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Keywords = underactuated surface vessels

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25 pages, 6353 KiB  
Article
Fractional-Order Controller for the Course Tracking of Underactuated Surface Vessels Based on Dynamic Neural Fuzzy Model
by Guangyu Li, Yanxin Li, Xiang Li, Mutong Liu, Xuesong Zhang and Hua Jin
Fractal Fract. 2024, 8(12), 720; https://doi.org/10.3390/fractalfract8120720 - 5 Dec 2024
Viewed by 472
Abstract
Aiming at the uncertainty problem caused by the time-varying modeling parameters associated with ship speed in the course tracking control of underactuated surface vessels (USVs), this paper proposes a control algorithm based on the dynamic neural fuzzy model (DNFM). The DNFM simultaneously adjusts [...] Read more.
Aiming at the uncertainty problem caused by the time-varying modeling parameters associated with ship speed in the course tracking control of underactuated surface vessels (USVs), this paper proposes a control algorithm based on the dynamic neural fuzzy model (DNFM). The DNFM simultaneously adjusts the structure and parameters during learning and fully approximates the inverse dynamics of ships. Online identification and modeling lays the model foundation for ship motion control. The trained DNFM, serving as an inverse controller, is connected in parallel with the fractional-order PIλDμ controller to be used for the tracking control of the ship’s course. Moreover, the weights of the model can be further adjusted during the course tracking. Taking the actual ship data of a 5446 TEU large container ship, simulation experiments are conducted, respectively, for course tracking, course tracking under wind and wave interferences, and comparison with five different controllers. This proposed controller can overcome the influence of the uncertainty of modeling parameters, tracking the desired course quickly and effectively. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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<p>Motion coordinate system.</p>
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<p>Corresponding nonlinear ship model.</p>
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<p>Dynamic neural fuzzy model structure.</p>
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<p>Identification process of inverse model for ship course control.</p>
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<p>Flow of inverse model identification for ship course control based on DNFM.</p>
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<p>Ship course control system.</p>
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<p>Change in ship speed V.</p>
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<p>Change in ship model parameters <math display="inline"><semantics> <mrow> <mi mathvariant="normal">K</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">T</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">α</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">β</mi> </mrow> </semantics></math>.</p>
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<p>DNFM generating fuzzy rules.</p>
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<p>DNFM identification results.</p>
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<p>Root mean squared error in learning.</p>
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<p>DNFM identification error.</p>
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<p>Ship course tracking.</p>
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<p>Rudder control for ship course.</p>
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<p>Equivalent rudder angle of wind.</p>
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<p>Equivalent rudder angle of waves.</p>
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<p>DNFM generating fuzzy rules under wind and wave disturbances.</p>
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<p>DNFM identification results under wind and wave disturbances.</p>
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<p>Root mean squared error under wind and wave disturbances.</p>
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<p>Identification error of DNFM.</p>
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<p>Course control and rudder angle curves under wind and wave disturbances.</p>
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<p>Comparison of five different controllers.</p>
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<p>Rudder angle using five different controllers.</p>
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20 pages, 8044 KiB  
Article
Distributed Improved RILOS Guidance-Based Formation Control of Underactuated ASVs for Cooperative Maritime Search
by Weili Guo, Cheng Liu, Feng Xu and Ting Sun
J. Mar. Sci. Eng. 2024, 12(11), 1911; https://doi.org/10.3390/jmse12111911 - 25 Oct 2024
Viewed by 579
Abstract
A distributed improved robust integral line-of-sight (RILOS) guidance-based sliding mode controller is designed for multiple underactuated autonomous surface vessels (ASVs) to perform cooperative maritime search operations. First, a parallel circle search pattern is designed based on the detection range of ASVs, which can [...] Read more.
A distributed improved robust integral line-of-sight (RILOS) guidance-based sliding mode controller is designed for multiple underactuated autonomous surface vessels (ASVs) to perform cooperative maritime search operations. First, a parallel circle search pattern is designed based on the detection range of ASVs, which can provide the reference formation shape. Second, an improved RILOS method is presented by introducing an integral term into the improved robust LOS method, which can counteract the disadvantageous effect of the unknown sideslip angle and kinematic discrepancy simultaneously. Third, distributed improved RILOS guidance is presented by integrating the extended second-order consensus algorithm into the improved RILOS method; then, the desired heading angle and desired velocity are generated for the control system simultaneously. Finally, the fuzzy logic system is integrated into the sliding mode control (SMC) method to approximate the unknown nonlinear function; then, a distributed improved RILOS guidance-based SMC controller is presented for multiple ASVs. The closed-loop signals are proved to be stable by the Lyapunov theory. The effectiveness of the presented method is verified by multiple simulations. Full article
(This article belongs to the Special Issue Optimal Maneuvering and Control of Ships—2nd Edition)
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<p>Illustration of the parallel circle search pattern.</p>
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<p>The geometry of LOS method.</p>
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<p>Diagram for the distributed improved RILOS guidance-based SMC controller for cooperative maritime search.</p>
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<p>The communication topology for four ASVs.</p>
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<p>The cooperative maritime search performed by four ASVs.</p>
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<p>The control inputs of four ASVs.</p>
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<p>The velocities of four ASVs.</p>
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<p>The results <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>f</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>r</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> of the fuzzy approximator.</p>
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<p>The results <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>f</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>u</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> of the fuzzy approximator.</p>
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<p>The switching topology for five ASVs.</p>
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<p>The performance of formation control under the switching topology.</p>
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<p>The control inputs of five ASVs under the switching topology.</p>
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<p>The velocities of five ASVs under the switching topology.</p>
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<p>The approximated results <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>f</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>r</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> of five ASVs.</p>
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<p>The approximated results <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>f</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>u</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> of five ASVs.</p>
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<p>Comparisons of tracking performance between the presented improved RILOS method and the LOS method in [<a href="#B39-jmse-12-01911" class="html-bibr">39</a>].</p>
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<p>Comparisons of tracking errors between the presented improved RILOS method and the LOS method in [<a href="#B39-jmse-12-01911" class="html-bibr">39</a>].</p>
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<p>Comparisons of control inputs between the presented improved RILOS method and the LOS method in [<a href="#B39-jmse-12-01911" class="html-bibr">39</a>].</p>
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19 pages, 5629 KiB  
Article
A Model-Free Adaptive Positioning Control Method for Underactuated Unmanned Surface Vessels in Unknown Ocean Currents
by Zihe Qin, Feng Zhang, Wenlin Xu, Yu Chen and Jinyu Lei
J. Mar. Sci. Eng. 2024, 12(10), 1801; https://doi.org/10.3390/jmse12101801 - 9 Oct 2024
Viewed by 704
Abstract
Aiming to address the problem of underactuated unmanned surface vehicles (USVs) performing fixed-point operations at sea without dynamic positioning control systems, this paper introduces an original approach to positioning control: the virtual anchor control method. This method is applicable in environments with currents [...] Read more.
Aiming to address the problem of underactuated unmanned surface vehicles (USVs) performing fixed-point operations at sea without dynamic positioning control systems, this paper introduces an original approach to positioning control: the virtual anchor control method. This method is applicable in environments with currents that change slowly and does not require prior knowledge of current information or vessel motion model parameters, thus offering convenient usability. This method comprises four steps. First, a concise linear motion model with unknown disturbances is proposed. Then, a motion planning law is designed by imitating underlying principles of ship anchoring. Next, an adaptive disturbance observer is proposed to estimate uncertainties in the motion model. In the last step, based on the observer, a sliding-mode method is used to design a heading control law, and a thrust control law is also designed by applying the Lyapunov method. Numerical simulation experiments with significant disturbances and tidal current variations are conducted, which demonstrate that the proposed method has a good control effect and is robust. Full article
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<p>Linear motion model of USV with 3-DOF on water surface.</p>
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<p>Schematic diagram of functional area division for virtual anchoring.</p>
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<p>A schematic diagram of the movement trajectory of a USV during virtual anchoring.</p>
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<p>The movement trajectory of the USV.</p>
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<p>Anchoring point distance–time curve.</p>
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<p>Heading angle–time curve.</p>
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<p>Rudder angle–time curve.</p>
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<p>Velocity–time curve.</p>
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<p>Propeller speed–time curve.</p>
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<p>Motion trajectories of the USV under different conditions (<b>a</b>–<b>h</b>).</p>
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<p>Current velocity (<b>a</b>) and current direction angle (<b>b</b>) over 24 h.</p>
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<p>The movement trajectory of the USV.</p>
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<p>Heading angle over 24 h.</p>
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<p>Rudder angle over 24 h.</p>
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<p>Velocity curve over 24 h.</p>
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<p>Propeller speed–time curve over 24 h.</p>
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20 pages, 3696 KiB  
Article
Quasi-Infinite Horizon Model Predictive Control with Fixed-Time Disturbance Observer for Underactuated Surface Vessel Path Following
by Wei Li, Hanyun Zhou and Jun Zhang
J. Mar. Sci. Eng. 2024, 12(6), 967; https://doi.org/10.3390/jmse12060967 - 8 Jun 2024
Cited by 2 | Viewed by 693
Abstract
As a flexible, autonomous and intelligent motion platform, underactuated surface vessels (USVs) are expected to be an ideal means of transport in dangerous and complex marine environments. The success and efficiency of maritime missions performed by USVs depend on their ability to accurately [...] Read more.
As a flexible, autonomous and intelligent motion platform, underactuated surface vessels (USVs) are expected to be an ideal means of transport in dangerous and complex marine environments. The success and efficiency of maritime missions performed by USVs depend on their ability to accurately follow paths and remain robust against wind and wave disturbances. To this end, this paper focuses on accurate and robust path following control for USVs under wave disturbances. Model predictive control with a quasi-infinite horizon is proposed which converts the objective function from an infinite horizon to an approximate finite horizon, providing the convergence performance in long prediction horizons and reducing the computation load explicitly. To enhance robustness against disturbances, a fixed-time disturbance observer is applied to estimate the time-varying and bounded disturbances. The estimated value is provided to the controller input to form a robust control framework with disturbance feedforward compensation and predictive control feedback correction, which is substantially different from existing works. The convergence and optimality of the proposed algorithm are presented mathematically. Finally, we demonstrate the advantages of the algorithm in both theory and simulation. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Illustration of the coordinates in the earth frame (inertial frame) {O}, the surface vessel body-fixed frame {B} and the Serret–Frenet {SF} frame.</p>
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<p>USV path following with disturbance compensation framework based on QiH-MPC and fixed-time observer.</p>
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<p>USV SL-20Y path following block diagram based on QiH-MPC with fixed-time observer.</p>
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<p>(<b>a</b>) Simulation results for USV desired path 1 following; (<b>b</b>) the states and controller output for desired path 1 following.</p>
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<p>(<b>a</b>) Simulation results for USV desired path 2 following; (<b>b</b>) the states and controller output for desired path 2 following.</p>
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<p>Comparisons between QiH-MPC and conventional MPC for desired path 1 following: (<b>a</b>) USV path 1 following result; (<b>b</b>) the states and controller output simulation result for target path 1.</p>
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<p>Comparisons between QiH-MPC and conventional MPC for desired path 2 following: (<b>a</b>) USV path 2 following result; (<b>b</b>) the states and controller output simulation result for target path 2.</p>
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<p>(<b>a</b>) Performance of QiH-MPC with and without FTO for USV path 1 following; (<b>b</b>) performance of QiH-MPC with and without FTO for USV path 2 following.</p>
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<p>(<b>a</b>) USV path following results of QiH-MPC with and without FTO; (<b>b</b>) the actual wave disturbances and their estimation based on FTO.</p>
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19 pages, 3219 KiB  
Article
The Non-Singular Terminal Sliding Mode Control of Underactuated Unmanned Surface Vessels Using Biologically Inspired Neural Network
by Donghao Xu, Zelin Li, Ping Xin and Xueqian Zhou
J. Mar. Sci. Eng. 2024, 12(1), 112; https://doi.org/10.3390/jmse12010112 - 7 Jan 2024
Cited by 5 | Viewed by 1228
Abstract
Underactuated Unmanned Surface Vessels (USVs) are widely used in civil and military fields due to their small size and high flexibility, and trajectory tracking control is a critical research area for underactuated USVs. This paper proposes a trajectory tracking control strategy using the [...] Read more.
Underactuated Unmanned Surface Vessels (USVs) are widely used in civil and military fields due to their small size and high flexibility, and trajectory tracking control is a critical research area for underactuated USVs. This paper proposes a trajectory tracking control strategy using the Biologically Inspired Neural Network (BINN) for USVs to improve tracking speed and accuracy. A virtual control law is designed to obtain the required virtual velocity for trajectory tracking control, in which the velocity error is calibrated to ensure that the position error converges to zero. To observe and compensate for unknown and complex environmental disturbances such as wind, waves, and currents, a nonlinear extended state observer (NESO) is designed. Then, a controller based on Non-singular Terminal Sliding Mode (NTSM) is designed to resolve the problems of singular value and controller chattering and to improve the controller response speed. A BINN is introduced to simplify the process of differentiation, reduce the input values of the initial state, and solve the problem of thruster input saturation. Finally, the Lyapunov stability theory is utilized to analyze the stability of the proposed algorithm. The simulation results show that the proposed algorithm has a higher trajectory tracking accuracy and speed than traditional methods. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Earth-fixed and Body-fixed coordinate frames of underactuated USVs.</p>
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<p>Trajectory tracking structure of underactuated USV.</p>
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<p>Simulation results of the straight path. (<b>a</b>) Trajectory tracking results for the USV; (<b>b</b>) Position tracking results for the USV; (<b>c</b>) Velocity tracking results for the USV; (<b>d</b>) Control inputs change over time.</p>
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<p>Simulation results of the straight path errors. (<b>a</b>) straight path position tracking errors; (<b>b</b>) straight path velocity tracking errors.</p>
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<p>Simulation results of the straight path observation. (<b>a</b>) Straight path position estimation curves using NESO; (<b>b</b>) Straight path velocity estimation curves using NESO; (<b>c</b>) Disturbance estimation curves using NESO and NDOB.</p>
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<p>Simulation results of the circular path. (<b>a</b>) Trajectory tracking results for the USV; (<b>b</b>) Position tracking results for the USV; (<b>c</b>) Velocity tracking results for the USV; (<b>d</b>) Control inputs change over time.</p>
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<p>Simulation results of the circular path errors. (<b>a</b>) circular path position tracking errors; (<b>b</b>) circular path velocity tracking errors.</p>
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<p>Simulation results of the circular path observation. (<b>a</b>) Circular path position estimation curves using NESO; (<b>b</b>) Circular path velocity estimation curves using NESO; (<b>c</b>) Disturbance estimation curves using NESO and NDOB.</p>
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18 pages, 3385 KiB  
Article
Model Predictive Control Based on State Space and Risk Augmentation for Unmanned Surface Vessel Trajectory Tracking
by Wei Li, Jun Zhang, Fang Wang and Hanyun Zhou
J. Mar. Sci. Eng. 2023, 11(12), 2283; https://doi.org/10.3390/jmse11122283 - 30 Nov 2023
Cited by 4 | Viewed by 1428
Abstract
The underactuated unmanned surface vessel (USV) has been identified as a promising solution for future maritime transport. However, the challenges of precise trajectory tracking and obstacle avoidance remain unresolved for USVs. To this end, this paper models the problem of path tracking through [...] Read more.
The underactuated unmanned surface vessel (USV) has been identified as a promising solution for future maritime transport. However, the challenges of precise trajectory tracking and obstacle avoidance remain unresolved for USVs. To this end, this paper models the problem of path tracking through the first-order Nomoto model in the Serret–Frenet coordinate system. A novel risk model has been developed to depict the association between USVs and obstacles based on SFC. Combined with an artificial potential field that accounts for environmental obstacles, model predictive control (MPC) based on state space is employed to achieve the optimal control sequence. The stability of the designed controller is demonstrated by means of the Lyapunov method and zero-pole analysis. Through simulation, it has been demonstrated that the controller is asymptotically stable concerning track error deviation, heading angle deviation, and heading angle speed, and its good stability and robustness in the presence of multiple risks are verified. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Illustration of the coordinates in the earth frame (inertial frame) {O}, the surface vessel body-fixed frame {B}, and the Serret–Frenet {SF} frame.</p>
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<p>MPC framework of closed-loop control with dynamic optimizer, const function and constraint, and plant model.</p>
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<p>MPC controller with optimization open loop, containing MPC controller, plant model, current state, input, and output signal with prediction horizon illustration.</p>
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<p>Risk obstacle model description on the desired path based on the SFC system for trajectory tracking of the USV.</p>
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<p>Zero-pole distribution of the system with output matrix <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mo stretchy="false">[</mo> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo stretchy="false">]</mo> </mrow> </semantics></math>.</p>
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<p>Zero-pole distribution of the system with output matrix <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mo stretchy="false">[</mo> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo stretchy="false">]</mo> </mrow> </semantics></math>.</p>
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<p>USV SL-20Y system. (<b>a</b>) SL-20Y model; (<b>b</b>) the control system block diagram of SL-20Y.</p>
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<p>Simulation results for target point following. (<b>a</b>) USV path simulation result with target point at <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>e</mi> </msub> </mrow> </semantics></math>; (<b>b</b>) simulation results for yaw velocity, heading error, tracking error, and controller output for target point following.</p>
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<p>Simulation results for a single obstacle. (<b>a</b>) USV path simulation result with a single obstacle at <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mrow> <mi>o</mi> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">[</mo> <mn>30</mn> <mo>,</mo> <mn>30</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math>; (<b>b</b>) simulation results for yaw velocity, heading error, tracking error, and controller output for trajectory tracking with a single obstacle.</p>
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<p>Simulation results for multiple obstacles. (<b>a</b>) USV path simulation result with multiple obstacles at <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mrow> <mi>o</mi> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">[</mo> <mn>30</mn> <mo>,</mo> <mn>30</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mrow> <mi>o</mi> <mi>b</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">[</mo> <mn>50</mn> <mo>,</mo> <mn>50</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math>; (<b>b</b>) simulation results for yaw velocity, heading error, tracking error, and controller output for trajectory tracking with multiple obstacles.</p>
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16 pages, 3193 KiB  
Article
Neural Network-Based Adaptive Sigmoid Circular Path-Following Control for Underactuated Unmanned Surface Vessels under Ocean Disturbances
by Yi Ren, Lei Zhang, Wenbin Huang and Xi Chen
J. Mar. Sci. Eng. 2023, 11(11), 2160; https://doi.org/10.3390/jmse11112160 - 13 Nov 2023
Cited by 4 | Viewed by 1333
Abstract
This study describes a circular curve path-following controller for an underactuated unmanned surface vessel (USV) experiencing unmodeled dynamics and external disturbances. Initially, a three degrees of freedom kinematic model of the USV is proposed for marine environmental disturbances and internal model parameter deterrence. [...] Read more.
This study describes a circular curve path-following controller for an underactuated unmanned surface vessel (USV) experiencing unmodeled dynamics and external disturbances. Initially, a three degrees of freedom kinematic model of the USV is proposed for marine environmental disturbances and internal model parameter deterrence. Then, the circular path guidance law and controller are designed to ensure that the USV can move along the desired path. During the design process, a proportional derivative (PD)-based sigmoid fuzzy function is applied to adjust the guidance law. To accommodate unknown system dynamics and perturbations, a radial basis function neural network and adaptive updating laws are adopted to design the surge motion and yaw motion controllers, estimating the unmodeled hydrodynamic coefficients and external disturbances. Theoretical analysis shows that tracking errors are uniformly ultimately bounded (UUB), and the closed-loop system is asymptotically stable. Finally, the simulation results show that the proposed controller can achieve good control effects while ensuring tracking accuracy and demonstrating satisfactory disturbance rejection capability. Full article
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<p>Coordinates of the USV motion.</p>
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<p>Schematic of the proposed LOS guidance and neural network controller for the USV.</p>
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<p>Line-of-sight-based circular path guidance model.</p>
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<p>Time responses of position trajectory and tracking error: (<b>a</b>) position trajectory and (<b>b</b>) transverse deviation <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>e</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Time responses of tracking errors: (<b>a</b>) the yaw angle error <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mi>e</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) the velocity error <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>e</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Time evolution of control inputs under different scenarios: (<b>a</b>) the control force <math display="inline"><semantics> <mrow> <msub> <mi>τ</mi> <mi>u</mi> </msub> </mrow> </semantics></math> in surge channel and (<b>b</b>) the control torque <math display="inline"><semantics> <mrow> <msub> <mi>τ</mi> <mi>r</mi> </msub> </mrow> </semantics></math> in the yaw channel.</p>
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<p>The norm of the adaptive update weight matrix under different scenarios: (<b>a</b>) the adaptive update <math display="inline"><semantics> <mrow> <mrow> <mo>‖</mo> <mrow> <msub> <mover accent="true"> <mi>W</mi> <mo>^</mo> </mover> <mi>r</mi> </msub> </mrow> <mo>‖</mo> </mrow> </mrow> </semantics></math> and (<b>b</b>) the adaptive update <math display="inline"><semantics> <mrow> <mrow> <mo>‖</mo> <mrow> <msub> <mover accent="true"> <mi>W</mi> <mo>^</mo> </mover> <mi>u</mi> </msub> </mrow> <mo>‖</mo> </mrow> </mrow> </semantics></math>.</p>
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23 pages, 8041 KiB  
Article
Affine Formation Maneuver Control for Multi-Heterogeneous Unmanned Surface Vessels in Narrow Channel Environments
by Yeye Liu, Xiaogong Lin and Chao Zhang
J. Mar. Sci. Eng. 2023, 11(9), 1811; https://doi.org/10.3390/jmse11091811 - 16 Sep 2023
Cited by 6 | Viewed by 1710
Abstract
This paper investigates the affine formation maneuver control for multi-heterogeneous unmanned surface vessels (USV), aiming to enable them to navigate through narrow channels in the near-sea environment. The approach begins with implementing an affine transformation to facilitate flexible configuration adjustments within the formation [...] Read more.
This paper investigates the affine formation maneuver control for multi-heterogeneous unmanned surface vessels (USV), aiming to enable them to navigate through narrow channels in the near-sea environment. The approach begins with implementing an affine transformation to facilitate flexible configuration adjustments within the formation system. The affine transformation of the entire formation is achieved by controlling the leaders’ positions. Second, this article introduces an anti-perturbation formation tracking controller for the underactuated vessels, which assume the role of leaders, to accurately follow the arbitrary formation transformation. Third, the followers consist of fully actuated vessels with the same kinematic model as the leaders but different dynamic models. This paper utilizes the affine localizability theorem to derive an expected virtual time-varying trajectory based on the leaders’ trajectory. The followers achieve the desired formation maneuver control by tracking this expected virtual time-varying trajectory through an anti-perturbation formation tracking controller. Finally, the efficacy of the introduced control law is confirmed and supported by the results obtained from rigorous simulation experiments. Full article
(This article belongs to the Section Ocean Engineering)
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<p>The control framework in <a href="#sec3-jmse-11-01811" class="html-sec">Section 3</a>.</p>
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<p>The formation maneuver trajectories of the heterogeneous formation system.</p>
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<p>The tracking error of the leaders.</p>
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<p>The tracking error of the followers.</p>
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<p>The velocities of leader 1, leader 2, and leader 3.</p>
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<p>The velocities of follower 4 and follower 5.</p>
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<p>The velocities of the follower 6 and follower 7.</p>
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<p>The forces and moments of the leaders.</p>
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<p>The forces and moments of follower 4 and follower 5.</p>
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<p>The forces and moments of follower 6 and follower 7.</p>
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<p>The lumped disturbance estimation of the leaders with LMI.</p>
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<p>The lumped disturbance estimation of follower 4 and follower 5 with LMI.</p>
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<p>The lumped disturbance estimation of follower 6 and follower 7 with LMI.</p>
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<p>The estimation error of follower 1 and follower 2.</p>
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<p>The estimation error of follower 4 and follower 5.</p>
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<p>The estimation error of follower 6 and follower 7.</p>
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20 pages, 4739 KiB  
Article
Event-Triggered Finite-Time Formation Control of Underactuated Multiple ASVs with Prescribed Performance and Collision Avoidance
by Xuehong Tian, Jianfei Lin, Haitao Liu and Xiuying Huang
Sensors 2023, 23(15), 6756; https://doi.org/10.3390/s23156756 - 28 Jul 2023
Viewed by 1121
Abstract
In this paper, an event-triggered finite-time controller is proposed for solving the formation control problems of underactuated multiple autonomous surface vessels (ASVs), including asymmetric mass matrix, collision avoidance, maintaining communication distances and prescribed performance. First, to not only avoid collisions between the follower [...] Read more.
In this paper, an event-triggered finite-time controller is proposed for solving the formation control problems of underactuated multiple autonomous surface vessels (ASVs), including asymmetric mass matrix, collision avoidance, maintaining communication distances and prescribed performance. First, to not only avoid collisions between the follower and leader but also maintain an effective communication distance, a desired tracking distance is designed to be maintained. Second, an improved barrier Lyapunov function (BLF) is proposed to implement the tracking error constraint. In addition, the relative threshold event-triggering strategy effectively solves the communication pressure problem and greatly saves communication resources. Finally, based on coordinate transformation, line of sight (LOS) and dynamic surface control (DSC), a comprehensive finite-time formation control method is proposed to avoid collisions and maintain communication distance. All the signals of the proposed control system can be stabilized in finite time (PFS). The numerical simulation results verify the effectiveness of the proposed control system. Full article
(This article belongs to the Section Sensors and Robotics)
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<p>The architecture of a group of leader-followers.</p>
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<p>Formation structure of underactuated ASVs.</p>
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<p>The formation control trajectory.</p>
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<p>The LOS range <math display="inline"><semantics><mrow><msub><mi>ω</mi><mi>i</mi></msub></mrow></semantics></math>.</p>
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<p>The tracking errors <math display="inline"><semantics><mrow><msub><mi>e</mi><mrow><mi>ϕ</mi><mi>i</mi></mrow></msub></mrow></semantics></math>.</p>
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<p>Control input of ASV1.</p>
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<p>Control input of ASV2.</p>
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<p>Control input of ASV3.</p>
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<p>Comparison of control input (ASV1).</p>
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<p>Comparison of the LOS range.</p>
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<p>Comparison of tracking errors.</p>
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<p>Comparisons of the LOS range <math display="inline"><semantics><mrow><msub><mi>ρ</mi><mn>1</mn></msub></mrow></semantics></math>.</p>
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<p>Comparisons of the tracking error <math display="inline"><semantics><mrow><msub><mi>e</mi><mrow><mi>ϕ</mi><mn>1</mn></mrow></msub></mrow></semantics></math>.</p>
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<p>Comparisons of the control inputs.</p>
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<p>Comparison of the LOS range with FET.</p>
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<p>Comparisons of the tracking error <math display="inline"><semantics><mrow><msub><mi>e</mi><mrow><mi>ϕ</mi><mn>1</mn></mrow></msub></mrow></semantics></math> with FET.</p>
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26 pages, 5547 KiB  
Article
Leader–Follower Formation Tracking Control of Underactuated Surface Vehicles Based on Event-Trigged Control
by Xiaoming Xia, Zhaodi Yang and Tianxiang Yang
Appl. Sci. 2023, 13(12), 7156; https://doi.org/10.3390/app13127156 - 15 Jun 2023
Cited by 6 | Viewed by 1197
Abstract
This paper investigates the leader–follower formation tracking control of underactuated surface vessels (USVs) with input saturation. Each vessel is subject to the uncertainties induced by model uncertainties and environmental disturbances. First, an event-triggered extended-state observer (ETESO) is used to recover the velocity, yaw [...] Read more.
This paper investigates the leader–follower formation tracking control of underactuated surface vessels (USVs) with input saturation. Each vessel is subject to the uncertainties induced by model uncertainties and environmental disturbances. First, an event-triggered extended-state observer (ETESO) is used to recover the velocity, yaw rate and uncertainties. Then, an estimator is used to estimate the velocity of the leader. An event-triggered controller (ETC) is constructed based on the estimator, the observer and extra variables. Specifically, extra variables are used to solve the problems of underactuation and input saturation. Stability analysis of the control system is conducted to prove that all signals are bounded. Simulations demonstrate that the ETESO can accurately estimate the uncertainties, velocity and yaw rate, and the ETC can largely reduce the action times of actuator. Full article
(This article belongs to the Section Marine Science and Engineering)
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<p>Earth-fixed frame and body-fixed frame.</p>
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<p>Leader–follower structure.</p>
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<p>Structure of the proposed ETC.</p>
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<p>Formation pattern with four followers and a leader.</p>
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<p>Tracking errors with perturbation effects.</p>
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<p>Input signals of four USVs.</p>
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<p>Leader–follower formation tracking control under four conditions, TTETC proposed in [<a href="#B23-applsci-13-07156" class="html-bibr">23</a>].</p>
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<p>Tracking errors under different controllers, TTETC proposed in [<a href="#B23-applsci-13-07156" class="html-bibr">23</a>].</p>
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<p>Control inputs with perturbation effects, TTETC proposed in [<a href="#B23-applsci-13-07156" class="html-bibr">23</a>].</p>
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<p>Locally enlarged diagram of <a href="#applsci-13-07156-f009" class="html-fig">Figure 9</a>. TTETC proposed in [<a href="#B23-applsci-13-07156" class="html-bibr">23</a>].</p>
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<p>The event-based release instants and release intervals of input signals.</p>
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<p>Comparisons of estimation performance.</p>
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<p>Approximation errors under different observers.</p>
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<p>The triggering instants for the ETESO and its locally enlarged drawing.</p>
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21 pages, 10541 KiB  
Article
Finite Time Trajectory Tracking with Full-State Feedback of Underactuated Unmanned Surface Vessel Based on Nonsingular Fast Terminal Sliding Mode
by Donghao Xu, Zipeng Liu, Jiuzhen Song and Xueqian Zhou
J. Mar. Sci. Eng. 2022, 10(12), 1845; https://doi.org/10.3390/jmse10121845 - 1 Dec 2022
Cited by 7 | Viewed by 1715
Abstract
Marine transportation and operations have attracted the attention of more and more countries and scholars in recent years. A full-state finite time feedback control scheme is designed for the model parameters uncertainty, unknown ocean environment disturbances, and unmeasured system states in the underactuated [...] Read more.
Marine transportation and operations have attracted the attention of more and more countries and scholars in recent years. A full-state finite time feedback control scheme is designed for the model parameters uncertainty, unknown ocean environment disturbances, and unmeasured system states in the underactuated Unmanned Surface Vessel (USV) trajectory tracking control. The external wind, wave and current environmental disturbances and model parameters perturbation are extended by Nonlinear Extended State Observer (NESO) to the state of the system, namely complex disturbances. The complex disturbances, positions and velocities of USV can be observed by NESO and feedback to USV control system. Next, the underactuated USV error model is obtained by operating the obtained feedback information and the virtual ship model. According to the error model, a Nonsingular Fast Terminal Sliding Model surface (NFTSM) is constructed to realize finite-time control. The control law is deduced through the Lyapunov stability theory to ensure the stability of the system. The results of MATLAB numerical simulations under different disturbances show that the trajectory tracking algorithm has fast responses, and a good convergence of the errors is observed, which verifies the effectiveness of the designed scheme. Full article
(This article belongs to the Special Issue Motion Control and Path Planning of Marine Vehicles)
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<p>Structure diagram of research.</p>
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<p>Earth-fixed <math display="inline"><semantics> <mrow> <mi>O</mi> <mo>−</mo> <msub> <mi>X</mi> <mi>o</mi> </msub> <msub> <mi>Y</mi> <mi>o</mi> </msub> </mrow> </semantics></math> and Body-fixed <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>−</mo> <mi>X</mi> <mi>Y</mi> </mrow> </semantics></math> coordinate frames of a USV.</p>
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<p>Virtual USV generation reference estimation schematic.</p>
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<p>Control scheme structure diagram.</p>
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<p>Simulation results of complex disturbances under four periods. (<b>a</b>) Complex disturbances tracking curve graph at period <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>5</mn> <mi>s</mi> </mrow> </semantics></math>; (<b>b</b>) Complex disturbances tracking curve graph at period <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>6</mn> <mi>s</mi> </mrow> </semantics></math>; (<b>c</b>) Complex disturbances tracking curve graph at period <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>7</mn> <mi>s</mi> </mrow> </semantics></math>; (<b>d</b>) Complex disturbances tracking curve graph at period <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>8</mn> <mi>s</mi> </mrow> </semantics></math>.</p>
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<p>Observation error results at four periods. (<b>a</b>) Graph of complex disturbances tracking error under four periods; (<b>b</b>) Graph of positions tracking error under four periods; (<b>c</b>) Graph of velocities tracking error under four periods.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>5</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>6</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>6</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>7</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>8</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Observation error results at four periods. (<b>a</b>) Graph of complex disturbances tracking error under four periods; (<b>b</b>) Graph of positions tracking error under four periods; (<b>c</b>) Graph of velocities tracking error under four periods.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>5</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>6</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>6</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>7</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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<p>Simulation results at disturbance period of <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>8</mn> <mi>s</mi> </mrow> </semantics></math>. (<b>a</b>) Trajectory tracking curves; (<b>b</b>) Position tracking error curves; (<b>c</b>) Velocity tracking error curves; (<b>d</b>) Surge force and yaw moment curves.</p>
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16 pages, 1475 KiB  
Article
Adaptive Formation Control of Multiple Underactuated Autonomous Underwater Vehicles
by Ji-Hong Li, Hyungjoo Kang, Min-Gyu Kim, Mun-Jik Lee, Gun Rae Cho and Han-Sol Jin
J. Mar. Sci. Eng. 2022, 10(9), 1233; https://doi.org/10.3390/jmse10091233 - 2 Sep 2022
Cited by 7 | Viewed by 2586
Abstract
In this paper, we present a 3D formation control scheme for a group of torpedo-type underactuated autonomous underwater vehicles (AUVs). These multiple AUVs combined with an unmanned surface vessel (USV) construct a sort of star-topology acoustic communication network where the USV is at [...] Read more.
In this paper, we present a 3D formation control scheme for a group of torpedo-type underactuated autonomous underwater vehicles (AUVs). These multiple AUVs combined with an unmanned surface vessel (USV) construct a sort of star-topology acoustic communication network where the USV is at the center point. Due to this kind of topological feature, this paper applies a virtual school concept. This is a geometric graph where each node is taken as a virtual leader for each specific AUV and assigned its own reference trajectory. For each individual vehicle, its formation strategy is simple: just follow the trajectory of its corresponding virtual leader so as for multiple AUVs to compose the given formation. As for the formation subject, this paper mainly focuses on the formation tracking problem rather than the formation producing. For the torpedo-type vehicle considered in this paper, there are only three control inputs (surge force, pitch, and yaw moments) available for its underwater 3D motion and therefore this is a typical underactuated system. For the following vehicle’s trajectory, a sort of potential field method is used for obstacle avoidance, and a neural network-based adaptive scheme is applied to on-line approximate the vehicle’s unknown nonlinear dynamics, and the uncertainty terms including modeling errors, measurement noises, and external disturbances are handled by the properly designed robust scheme. The proposed formation method can guarantee the uniform ultimate boundedness (UUB) of the closed-loop system. Numerical studies are also carried out to verify the effectiveness of the proposed scheme. Full article
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<p>Star-topological acoustic communication network for a group of AUVs and a USV.</p>
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<p>Virtual structure based multiple AUVs schooling.</p>
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<p>Obstacle detection and its modeling using occupancy grid map.</p>
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<p>Virtual leaders trajectories and their trajectory with obstacle avoidance using the proposed formation scheme.</p>
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<p>Each vehicle’s trajectory following with obstacle avoidance on the horizontal plane.</p>
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<p>UUB stability of proposed formation scheme in terms of spherical coordinate frame.</p>
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<p>Some of coefficients estimations using the adaptation laws (<a href="#FD37-jmse-10-01233" class="html-disp-formula">37</a>)–(<a href="#FD39-jmse-10-01233" class="html-disp-formula">39</a>).</p>
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12 pages, 6478 KiB  
Article
Formation Control of Multiple Underactuated Surface Vessels with a Disturbance Observer
by Zhiyuan Sun, Hanbing Sun, Ping Li and Jin Zou
J. Mar. Sci. Eng. 2022, 10(8), 1016; https://doi.org/10.3390/jmse10081016 - 25 Jul 2022
Cited by 11 | Viewed by 2040
Abstract
To maintain the formation of underactuated surface vessels (USVs), this study designs a formation controller based on a virtual structure strategy. The problem of formation control is transformed into the problems of tracking the USV position and the virtual structure point position. Meanwhile, [...] Read more.
To maintain the formation of underactuated surface vessels (USVs), this study designs a formation controller based on a virtual structure strategy. The problem of formation control is transformed into the problems of tracking the USV position and the virtual structure point position. Meanwhile, to eliminate the effects of model parameter uncertainties and external environment disturbances on USV tracking control, a compensation control algorithm based on disturbance estimation is proposed. The Lyapunov theorem is introduced to ensure that the trajectory tracking error of the proposed control algorithm eventually converges to any small region, which confirms global stability of the designed tracking error. The simulation results demonstrate that the proposed controller can eliminate the effect of external uncertain interference and maintain the formation of multiple USVs. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Geometrical illustration of LOS guidance.</p>
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<p>Estimation of external disturbances with different methods. (<b>a</b>) Disturbance observed value <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>w</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>e</mi> <mi>u</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Error of the <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>w</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>e</mi> <mi>u</mi> </mrow> </msub> </mrow> </semantics></math> with different methods. (<b>c</b>) Disturbance observed value <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>w</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>d</b>) Error of the <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>w</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math> with different methods.</p>
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<p>Schematic diagram of path tracking.</p>
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<p>Path tracking error curves. (<b>a</b>) Longitudinal tracking errors. (<b>b</b>) Lateral tracking errors.</p>
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<p>Control input under time-varying disturbance. (<b>a</b>) Yaw moment. (<b>b</b>) Longitudinal force.</p>
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<p>USVs’ heading angle curves.</p>
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<p>Speed curves of USVs.</p>
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19 pages, 5721 KiB  
Article
Fractional-Order Controller for Course-Keeping of Underactuated Surface Vessels Based on Frequency Domain Specification and Improved Particle Swarm Optimization Algorithm
by Guangyu Li, Yanxin Li, Huayue Chen and Wu Deng
Appl. Sci. 2022, 12(6), 3139; https://doi.org/10.3390/app12063139 - 18 Mar 2022
Cited by 77 | Viewed by 4043
Abstract
In this paper, a new fractional-order (FO) PIλDµ controller is designed with the desired gain and phase margin for the automatic rudder of underactuated surface vessels (USVs). The integral order λ and the differential order μ are introduced in the [...] Read more.
In this paper, a new fractional-order (FO) PIλDµ controller is designed with the desired gain and phase margin for the automatic rudder of underactuated surface vessels (USVs). The integral order λ and the differential order μ are introduced in the controller, and the two additional adjustable factors make the FO PIλDµ controller have better accuracy and robustness. Simulations are carried out for comparison with a ship’s digital PID autopilot. The results show that the FO PIλDµ controller has the advantages of a small overshoot, short adjustment time, and precise control. Due to the uncertainty of the model parameters of USVs and two extra parameters, it is difficult to compute the parameters of an FO PIλDµ controller. Secondly, this paper proposes a novel particle swarm optimization (PSO) algorithm for dynamic adjustment of the FO PIλDµ controller parameters. By dynamically changing the learning factor, the particles carefully search in their own neighborhoods at the early stage of the algorithm to prevent them from missing the global optimum and converging on the local optimum, while at the later stage of evolution, the particles converge on the global optimal solution quickly and accurately to speed up PSO convergence. Finally, comparative experiments of four different controllers under different sailing conditions are carried out, and the results show that the FO PIλDµ controller based on the IPSO algorithm has the advantages of a small overshoot, short adjustment time, precise control, and strong anti-disturbance control. Full article
(This article belongs to the Special Issue Soft Computing Application to Engineering Design)
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<p>Ship motion model.</p>
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<p>Responding nonlinear ship model.</p>
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<p>PID controller and FO PI<sup>λ</sup>D<sup>µ</sup> controller: (<b>a</b>) PID controller and (<b>b</b>) FO PI<sup>λ</sup>D<sup>µ</sup> controller.</p>
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<p>FO PI<sup>λ</sup>D<sup>µ</sup> control system of a ship’s course.</p>
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<p>Distribution chart of test functions.</p>
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<p>Performance comparison of PSO and IPSO algorithms.</p>
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<p>FO PI<sup>λ</sup>D<sup>µ</sup> control system of ship’s course based on IPSO.</p>
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<p>Process of IPSO optimizing the FO PI<sup>λ</sup>D<sup>µ</sup> controller.</p>
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<p>Course-keeping curve with FO PI<sup>λ</sup>D<sup>µ</sup> controller and the PID controller.</p>
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<p>Rudder angle curve with FO PI<sup>λ</sup>D<sup>µ</sup> controller and the PID controller.</p>
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<p>Steady state error curve with FO PI<sup>λ</sup>D<sup>µ</sup> controller and the PID controller.</p>
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<p>Course-tracking curves with FO PI<sup>λ</sup>D<sup>µ</sup> controller and PID controller.</p>
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<p>Rudder angle curves with FO PI<sup>λ</sup>D<sup>µ</sup> controller and PID controller.</p>
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<p>Course-keeping curves without disturbance.</p>
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<p>Rudder angle curves without disturbance.</p>
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<p>The output curve of wind and wave disturbances.</p>
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<p>Course-keeping curves under wind and wave disturbances.</p>
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<p>Rudder angle curves under wind and wave disturbances.</p>
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17 pages, 7670 KiB  
Article
Trajectory Tracking of Underactuated Unmanned Surface Vessels: Non-Singular Terminal Sliding Control with Nonlinear Disturbance Observer
by Donghao Xu, Zipeng Liu, Xueqian Zhou, Liu Yang and Ling Huang
Appl. Sci. 2022, 12(6), 3004; https://doi.org/10.3390/app12063004 - 15 Mar 2022
Cited by 13 | Viewed by 2608
Abstract
An underactuated unmanned surface vessel (USV) is a nonholonomic system, in which trajectory tracking is a challenging problem that has drawn more and more attention from researchers recently. The control of trajectory tracking is of critical importance since it determines whether the task [...] Read more.
An underactuated unmanned surface vessel (USV) is a nonholonomic system, in which trajectory tracking is a challenging problem that has drawn more and more attention from researchers recently. The control of trajectory tracking is of critical importance since it determines whether the task can be carried out successfully. In this paper, a non-singular terminal sliding model (NTSM) controller is proposed for the trajectory tracking control of the underactuated USV, with a nonlinear disturbance observer which is designed to measure complex environmental disturbances such as wind, waves, and currents. Exploratory simulations were carried out and the results show that the proposed controller is effective and robust for the trajectory tracking of underactuated USVs in the presence of environmental disturbances. Full article
(This article belongs to the Section Marine Science and Engineering)
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<p>Earth-fixed <math display="inline"><semantics> <mrow> <mi>O</mi> <mo>−</mo> <msub> <mi>X</mi> <mi>o</mi> </msub> <msub> <mi>Y</mi> <mi>o</mi> </msub> </mrow> </semantics></math> and body-fixed <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>−</mo> <mi>X</mi> <mi>Y</mi> </mrow> </semantics></math> coordinate frames of a USV.</p>
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<p>Straight-line trajectory tracking in three cases: (<b>a</b>) trajectory tracking in the <span class="html-italic">xy</span> plane; (<b>b</b>) trajectory tracking in the <span class="html-italic">x</span>-axis and the <span class="html-italic">y</span>-axis directions.</p>
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<p>Disturbance observer simulation results: (<b>a</b>) actual values and observed values for constant disturbances; (<b>b</b>) actual values and observed values for time-varying disturbances; (<b>c</b>) constant disturbance errors; (<b>d</b>) time-varying disturbance errors.</p>
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<p>Disturbance observer simulation results: (<b>a</b>) actual values and observed values for constant disturbances; (<b>b</b>) actual values and observed values for time-varying disturbances; (<b>c</b>) constant disturbance errors; (<b>d</b>) time-varying disturbance errors.</p>
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<p>Position and velocity curves: (<b>a</b>) the actual position of USV in three cases; (<b>b</b>) the actual velocity of USV in three cases; (<b>c</b>) position tracking errors in three cases; (<b>d</b>) velocity tracking errors in three cases.</p>
Full article ">Figure 4 Cont.
<p>Position and velocity curves: (<b>a</b>) the actual position of USV in three cases; (<b>b</b>) the actual velocity of USV in three cases; (<b>c</b>) position tracking errors in three cases; (<b>d</b>) velocity tracking errors in three cases.</p>
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<p>Surge force and yaw moment in three cases.</p>
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<p>Circular trajectory tracking in three cases: (<b>a</b>) trajectory tracking in the <span class="html-italic">x</span>-<span class="html-italic">y</span> plane; (<b>b</b>) trajectory tracking in the <span class="html-italic">x</span>-axis and the <span class="html-italic">y</span>-axis directions.</p>
Full article ">Figure 7
<p>Position and velocity curves: (<b>a</b>) the actual position of USV in three cases; (<b>b</b>) the actual velocity of USV in three cases; (<b>c</b>) position tracking errors in three cases; (<b>d</b>) velocity tracking errors in three cases.</p>
Full article ">Figure 8
<p>Surge force and yaw moment in three cases.</p>
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