V. Stojanovic and N. Nedic, “Identification of time-varying OE models in presence of non-Gaussian noise: Application to pneumatic servo drives”, International Journal of Robust and Nonlinear Control, vol. 26, no. 18, pp. 3974–3995, December 2016.
V. Filipovic, N. Nedic, and V. Stojanovic, “Robust identification of pneumatic servo actuators in the real situations”, Forschung im Ingenieurwesen/Engineering Research, vol. 75, no. 4, pp. 183–196, December 2011.
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Recommended by Associate Editor Muhammad Rehan under the direction of Editor Myo Taeg Lim. This work was supported by the National Natural Science Foundation of China (grand number 51609033), the Natural Science Foundation of Liaoning Province (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 numbers 3132019005, 3132019311).
Bingbing Qiu received his M.S. degree in Control theory and Engineering from Dalian Maritime University, Dalian, China, in 2017. He is now pursuing a Ph.D. degree in control theory and control engineering at Dalian Maritime University. His research interests include nonlinear control and intelligent control of unmanned surface vehicle.
Guobeng Wang received his Ph.D. degree from Dalian Maritime University. He is currently a Professor in Dalian Maritime University, and his research interests include ship automation, advanced ship borne detection device and advanced power transmission.
Yunbheng Fan received his Ph.D. degree from Dalian Maritime University in 2012. He is currently a Lecturer in Dalian Maritime University, and his research interests are ship intelligent control and its application.
Dongdong Mu received his M.S. degree in Control theory and Engineering from Dalian Maritime University in 2015, and he is now pursuing a Ph.D. degree in control theory and control engineering at Dalian Maritime University. His research interests include modeling and intelligent control of unmanned surface vehicle.
Xiaojie Sun received his M.E. degree in control engineering from Dalian Maritime University, Dalian, China, in 2016, and he is now pursuing a Ph.D. degree in control theory and control engineering at Dalian Maritime University. His research interests include modeling and collision avoidance control of unmanned surface vehicle.
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Qiu, B., Wang, G., Fan, Y. et al. Path Following of Underactuated Unmanned Surface Vehicle Based on Trajectory Linearization Control with Input Saturation and External Disturbances. Int. J. Control Autom. Syst. 18, 2108–2119 (2020). https://doi.org/10.1007/s12555-019-0659-3
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DOI: https://doi.org/10.1007/s12555-019-0659-3