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Keywords = underactuated underwater vehicle

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22 pages, 14847 KiB  
Article
Formation Control of Underactuated AUVs Using a Fractional-Order Sliding Mode Observer
by Long He, Mengting Xie, Ya Zhang, Shizhong Li, Bo Li, Zehui Yuan and Chenrui Bai
Fractal Fract. 2025, 9(7), 465; https://doi.org/10.3390/fractalfract9070465 - 18 Jul 2025
Viewed by 325
Abstract
This paper proposes a control method that combines a fractional-order sliding mode observer and a cooperative control strategy to address the problem of path-following for underactuated autonomous underwater vehicles (AUVs) in complex marine environments. First, a fractional-order sliding mode observer is designed, combining [...] Read more.
This paper proposes a control method that combines a fractional-order sliding mode observer and a cooperative control strategy to address the problem of path-following for underactuated autonomous underwater vehicles (AUVs) in complex marine environments. First, a fractional-order sliding mode observer is designed, combining fractional calculus and double-power convergence laws to enhance the estimation accuracy of high-frequency disturbances. An adaptive gain mechanism is introduced to avoid dependence on the upper bound of disturbances. Second, a formation cooperative control strategy based on path parameter coordination is proposed. By setting independent reference points for each AUV and exchanging path parameters, formation consistency is achieved with low communication overhead. For the followers’ speed control problem, an error-based expected speed adjustment mechanism is introduced, and a hyperbolic tangent function is used to replace the traditional arctangent function to improve the response speed of the system. Numerical simulation results show that this control method performs well in terms of path-following accuracy, formation maintenance capability, and disturbance suppression, verifying its effectiveness and robustness in complex marine environments. Full article
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33 pages, 4497 KiB  
Article
Tracking Control for Asymmetric Underactuated Sea Vehicles in Slow Horizontal Movement
by Przemyslaw Herman
Sensors 2025, 25(13), 4205; https://doi.org/10.3390/s25134205 - 5 Jul 2025
Viewed by 248
Abstract
In this paper, a robust tracking control problem for underactuated underwater vehicles in horizontal motion is investigated. The presented control scheme that performs the trajectory tracking task is a combination of the backstepping technique and the integral sliding mode control method using the [...] Read more.
In this paper, a robust tracking control problem for underactuated underwater vehicles in horizontal motion is investigated. The presented control scheme that performs the trajectory tracking task is a combination of the backstepping technique and the integral sliding mode control method using the inertial quasi velocities (IQVs) resulting from the inertia matrix decomposition. Unlike many known solutions, the proposed approach allows not only trajectory tracking, but also, due to the fact that IQV includes dynamic and geometric model parameters, allows us to obtain additional information about changes in vehicle behavior during movement. In this way, some insight into its dynamics is obtained. Moreover, the control strategy takes into account model inaccuracies and external disturbances, which makes it more useful from a technical point of view. Another advantage of this work is to indicate problems occurring during the implementation of trajectory tracking in algorithms with a dynamics model containing a diagonal inertia matrix, i.e., without inertial couplings. The theoretical results are illustrated by simulation tests conducted on two models of underwater vehicles with three degrees of freedom (DOF). Full article
(This article belongs to the Special Issue Sensing for Automatic Control and Measurement System)
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24 pages, 16899 KiB  
Article
Spatial Trajectory Tracking of Underactuated Autonomous Underwater Vehicles by Model–Data-Driven Learning Adaptive Robust Control
by Linyuan Guo, Ran Zhou, Qingchang Guo, Liran Ma, Chuxiong Hu and Jianbin Luo
J. Mar. Sci. Eng. 2025, 13(6), 1151; https://doi.org/10.3390/jmse13061151 - 10 Jun 2025
Viewed by 525
Abstract
This paper aims to solve the spatial trajectory tracking control problem of underactuated autonomous underwater vehicles (AUVs) in the presence of system parameter uncertainties and complex external disturbances. To accomplish this goal, a model–data-driven learning adaptive robust control (LARC) strategy is introduced for [...] Read more.
This paper aims to solve the spatial trajectory tracking control problem of underactuated autonomous underwater vehicles (AUVs) in the presence of system parameter uncertainties and complex external disturbances. To accomplish this goal, a model–data-driven learning adaptive robust control (LARC) strategy is introduced for AUVs. Firstly, a serial iterative learning control (ILC) approach is introduced as feedforward compensation, and then the corresponding trajectory tracking error dynamics model, the Feedforward Compensation–Line of Sight (FFC-LOS) guidance law, and the feedforward compensation-based kinematics controller are designed. Secondly, the dynamics controller is designed for AUVs, which consists of a linear feedback term, a nonlinear robust feedback term, an adjustable model compensation term, and a fast dynamic compensation term. In this control framework, the robust control and fast dynamic compensation parts are utilized to deal with nonlinear uncertainties and disturbances, the projection-type adaptive control part solves the influence caused by the uncertainty of system parameters, and the serial ILC part that is a data-driven learning method can further improve the trajectory tracking accuracy for repetitive tasks. Finally, comparative simulations under different scenarios and different types of disturbances are performed to verify the effectiveness of the proposed control strategy for AUVs. Full article
(This article belongs to the Section Ocean Engineering)
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23 pages, 2564 KiB  
Article
Hierarchical Adaptive Fixed-Time Formation Control for Multiple Underactuated Autonomous Underwater Vehicles Under Uncertain Disturbances and Input Saturation
by Jiacheng Chang, Lanyong Zhang, Yifan Tan, Xue Fu and Hongjun Yu
J. Mar. Sci. Eng. 2025, 13(6), 1146; https://doi.org/10.3390/jmse13061146 - 9 Jun 2025
Viewed by 483
Abstract
Recent advances in multiple autonomous underwater vehicles (AUVs) have highlighted formation control as a critical challenge for underwater collaborative operations. To address the inherent coupling between formation coordination and individual control in conventional approaches, this paper proposes a novel hierarchical framework of adaptive [...] Read more.
Recent advances in multiple autonomous underwater vehicles (AUVs) have highlighted formation control as a critical challenge for underwater collaborative operations. To address the inherent coupling between formation coordination and individual control in conventional approaches, this paper proposes a novel hierarchical framework of adaptive fixed-time formation control for multiple underactuated AUVs. This framework decouples AUVs’ formation requirements and individual control challenges into two distinct layers: the Collision-free Formation Trajectories Generation (CFTG) Layer and the Adaptive Trajectories Tracking (ATT) Layer. In the CFTG Layer, a consensus-based controller is developed to generate the desired trajectories for the AUVs to meet the requirements of complex formation tasks. And an improved artificial potential field method is proposed to ensure AUVs can reach the target point when the target is close to obstacles. In the ATT Layer, an auxiliary compensation system is designed to address the issue of input saturation. Furthermore, the adaptive fixed-time controllers are proposed to handle the uncertain parameters in the model, enabling underactuated AUVs to track the desired trajectory precisely. Both layers guarantee fixed-time convergence to increase the convergence speed. Simulations are conducted to demonstrate the effectiveness and better performance of the proposed method. Full article
(This article belongs to the Special Issue Design and Application of Underwater Vehicles)
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20 pages, 2369 KiB  
Article
Event-Triggered Adaptive Backstepping Control of Underactuated AUVs with Input Saturation
by Feng Qian, Yusheng Zheng, Ao Wang and Jianping Cai
Electronics 2025, 14(9), 1839; https://doi.org/10.3390/electronics14091839 - 30 Apr 2025
Cited by 1 | Viewed by 398
Abstract
This paper proposes a dynamic event-triggered adaptive backstepping control for underactuated autonomous underwater vehicle systems (AUVs) with input saturation. The proposed method ensures the system’s stability by introducing a new auxiliary signal system to compensate for the input saturation. Firstly, the underactuated AUVs [...] Read more.
This paper proposes a dynamic event-triggered adaptive backstepping control for underactuated autonomous underwater vehicle systems (AUVs) with input saturation. The proposed method ensures the system’s stability by introducing a new auxiliary signal system to compensate for the input saturation. Firstly, the underactuated AUVs is separated into the underactuated part and the actuated part, and then the dynamic auxiliary signal system is introduced. A transformation is used to combine the actuated part with the auxiliary signal system. The controller is designed using the adaptive backstepping method, and a dynamic event-triggering mechanism is constructed to obtain the event-triggering controller. A strict theoretical analysis is provided to avoid the Zeno phenomenon. Finally, the effectiveness of the dynamic event-triggered adaptive backstepping controller is verified by simulation. Full article
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19 pages, 7302 KiB  
Article
Safe and Optimal Motion Planning for Autonomous Underwater Vehicles: A Robust Model Predictive Control Framework Integrating Fast Marching Time Objectives and Adaptive Control Barrier Functions
by Zhonghe Tian and Mingzhi Chen
Drones 2025, 9(4), 273; https://doi.org/10.3390/drones9040273 - 3 Apr 2025
Viewed by 753
Abstract
Autonomous Underwater Vehicles (AUVs) have shown significant promise across various underwater applications, yet face challenges in dynamic environments due to the limitations of traditional motion planning methods while Artificial Potential Field (APF)-based control barrier functions focus solely on obstacle proximity and distance-based methods [...] Read more.
Autonomous Underwater Vehicles (AUVs) have shown significant promise across various underwater applications, yet face challenges in dynamic environments due to the limitations of traditional motion planning methods while Artificial Potential Field (APF)-based control barrier functions focus solely on obstacle proximity and distance-based methods oversimplify obstacle geometries, and both fail to ensure safety and satisfy turning radius constraints for under-actuated AUVs in intricate environments. This paper proposes a robust Model Predictive Control (MPC) framework integrating an enhanced fast marching control barrier function, specifically designed for AUVs equipped with fully directional sonar systems. The framework introduces a novel improvement for moving obstacles by extending the control barrier function field propagation along the obstacle’s movement direction. This enhancement generates precise motion plans that ensure safety, satisfy kinematic constraints, and effectively handle static and dynamic obstacles. Simulation results demonstrate superior obstacle avoidance and motion planning performance in complex scenarios, with key outcomes including a minimum safety margin of 1.86 m in cluttered environments (vs. 0 m for A* and FMM) and 1.76 m in dynamic obstacle scenarios (vs. 0.13 m for MPC-APFCBF), highlighting the framework’s ability to enhance navigation safety and efficiency for real-world AUV deployments in unpredictable marine environments. Full article
(This article belongs to the Special Issue Advances in Intelligent Coordination Control for Autonomous UUVs)
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23 pages, 844 KiB  
Article
Optimal Trajectory Tracking for Underactuated Systems via the Takagi–Sugeno Framework: An Autonomous Underwater Vehicle Mission Case Study
by Georgios P. Kladis, Lefteris Doitsidis and Nikos C. Tsourveloudis
Robotics 2025, 14(4), 45; https://doi.org/10.3390/robotics14040045 - 1 Apr 2025
Viewed by 523
Abstract
Autonomy of underwater vehicles has become an imperative feature due to increasingly challenging deep sea mission scenarios. In particular, for trajectory-tracking problems of Autonomous Underwater Vehicles (AUVs), the use of Lyapunov theory tools in state-of-the-art methods is common practice. These often require special [...] Read more.
Autonomy of underwater vehicles has become an imperative feature due to increasingly challenging deep sea mission scenarios. In particular, for trajectory-tracking problems of Autonomous Underwater Vehicles (AUVs), the use of Lyapunov theory tools in state-of-the-art methods is common practice. These often require special assumptions, according to the application considered, and ‘intuition’ for the choice of a control law, which often leads to conservative results. This article suggests a systematic analysis for the horizontal motion of an AUV which ensures global asymptotic stability for the closed loop system. A nonlinear underactuated AUV system is considered with linear and angular velocity constraints. The Takagi–Sugeno (TS) framework design is adopted for the representation of the original nonlinear system. The control law is synthesised using the standard parallel distributed compensation (PDC) control law structure and stability is guaranteed for the closed loop system. The design criteria are posed as linear matrix inequalities (LMIs) where sufficient conditions for the design of the control law are shown. The proposed approach can be easily adopted for different types of autonomous vehicles with minor modifications. Full article
(This article belongs to the Special Issue Autonomous Robotics for Exploration)
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22 pages, 1480 KiB  
Article
Predefined-Time Three-Dimensional Trajectory Tracking Control for Underactuated Autonomous Underwater Vehicles
by Jinzhong Wen, Jing Zhang and Guoyan Yu
Appl. Sci. 2025, 15(4), 1698; https://doi.org/10.3390/app15041698 - 7 Feb 2025
Cited by 1 | Viewed by 651
Abstract
This paper addresses the three-dimensional trajectory tracking problem of underactuated autonomous underwater vehicles (AUVs) operating in the presence of external disturbances and unmodeled dynamics by proposing a predefined-time adaptive control scheme. Firstly, the underactuated AUV system was decoupled into drive and non-drive subsystems [...] Read more.
This paper addresses the three-dimensional trajectory tracking problem of underactuated autonomous underwater vehicles (AUVs) operating in the presence of external disturbances and unmodeled dynamics by proposing a predefined-time adaptive control scheme. Firstly, the underactuated AUV system was decoupled into drive and non-drive subsystems to facilitate the design of a controller that does not rely on specific model parameters. Radial basis function neural networks (RBFNNs) were employed to estimate the external disturbances. To enhance tracking performance, a predefined-time adaptive control law was designed to ensure that tracking errors converged to a small neighborhood around the origin within the predefined time. The adaptive control law compensated for the unmodeled components. Finally, we used theoretical proofs and simulations to show that our method is effective and superior. Full article
(This article belongs to the Section Marine Science and Engineering)
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25 pages, 7861 KiB  
Article
System Identification and Navigation of an Underactuated Underwater Vehicle Based on LSTM
by Changhao Li, Zetao Hu, Desheng Zhang and Xin Wang
J. Mar. Sci. Eng. 2025, 13(2), 276; https://doi.org/10.3390/jmse13020276 - 31 Jan 2025
Cited by 1 | Viewed by 1047
Abstract
Modeling and system identification are critical for the design, simulation, and navigation of underwater vehicles. This study presents a six degree-of-freedom (DoF) nonlinear model for a finless underactuated underwater vehicle, incorporating port-starboard symmetry and cross-flow terms. Then, hydrodynamic damping parameters are identified using [...] Read more.
Modeling and system identification are critical for the design, simulation, and navigation of underwater vehicles. This study presents a six degree-of-freedom (DoF) nonlinear model for a finless underactuated underwater vehicle, incorporating port-starboard symmetry and cross-flow terms. Then, hydrodynamic damping parameters are identified using an optimized Extended Kalman Filter (EKF), establishing a steady validation framework for computational fluid dynamics (CFD) simulation coefficients. Additionally, system identification is further enhanced with a Long Short-Term Memory (LSTM) neural network and a comprehensive dataset construction method, enabling time-series predictions of linear and angular velocities. To mitigate position divergence in dead reckoning (DR) caused by LSTM, a Nonlinear Explicit Complementary Filter (NECF) is integrated for attitude estimation, providing accurate yaw computation and reliable localization without dependence on acoustic sensors or machine vision. Finally, validation and evaluation are conducted to demonstrate model accuracy, EKF convergence, and the reliability of LSTM-based navigation. Full article
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25 pages, 3925 KiB  
Article
Finite-Time Path-Following Control of Underactuated AUVs with Actuator Limits Using Disturbance Observer-Based Backstepping Control
by MohammadReza Ebrahimpour and Mihai Lungu
Drones 2025, 9(1), 70; https://doi.org/10.3390/drones9010070 - 18 Jan 2025
Cited by 4 | Viewed by 862
Abstract
This paper presents a three-dimensional (3D) robust adaptive finite-time path-following controller for underactuated Autonomous Underwater Vehicles (AUVs), addressing model uncertainties, external disturbances, and actuator magnitude and rate saturations. A path-following error system is built in a path frame using the virtual guidance method. [...] Read more.
This paper presents a three-dimensional (3D) robust adaptive finite-time path-following controller for underactuated Autonomous Underwater Vehicles (AUVs), addressing model uncertainties, external disturbances, and actuator magnitude and rate saturations. A path-following error system is built in a path frame using the virtual guidance method. The proposed cascaded closed-loop control scheme can be described in two separate steps: (1) A kinematic law based on a finite-time backstepping control (FTBSC) is introduced to transform the 3D path-following position errors into the command velocities; (2) The actual control inputs are designed in the dynamic controller using an adaptive fixed-time disturbance observer (AFTDO)-based FTBSC to stabilize the velocity tracking errors. Moreover, the adverse effects of magnitude and rate saturations are reduced by an auxiliary compensation system. A Lyapunov-based stability analysis proves that the path-following errors converge to an arbitrarily small region around zero within a finite time. Comparative simulations illustrate the effectiveness and robustness of the proposed controller. Full article
(This article belongs to the Special Issue Advances in Autonomy of Underwater Vehicles (AUVs))
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19 pages, 9913 KiB  
Article
Enhanced Control Strategies for Underactuated AUVs Using Backstepping Integral Sliding Mode Techniques for Ocean Current Challenges
by Qingdong Chen, Jianping Yuan, Zhihui Dong, Zhuohui Chai and Lei Wan
J. Mar. Sci. Eng. 2024, 12(12), 2201; https://doi.org/10.3390/jmse12122201 - 1 Dec 2024
Cited by 1 | Viewed by 1316
Abstract
This paper examines the control challenges faced by underactuated Autonomous Underwater Vehicles (AUVs) under ocean current disturbances. It proposes a Backstepping Integral Sliding Mode Control (BISMC) strategy to enhance their adaptability and robustness. The BISMC strategy integrates the system decomposition capability of the [...] Read more.
This paper examines the control challenges faced by underactuated Autonomous Underwater Vehicles (AUVs) under ocean current disturbances. It proposes a Backstepping Integral Sliding Mode Control (BISMC) strategy to enhance their adaptability and robustness. The BISMC strategy integrates the system decomposition capability of the backstepping control method with the rapid response and robustness advantages of the Sliding Mode Control method, enabling the design of a heading controller and a double closed-loop depth controller. By introducing an integral component, the strategy eliminates steady-state errors caused by ocean currents, accelerating system convergence and improving accuracy. Furthermore, a saturation function is employed to mitigate output chattering issues. Simulation results demonstrate that the BISMC controller significantly enhances the control precision and anti-disturbance capabilities of AUVs under low-frequency ocean current disturbances, showcasing exceptional adaptive and self-disturbance rejection performance. Full article
(This article belongs to the Section Ocean Engineering)
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20 pages, 6803 KiB  
Article
Attitude Practical Stabilization of Underactuated Autonomous Underwater Vehicles in Vertical Plane
by Yuliang Wang, Han Bao, Yiping Li and Hongbin Zhang
J. Mar. Sci. Eng. 2024, 12(11), 1940; https://doi.org/10.3390/jmse12111940 - 30 Oct 2024
Viewed by 1083
Abstract
Due to the singularity of Euler angles and the ambiguity of quaternions, to further expand the attitude reachable range of underactuated AUVs in the vertical plane, SO(3) is used to represent the attitude change of underactuated AUVs. The transverse [...] Read more.
Due to the singularity of Euler angles and the ambiguity of quaternions, to further expand the attitude reachable range of underactuated AUVs in the vertical plane, SO(3) is used to represent the attitude change of underactuated AUVs. The transverse function of the attitude on SO(3) is designed, and the exponential mapping method is used to construct the attitude kinematic controller of underactuated AUVs. Considering the changes in the model and ocean current during motion, interval type II fuzzy systems (IT2-FLSs) are used to estimate these changes. The backstepping method and the small gain theorem are adopted to design dynamic controllers to ensure the stability and robustness of the system. A novel saturation auxiliary system is designed to compensate for the influence of actuator saturation characteristics. Finally, the simulation results verify the effectiveness of the proposed controller and ensure the practical stabilization of the underactuated AUV attitude. Full article
(This article belongs to the Special Issue Motion Control and Path Planning of Marine Vehicles—3rd Edition)
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17 pages, 7151 KiB  
Article
Gaze-Assisted Prescribed Performance Controller for AUV Trajectory Tracking in Time-Varying Currents
by Zhuoyu Zhang, Mingwei Lin, Dejun Li and Ri Lin
J. Mar. Sci. Eng. 2024, 12(9), 1643; https://doi.org/10.3390/jmse12091643 - 13 Sep 2024
Cited by 1 | Viewed by 930
Abstract
Trajectory tracking for underactuated autonomous underwater vehicles (AUVs) is challenging due to coupling dynamics, modeling inaccuracies, and unknown disturbances. To tackle this, we propose a decoupling gaze-assisted prescribed performance controller (GAPPC). We first use an error transformation approach to achieve the prescribed performance, [...] Read more.
Trajectory tracking for underactuated autonomous underwater vehicles (AUVs) is challenging due to coupling dynamics, modeling inaccuracies, and unknown disturbances. To tackle this, we propose a decoupling gaze-assisted prescribed performance controller (GAPPC). We first use an error transformation approach to achieve the prescribed performance, incorporating the line-of-sight (LOS) algorithm and an event-triggering mechanism to handle the kinematic characteristics of underactuated AUVs. Next, we develop a control strategy for the transformed error that does not require knowledge of the model parameters, including fast dynamic compensation to reduce steady-state errors. Finally, we analyze the controller’s stability and present simulation results. Simulations, which account for modeling inaccuracies and unknown ocean currents, show that the GAPPC improves stability errors by 67.3% compared to the adaptive robust controller. Full article
(This article belongs to the Section Ocean Engineering)
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19 pages, 10639 KiB  
Article
Prescribed Performance Formation Tracking Control for Underactuated AUVs under Time-Varying Communication Delays
by Haitian Zhang, Yanqing Jiang, Rui Gao, Hang Li and Ao Li
J. Mar. Sci. Eng. 2024, 12(9), 1533; https://doi.org/10.3390/jmse12091533 - 3 Sep 2024
Cited by 1 | Viewed by 1257
Abstract
Achieving formation tracking control of underactuated autonomous underwater vehicles (AUVs) under communication delays presents a significant challenge. To address this challenge, a distributed prescribed performance control protocol based on a real-time state information online predictor (RSIOP) is proposed in this paper. First, we [...] Read more.
Achieving formation tracking control of underactuated autonomous underwater vehicles (AUVs) under communication delays presents a significant challenge. To address this challenge, a distributed prescribed performance control protocol based on a real-time state information online predictor (RSIOP) is proposed in this paper. First, we innovatively designed an RSIOP to achieve active compensation for the delayed state information of neighboring AUVs. Next, considering formation performance and safety, a low-complexity and practical nonlinear mapping function was used to implement prescribed performance tracking control for the AUV formation. Additionally, the adverse effects of external disturbance uncertainties and input saturation are also considered. Finally, the simulation tests demonstrated that the proposed formation control protocol can successfully achieve the predetermined formation tracking tasks in the presence of time-varying communication delays and external disturbances, while also enabling real-time changes in formation configuration during the process. Throughout, the protocol maintains input saturation limits, and the actual control inputs remain smooth, with no significant oscillations. Furthermore, comparative simulation tests verified the necessity of the RSIOP developed in this study and quantitatively demonstrated that the proposed control method exhibits superior performance in terms of formation control accuracy, error convergence speed, and transient-state constraints. Full article
(This article belongs to the Special Issue Autonomous Marine Vehicle Operations—2nd Edition)
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19 pages, 1621 KiB  
Article
Trajectory Tracking Control for an Underactuated AUV via Nonsingular Fast Terminal Sliding Mode Approach
by Yuan Wang and Zhenbin Du
J. Mar. Sci. Eng. 2024, 12(8), 1442; https://doi.org/10.3390/jmse12081442 - 21 Aug 2024
Cited by 3 | Viewed by 1409
Abstract
This paper studies the trajectory tracking issue for an underactuated autonomous underwater vehicle (AUV) in the horizontal plane. The desired velocity–tracking error relationship (DVTER) is constructed according to the kinematics and kinetic equation, which means that the expected velocities are built so that [...] Read more.
This paper studies the trajectory tracking issue for an underactuated autonomous underwater vehicle (AUV) in the horizontal plane. The desired velocity–tracking error relationship (DVTER) is constructed according to the kinematics and kinetic equation, which means that the expected velocities are built so that the position tracking errors converge to 0. Moreover, the limitation of obtaining the expected velocity by directly differentiating the desired position values is avoided. Then, the nonsingular fast terminal sliding mode (TSM) controller is developed to ensure that the velocities converge to the designed expected values in finite time, and tracking speed is improved by comparing with the traditional nonsingular terminal sliding mode method. It turns out that the expected trajectory can be tracked by an underactuated AUV. Finally, the efficiency of the constructed control mechanism is confirmed by simulation results. Full article
(This article belongs to the Section Ocean Engineering)
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