Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm Optimization

An adaptive sliding mode controller (SMC) design with a reinforcement-learning parameter optimization method is proposed for variable-speed trajectory tracking control of underactuated vessels under scenarios involving model uncertainties and external environmental disturbances. First, considering t...

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Main Authors: Shiya Zhu, Gang Zhang, Qin Wang, Zhengyu Li
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Journal of Marine Science and Engineering
Subjects:
Online Access:https://www.mdpi.com/2077-1312/13/1/99
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author Shiya Zhu
Gang Zhang
Qin Wang
Zhengyu Li
author_facet Shiya Zhu
Gang Zhang
Qin Wang
Zhengyu Li
author_sort Shiya Zhu
collection DOAJ
description An adaptive sliding mode controller (SMC) design with a reinforcement-learning parameter optimization method is proposed for variable-speed trajectory tracking control of underactuated vessels under scenarios involving model uncertainties and external environmental disturbances. First, considering the flexible control requirements of the vessel’s propulsion system, the desired navigation speed is designed to satisfy an S-curve acceleration and deceleration process. The rate of change of the trajectory parameters is derived. Second, to address the model uncertainties and external disturbances, an extended state observer (ESO) is designed to estimate the unknown bounded disturbances and to provide feedforward compensation. Moreover, an adaptive law is designed to estimate the upper bound of the unknown disturbances, ensuring system stability even in the presence of asymptotic observation errors. Finally, the Twin-Delayed Deep Deterministic Policy Gradient (TD3) algorithm is employed for real-time controller parameter tuning. Numerical simulation results demonstrate that the proposed method significantly improves the trajectory tracking accuracy and dynamic response speed of the underactuated vessel. Specifically, for a sinusoidal trajectory with an amplitude of 200 m and a frequency of 0.01, numerical results show that the proposed method achieves convergence of the longitudinal tracking error to zero, while the lateral tracking error remains stable within 1 m. For the circular trajectory with a radius of 300 m, the numerical results indicate that both the longitudinal and lateral tracking errors are stabilized within 1 m. Compared with the fixed-value sliding mode controller, the proposed method demonstrates superior trajectory tracking accuracy and smoother control performance.
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institution Kabale University
issn 2077-1312
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publishDate 2025-01-01
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spelling doaj-art-2eaed5cba7864c4fafd92defe46025512025-01-24T13:36:51ZengMDPI AGJournal of Marine Science and Engineering2077-13122025-01-011319910.3390/jmse13010099Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm OptimizationShiya Zhu0Gang Zhang1Qin Wang2Zhengyu Li3Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, ChinaFaculty of Maritime and Transportation, Ningbo University, Ningbo 315211, ChinaFaculty of Maritime and Transportation, Ningbo University, Ningbo 315211, ChinaFaculty of Maritime and Transportation, Ningbo University, Ningbo 315211, ChinaAn adaptive sliding mode controller (SMC) design with a reinforcement-learning parameter optimization method is proposed for variable-speed trajectory tracking control of underactuated vessels under scenarios involving model uncertainties and external environmental disturbances. First, considering the flexible control requirements of the vessel’s propulsion system, the desired navigation speed is designed to satisfy an S-curve acceleration and deceleration process. The rate of change of the trajectory parameters is derived. Second, to address the model uncertainties and external disturbances, an extended state observer (ESO) is designed to estimate the unknown bounded disturbances and to provide feedforward compensation. Moreover, an adaptive law is designed to estimate the upper bound of the unknown disturbances, ensuring system stability even in the presence of asymptotic observation errors. Finally, the Twin-Delayed Deep Deterministic Policy Gradient (TD3) algorithm is employed for real-time controller parameter tuning. Numerical simulation results demonstrate that the proposed method significantly improves the trajectory tracking accuracy and dynamic response speed of the underactuated vessel. Specifically, for a sinusoidal trajectory with an amplitude of 200 m and a frequency of 0.01, numerical results show that the proposed method achieves convergence of the longitudinal tracking error to zero, while the lateral tracking error remains stable within 1 m. For the circular trajectory with a radius of 300 m, the numerical results indicate that both the longitudinal and lateral tracking errors are stabilized within 1 m. Compared with the fixed-value sliding mode controller, the proposed method demonstrates superior trajectory tracking accuracy and smoother control performance.https://www.mdpi.com/2077-1312/13/1/99underactuated vesselsvariable-speed trajectory trackingextended state observersliding mode control
spellingShingle Shiya Zhu
Gang Zhang
Qin Wang
Zhengyu Li
Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm Optimization
Journal of Marine Science and Engineering
underactuated vessels
variable-speed trajectory tracking
extended state observer
sliding mode control
title Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm Optimization
title_full Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm Optimization
title_fullStr Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm Optimization
title_full_unstemmed Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm Optimization
title_short Sliding Mode Control for Variable-Speed Trajectory Tracking of Underactuated Vessels with TD3 Algorithm Optimization
title_sort sliding mode control for variable speed trajectory tracking of underactuated vessels with td3 algorithm optimization
topic underactuated vessels
variable-speed trajectory tracking
extended state observer
sliding mode control
url https://www.mdpi.com/2077-1312/13/1/99
work_keys_str_mv AT shiyazhu slidingmodecontrolforvariablespeedtrajectorytrackingofunderactuatedvesselswithtd3algorithmoptimization
AT gangzhang slidingmodecontrolforvariablespeedtrajectorytrackingofunderactuatedvesselswithtd3algorithmoptimization
AT qinwang slidingmodecontrolforvariablespeedtrajectorytrackingofunderactuatedvesselswithtd3algorithmoptimization
AT zhengyuli slidingmodecontrolforvariablespeedtrajectorytrackingofunderactuatedvesselswithtd3algorithmoptimization