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Adaptive energy-efficient tracking control of a X rudder AUV with actuator dynamics and rolling restriction
Abstract
This paper investigates the problem of trajectory tracking control for a X rudder autonomous underwater vehicle (AUV) subjects to nonlinearities, uncertainties, and complex actuator dynamics. Under an adaptive energy-efficient tracking control scheme, the trajectory tracking problem is decomposed into kinematics and dynamics control. In kinematics control loop, an improved line-of-sight (LOS) guidance law is proposed with fuzzy-based look-ahead distance optimization mechanism, and feedback kinematics control law is designed utilizing Lyapunov method. The dynamics control loop is divided into two subsystems, namely surge tracking and course tracking. Adaptive chattering-free terminal sliding mode control is employed to improve the tracking performance and converging rate, which introduces fuzzy based parameter optimization method to tackle the chattering problem, and robustness to unknown disturbances is addressed by disturbance observers. The influence of complex actuator dynamics is fully considered, where an energy-efficient rudder allocation method is proposed to deal with the multi-objective optimization problem with multi-constraints, including rudder saturations, rolling restriction, etc., and radial-basis-function neural network (RBFNN) based compensator is utilized to deal with the propeller saturation problem. Finally, plenty of comparative numerical simulations are provided to demonstrate the robustness and effectiveness of the proposed approach.
... In recent years, autonomous underwater vehicles (AUVs) have provided researchers great flexibility to conduct marine scientific research and oceanic exploitation, including but not limited to seafloor mapping, subsea cable inspection, and seafloor sediment sampling (Singh et al., 2004;Sahoo et al., 2019;Zhang et al., 2015;Chang et al., 2019). X-Rudder AUV (XAUV) is a typical kind of isomeric AUV equipped with a X-shaped separated rudder system (Dubbioso et al., 2017;Xia et al., 2021;Wang et al., 2020a,b;Wang et al., 2020Wang et al., , 2020Zhang et al., 2017), which not only has the advantages of better maneuverability, higher safety, and lower flow noise, but also has roll control ability, making it possible to achieve dynamic roll stability. Within the current trajectory tracking control scheme for an AUV, roll is usually a neglected motion to simplify the control design. ...
... Moreover, compared with the existing roll control strategies (Ebrahimi and Salehi, 2021;Ebrahimi and Salehi, 2021;Hong and Chitre, 2015;Pugi et al., 2018), the proposed roll control method by using X-Rudder is more energy-conserving and simpler. Additionally, compared with Xia et al. (2021), the proposed control scheme extends the horizontal trajectory tracking to 3D space and fully considers roll dynamics, where roll control is deeply integrated in both the kinematics and dynamics controllers instead of considering roll restriction only in rudder angle allocation. ...
... Assumption 2. (Xia et al., 2021). The unknown disturbances d u , d v , d w , d p , d q and d r are bounded and continuous, and their derivatives are ...
In this article, a novel adaptive robust trajectory tracking framework with roll control is created for a X-Rudder autonomous underwater vehicle (XAUV) subjects to system nonlinearities, unknown disturbances, and complex actuator dynamics. First, a roll control law is introduced to the kinematics control loop, and the hyperbolic-tangent Line-of-sight (HLOS) based guidance law is proposed, which considers the three-dimensional (3D) tracking errors, collaboratively governing heading, pitch, and roll. Second, a novel super-hyperbolic switching algorithm (SHSA) based sliding mode controller is deployed in the dynamics control loop to achieve trajectory tracking and roll control, which combines the advantages of the two hyperbolic functions, avoids the chattering problem while achieving rapid convergence, this enhancing the control accuracy and stability simultaneously. Besides, the robustness to unknown disturbances (including environmental disturbances and propeller reaction torque) is enhanced by nonlinear disturbance observers. To tackle the potential instabilities from compound actuator dynamics, an anti-windup compensator is resorted to compensate for the control truncation of propulsion system, and an optimal X-Rudder allocator is utilized to solve the rudder angle assignment problem with multiple constraints. Finally, comparative numerical simulations are carried out to verify the effectiveness of proposed controller.
... To cope with actuator saturation and state constraints, an adaptive energy-saving trajectory tracking control strategy for AUVs was proposed in [22]. A compensator based on radial basis function neural network was used to solve the problems of saturation of the actuator and multi-objective optimization. ...
... x i2 is always feasible for the DLMPC optimization problem (18). Consider the following Lyapunov function: (22) and the proof of Theorem ...
This paper focuses on the formation tracking issue of autonomous underwater vehicles (AUVs) subject to multiple constraints in three-dimensional space. We developed a novel distributed Lyapunov-based model predictive controller (DLMPC) with a fast finite-time extended state observer (FFTESO). Initially, the external disturbances and internal uncertainties of each AUV were precisely compensated using the designed FFTESO. Subsequently, we proposed DLMPC-based position tracking and velocity tracking controllers, which solved an online optimization problem to determine optimal velocities and control forces. This hierarchical framework effectively managed system constraints, such as state constraints and actuator saturation. Additionally, the Lyapunov-based backstepping control law was applied to construct stability constraints in the distributed optimization problem, ensuring the recursive feasibility and closed-loop system stability of the proposed scheme. Sufficient conditions and attraction regions to ensure stability were explicitly provided. Finally, the simulation results demonstrated that the proposed method improved both the convergence speed and tracking accuracy by at least 30% compared to other methods.
... Wan et al. propose a multi-strategy fusion control with delay method, avoiding the chattering caused by frequent switching [9]. Xia et al. combine the Lyapunov method with line-of-sight guidance to design dynamic control laws, and utilize fuzzy parameter optimization to solve the chattering of controllers [10]. Fang et al. propose a neural network-based gain observer to design dynamic and kinematic controllers [11]. ...
... And the actor model is Therefore, ψ e is limited such that the vehicle can approach the desired signal in the direction of the small semicircle. The error can be written as ψ e , |ψ e | < π ψ e = ψ e + 2π, ψ e < -π (10) ψ e -2π, ψ e > π ...
In this article, a deep reinforcement learning based three-dimensional path following control approach is proposed for an underactuated autonomous underwater vehicle (AUV). To be specific, kinematic control laws are employed by using the three-dimensional line-of-sight guidance and dynamic control laws are employed by using the twin delayed deep deterministic policy gradient algorithm (TD3), contributing to the surge velocity, pitch angle and heading angle control of an underactuated AUV. In order to solve the chattering of controllers, the action filter and the punishment function are built respectively, which can make control signals stable. Simulations are carried out to evaluate the performance of the proposed control approach. And results show that the AUV can complete the control mission successfully.
... In [17], considering prior model parameters, the SMC was designed for known models to get desired control moments, and a non-model based iterative SMC was designed to calculate virtual rudder commands in the vertical plane. In [18], an adaptive TSMC (ATSMC) method was designed based on the fuzzy optimization to solve the chattering phenomenon and improve tracking accuracy in the horizontal plane. The deep reinforcement learning method was also used for tracking control. ...
... According to Assumption 4, the dynamic model of the X-AUV in the horizontal plane is simplified as follows [18]: ...
This paper analyzes the trajectory tracking problem in decoupled planes for X-rudder AUVs under time-varying, unknown environmental interferences. The proposed scheme consists of the kinematic control law based on the compound line-of-sight guidance law and the dynamic control law based on a non-singular adaptive integral terminal sliding mode control (NAITSMC) to avoid the chattering problems, parameter perturbation, and time-varying disturbances. Meanwhile, we introduce a reduced-order extended state observer (RESO) to compensate for unknown ocean currents by the first-order Gauss–Markov process. We verify the whole system of the proposed scheme through global asymptotic stability, then present a set of numerical simulations revealing robustness and adaptability performances in decoupled planes.
... Assumption 1. The unknown oceanic disturbances d o (o = u, v, w, q, r) are characterized as continuous and bounded by unknown upper limits [40]. ...
In this study, we present a novel dual-loop robust trajectory tracking framework for autonomous underwater vehicles, with the objective of enhancing their performance in underwater searching tasks amidst oceanic disturbances. Initially, a real-world AUV experiment is conducted to validate the efficacy of a cross-rudder AUV configuration in maintaining sailing angle stability during the diving stage, which exhibits a strong capability for straight-line sailing. Building upon the experimental findings, we introduce a state-transform-model predictive guide law to compute the desired velocity for the dynamics loop. This guide law dynamically adjusts the controller across varying depths, thereby reducing model predictive control (MPC) computation while optimizing timing without compromising precision or convergence speed. Subsequently, we incorporate a sliding mode controller with a prescribed disturbance observer into the velocity control loop to concurrently enhance the robustness and convergence rate of the system. This innovative amalgamation of controllers significantly improves tracking precision and convergence rate, while also alleviating the computational burden—a pervasive challenge in AUV MPC control. Finally, various condition simulations are conducted to validate the robustness, effectiveness, and superiority of the proposed method. These simulations underscore the enhanced performance and reliability of our proposed trajectory tracking framework, highlighting its potential utility in real-world AUV applications.
... As mentioned above, energy consumption is also a critical factor to be taken into account in the control law design. For example, in Xia et al. (2022) the rudder angle control directly affects energy consumption, and a weight coefficient is introduced in the optimisation to adaptively adjust trajectory tracking performance or energy consumption, although the model presented is not valid for the AUV used in the present work, which uses thrusters instead of rudders. Likewise, Yao et al. (2019) deal with energy consumption reduction using MPC based on the state space model of an overactuated AUV for trajectory tracking control and adds a quadratic energy consumption term into the cost function. ...
... Regarding experimental research on the X-rudder, relevant published information is relatively scarce. On the one hand, the manipulation of the X-rudders poses higher requirements on the control system [26][27][28][29]; on the other hand, when using Particle Image Velocity measurements, the diffuse reflection on the rudder surface causes interference with the incident laser ...
Flow field performance tests of submarine models with cross-rudder and X-rudder stern control surfaces were conducted to study X-rudders’ performance in non-uniform flow fields. The tests compared performance parameters such as resistance, lateral steering force, yaw moment, stern velocity field, and flow field inhomogeneity coefficient under low- and high-speed conditions. The test results show that, at low speed, the resistance of the X-rudder submarine is smaller than that of the cross-rudder one at the same rudder angle. In contrast, at high speed, the resistance of the cross-rudder submarine is smaller than that of the X-rudder submarine. Under low- and high-speed conditions, the X-rudder’s lateral steering force and yaw moment are larger than those of the cross rudder at the same rudder angle. The superiority of the maneuverability of the X-rudder becomes more apparent with increasing rudder angle. At a rudder angle of 10°, the X-rudder’s lateral steering force and yaw moment are about two times larger than the cross rudder’s. In the small-radius area of the propeller plane, the inhomogeneity coefficient of the X-rudder is generally smaller than that of the cross rudder. This is probably because the cross-rudder stern control surfaces have fixed stabilizers with flaps, and the X-rudder stern control surfaces are all-moving, with a small fixed part next to the submarine. This test provides a reference for designing the stern control surface of low-noise submarines.
... The uncertainties in dynamics modeling and external disturbances in practice lead to a reduction in control accuracy and, therefore, need to be estimated. Extended observers [18,20,21] and RBFNN [22,23] are two kinds of uncertainty estimation methods commonly used in a control field at present. Compared with external observers, RBFNN is characterized by a simple structure, self-learning ability, and ability to estimate nonlinearity [24]. ...
This paper addresses the lateral motion control of a supercavitating vehicle and studies its ability to maneuver. According to the unique hydrodynamic characteristics of the supercavitating vehicle, highly coupled nonlinear 6-degree-of-freedom (DOF) dynamic and kinematic models are constructed considering time-delay effects. A control scheme utilizing radial basis function (RBF) neural-network-(NN)-based adaptive sliding with planing force avoidance is proposed to simultaneously control the longitudinal stability and lateral motion of the supercavitating vehicle in the presence of external ocean-induced disturbances. The online estimation of nonlinear disturbances is conducted in real time by the designed NN and compensated for the dynamic control laws. The adaptive laws of the NN weights and control parameters are introduced to improve the performance of the NN. The least squares method is utilized to solve the actuator control efforts with rolling restriction in real-time online. Rigorous theoretical proofs based on the Lyapunov theory prove the globally asymptotic stability of the proposed controller. Finally, numerical simulations were performed to obtain maximum maneuverability and verify the effectiveness and robustness of the proposed control scheme.
... It is corroborative that sliding mode control (SMC) can be widely employed in AUV tracking systems with unexpected dynamics due to its excellent robustness property Wang et al., 2023a;Xia et al., 2022aXia et al., , 2022b. With the enhancement of tracking performance and convergence, a fuzzy-based robust SMC law ) and a super-twisting SMC method have been designed (Xia et al., 2022b), respectively. ...
... The buoyancy of the UUV is equal to the gravity, and the center of buoyancy coincides with the center of gravity located at the origin of the vehicle coordinate system. Assumption 2 [48]. The unknown disturbances τ d1 , τ d2 , τ d3 , τ d4 , τ d5 , and τ d6 are bounded. ...
To address the search-and-docking problem in multi-stage prescribed performance switching (MPPS) scenarios, this paper presents a novel compound control method for three-dimensional (3D) underwater trajectory tracking control of unmanned underwater vehicles (UUVs) subjected to unknown disturbances. The proposed control framework can be divided into two parts: kinematics control and dynamics control. In the kinematics control loop, a novel parallel model predictive control (PMPC) law is proposed, which is composed of a soft-constrained model predictive controller (SMPC) and hard-constrained model predictive controller (HMPC), and utilizes a weight allocator to enable switching between soft and hard constraints based on task goals, thus achieving global optimal control in MPPS scenarios. In the dynamics control loop, a finite-time terminal sliding mode control (FTTSMC) method combining a finite-time radial basis function neural network adaptive disturbance observer (RBFNN-FTTSMC) is proposed to achieve disturbance estimation and fast convergence of velocity tracking errors. The simulation results demonstrate that the proposed PMPC-FTTSMC approach achieved an average improvement of 33% and 80% in the number of iterations compared with MPC with sliding mode control (MPC-SMC) and traditional MPC methods, respectively. Furthermore, the approach improved the speed of response by 35% and 44%, respectively, while accurately achieving disturbance observation and enhancing the system robustness.
... In marine craft tests, the data accuracy is influenced by the onboard position and posture sensors, which leads to the test dataset being always sparse and not smooth. Numerical simulations based on the AUV model lead to the conclusion that the longer the sampling period, the larger the identification error [40]. In order to improve the identification accuracy, a CH-based data preprocessing strategy is utilized to densify and smooth the data. ...
This paper combines the piecewise Cubic Hermite (CH) interpolation algorithm and the weighted least square support vector machine (WLS-SVM) to improve identification accuracy for marine crafts built based on the characteristic model. The characteristic model is first used to describe the heading dynamics of marine crafts and is a superior model to the traditional response model in both accuracy and complexity. Especially in order to improve identification accuracy, a CH-based data preprocessing strategy is utilized to densify and smooth data for further accurate identification. Subsequently, the combination of the linear kernel function and the Gaussian kernel function is introduced in the conventional WLS-SVM method, which renders global and local performance improvements compared with the conventional WLS-SVM method. Finally, informative maneuvers composed of Zigzag and Sine are carried out to test the performance of the improved identification method. Compared to the conventional LS-SVM method based on the response model, the root mean square error of the proposed CH-MK-WLS-SVM method based on the characteristic model is reduced by an order of magnitude in the presence of sensor noise.
... Ignoring this problem may reduce the performance of the controller or even cause instability. At present, the auxiliary variable system [24][25][26][27], adaptive method [28], FL [29], NN [30], MPC [31,32], and DAI [33,34] are common means used to address actuator saturation. In [27], the saturation effects of rudder angle in diving control of AUVs were compensated by a modified auxiliary system with time-varying nonlinear gains. ...
In this paper, contraction theory is applied to design a control law to address the horizontal trajectory tracking problem of an underactuated autonomous underwater vehicle. Suppose that the vehicle faces challenges such as model uncertainties, external environmental disturbances, and actuator saturation. Firstly, a coordinate transformation is introduced to solve the problem of underactuation. Then, a disturbance observer is designed to estimate the total disturbances, which are composed of model uncertainties and external environmental disturbances. Next, a saturated controller is designed based on singular perturbation theory and contraction theory. Meanwhile, contraction theory is used to analyse the convergence properties of the observer and the full singular perturbation system, and make quantitative analysis of the estimation error and the tracking error. Finally, the results of numerical simulations prove that the method in this paper enables the vehicle to track the desired trajectory with relatively high accuracy, while the control inputs do not exceed the limitations of the actuators.
... It is corroborative that sliding mode control (SMC) can be widely employed in AUV tracking systems with unexpected dynamics due to its excellent robustness property Wang et al., 2023a;Xia et al., 2022aXia et al., , 2022b. With the enhancement of tracking performance and convergence, a fuzzy-based robust SMC law ) and a super-twisting SMC method have been designed (Xia et al., 2022b), respectively. ...
... In Yu et al. (2017), an adaptive fuzzy control system based on universal approximation theorem was employed to compensate the effect of actuator saturation. Xia et al. (2022) applied an energy-efficient rudder allocation method to deal with the multi-objective optimization problem with multi-constraints, including rudder saturations, rolling restriction and so forth, and radial-basisfunction neural network (RBFNN) based compensator was utilized to deal with the actuator saturation problem. ...
Autonomous underwater vehicle (AUV) is a complex nonlinear system and its control is accompanied by various challenges. This paper focuses on the three dimensional (3D) trajectory tracking control of a fully-actuated AUV in the presence of model uncertainties, unmeasured velocity, time-varying external disturbance and input saturation. First, taking the model uncertainties and external disturbances as the total disturbances, an extended state observer (ESO) is designed to estimate the unmeasured velocity and total disturbances. Then, the saturated controller based on contraction theory and its application in singular perturbation system (SPS) is obtained so that the AUV tracks the desired trajectory and avoids exceeding the limit of the actuator. The estimation error, tracking error and the error between the ideal controller and the actual controller are analyzed by contraction theory, and the explicit bounds of these errors are given. At last, comparative numerical simulations are provided to show the effectiveness of the ESO and the advantages of the saturated controller.
... Finally, comparative simulation cases of two different scenarios are carried out: Case 1 proves that the proposed control method has good adaptability to different initial conditions and different unknown disturbances; Case 2 shows that compared with three other commonly used control methods [39][40][41], the proposed method has obvious advantages in convergence speed, tracking accuracy, stability, and energy consumption. Compared with the existing literature on XAUV control [3, 4,42], this paper extends the research to the three-dimensional and introduces the idea of finite time convergence control with more constraints considered, thus making it more practical. ...
This paper proposes a novel three-dimensional trajectory tracking control methodology for a heterogeneous X-rudder autonomous underwater vehicle (XAUV) that can achieve finite-time convergence, complex actuator dynamics handling, and energy-efficient optimized rudder allocation. Under a compound robust control scheme, the trajectory tracking problem is decomposed into three sub-problems: kinematics control, dynamics control, and rudder allocation. For kinematics control, a novel finite-time line-of-sight (FTLOS) guidance law is proposed, which can achieve faster position and orientation tracking when compared with classical LOS guidance, and is rarely studied in the existing finite time control methods. In the dynamics control loop, global finite-time terminal sliding mode control (FTTSMC) laws are provided to solve the heading control, pitching control, and surge velocity tracking control problems, where finite-time convergence is achieved in both the approaching stage and sliding mode holding stage. The multi-source uncertainties with unknown upper bounds in both kinematics and dynamics loops are well treated by finite-time extended disturbance observers (FTEDOs), thus ensuring the system robustness. Moreover, the influence of complex actuator dynamics is fully considered by employing a RBFNN compensator to deal with the propeller saturation and proposing an energy-efficient optimal rudder allocator to tackle the multi-objective and multi-constraint heterogeneous X-rudder angle assignment problem. Finally, simulation verifications are carried out for two different scenarios, where Case 1 focuses on the adaptability of the algorithm to different conditions and Case 2 focuses on the superiority of the algorithm over three other commonly used algorithms. The comparative simulation results show that the proposed controller has good adaptability to different initial and disturbance conditions, and performs better than three other classical controllers, especially in convergence speed, tracking accuracy, stability, and energy consumption.
To achieve the efficient and precise control of autonomous underwater vehicles (AUVs) in dynamic ocean environments, this paper proposes an innovative Gaussian-Process-based Model Predictive Control (GP-MPC) method. This method combines the advantages of Gaussian process regression in modeling uncertainties in nonlinear systems, and MPC’s constraint optimization and real-time control abilities. To validate the effectiveness of the proposed GP-MPC method, its performance is first evaluated for trajectory tracking control tasks through numerical simulations based on a 6-degrees-of-freedom, fully actuated, AUV dynamics model. Subsequently, for 3D scenarios involving static and dynamic obstacles, an AUV horizontal plane decoupled motion model is constructed to verify the method’s obstacle avoidance capability. Extensive simulation studies demonstrate that the proposed GP-MPC method can effectively manage the nonlinear motion constraints faced by AUVs, significantly enhancing their intelligent obstacle avoidance performance in complex dynamic environments. By effectively handling model uncertainties and satisfying motion constraints, the GP-MPC method provides an innovative and efficient solution for the design of AUV control systems, substantially improving the control performance of AUVs.
Aiming at the trajectory tracking control problem of x-rudder AUV with nonholonomic constraints and parameter perturbations, a trajectory tracking controller based on global backstepping sliding mode is designed in the paper. The trajectory tracking problem is decomposed into kinematics and dynamics control. Utilizing Lyapunov method, a kinematics control law in kinematics control loop is designed. The dynamics control loop is divided into two subsystems, including surge tracking subsystem and course tracking subsystem. At the same time, considering the actuator saturation constraints and undesired rolling torque, an IPSO multi-objective energy-efficient rudder angle allocation is presented. Simulations are provided to demonstrate the robustness and effectiveness of the proposed approach.
The marine vehicle is one of the most important platforms in oceanic research and development. During the evolution of marine vehicle design, hull optimization is a key topic consisting of various steps such as hull deformation analysis, optimization algorithm selection and hydrodynamic performance evaluation. For hull deformation analysis, radial based function interpolation technique is usually applied with Wendland’s ψ3,1 function, which requires a great number of fixed points. To improve the optimization effect, this paper proposes a novel radial basis function for better support radius condition. According to the support radius condition, the effect of different deformation functions acting on hull form is studied. To verify the effectiveness of the improved radial basis function in marine vehicle hull optimization, a Series 60 hull is taken as the initial hull, and the Rankine source method is utilized as the solver to calculate the wave resistance coefficient. The Non-dominated Sorting Genetic Algorithm (NSGA) is applied to determine the optimal hull form at given speeds. By comparing the optimization results, the benefits and drawbacks of the improved radial basis function are analyzed. The results show that the number of fixed control points can be reduced by applying the improved radial basis function. When different deformation functions are acting on the marine vehicle hull, the improved radial basis function makes the gradient transition smoother. In the process of hull optimization, the wave resistance coefficient obtained by utilizing the improved function to deform the hull is smaller than that of using Wendland’s ψ3,1 function under different support radii.
This study focuses on the fault reconstruction for a class of second-order multi-input and multi-output (MIMO) nonlinear systems with uncertainties. An innovative design scheme of terminal sliding mode observer (TSMO) is presented for which the relative degree of the system is two. In comparison with the common sliding mode observer (SMO), the proposed TSMO can converge all state estimation errors to zero in finite time, even when some states cannot be measured directly. Given that state estimation errors converge to zero in finite time, a fault reconstruction method based on an equivalent output error injection concept and a SMO-based fault isolation strategy are presented, so that the fault information after isolating disturbances can be accurately known. Simulation examples of fault reconstruction on a small unmanned underwater vehicle are presented to demonstrate the effectiveness of the proposed method.
This paper investigates the path following control problem for an underactuated unmanned surface vehicle (USV) in the presence of dynamical uncertainties and time-varying external disturbances. Based on fuzzy optimization algorithm, an improved adaptive line-of-sight (ALOS) guidance law is proposed, which is suitable for straight-line and curve paths. On the basis of guidance information provided by LOS, a three-degree-of-freedom (DOF) dynamic model of an underactuated USV has been used to design a practical path following controller. The controller is designed by combining backstepping method, neural shunting model, neural network minimum parameter learning method, and Nussbaum function. Neural shunting model is used to solve the problem of “explosion of complexity,” which is an inherent illness of backstepping algorithm. Meanwhile, a simpler neural network minimum parameter learning method than multilayer neural network is employed to identify the uncertainties and time-varying external disturbances. In particular, Nussbaum function is introduced into the controller design to solve the problem of unknown control gain coefficient. And much effort is made to obtain the stability for the closed-loop control system, using the Lyapunov stability theory. Simulation experiments demonstrate the effectiveness and reliability of the improved LOS guidance algorithm and the path following controller.
This paper focuses on vertical-plane trajectory tracking of an under-actuated autonomous underwater
vehicle (AUV) subject to actuator saturation and external disturbances. A successive guidance and control frame is designed to avoid the cascade analysis between the kinematics guidance and the dynamics control, and the complete Lyapunov function is chosen to analyze the asymptotic stability of trajectory tracking system. In the guidance loop, the line-of-sight guidance law is applied to trajectory tracking of AUVs, which transforms the depth tracking error into the elevation angle tracking error and solves the problem of the under-actuated configuration in heave. In the control loop, direct adaptive fuzzy control is adopted to compensate for the effect of actuator saturation, which guarantees the system stability of trajectory tracking
in the presence of actuator saturation. Finally, comparative numerical simulations are provided to illustrate the robust and bounded performance of the designed trajectory tracking control system.
This paper develops a novel adaptive fuzzy sliding mode controller for the diving control of autonomous underwater vehicle (AUV). Unlike most previous AUVs’ control approaches, in this paper, the problem of input saturation constraint of rudder angle is considered, and the new auxiliary systems are proposed. Considering the modeling uncertainty of the dynamic model, an adaptive sliding mode controller based on fuzzy logic system is proposed, and the new update laws of control parameters are given. For the adaptive sliding mode controller design, although the input gain of each subsystem is partially known, only one fuzzy logic system is needed for online identification, which is a distinct difference from the previous adaptive sliding mode controllers. The uniformly ultimately boundedness of tracking error is proven by Lyapunov theorem. The effectiveness of the proposed control scheme is illustrated by simulation.
In this article, a sliding mode control scheme for the autopilot system of a ship is presented, which also incorporates actuator saturation. Under the designed controller, the actuator doesn’t enter its saturation mode. Meanwhile, the stability of the closed-loop system can be guaranteed for the ship with input saturation. Fuzzy logic is used to handle gain to avoid the chattering effect, and it is compared with saturation function. The control system for the mathematical model of a scale replica of an “Esso Osaka” tanker is simulated in time domain for the effectiveness of the controller. The simulation results show that the proposed controller is more efficient as compared to the traditional and saturation function methods.
The IEEE Robotics and Automation Society (RAS) Marine Robotics Technical Committee (MRTC) was first established in 2008 following the dismissal of the Underwater Robotics Technical Committee in spring 2008. The goal of the MRTC is to foster research on robots and intelligent systems that extend the human capabilities in marine environments and to promote maritime robotic applications important to science, industry, and defense. The TC organizes conferences, workshops, and special issues that bring marine robotics research to the forefront of the broader robotics community. The TC also introduces its members to the latest development of marine robotics through Web sites and online social media.
Autonomous Underwater Vehicles (AUVs) have a wide range of applications in marine geoscience, and are increasingly being used in the scientific, military, commercial, and policy sectors. Their ability to operate autonomously of a host vessel makes them well suited to exploration of extreme environments, from the World’s deepest hydrothermal vents to beneath polar ice sheets. They have revolutionized our ability to image the seafloor, providing higher resolution seafloor mapping data than can be achieved from surface vessels, particularly in deep water. This contribution focuses on the major advances in marine geoscience that have resulted from AUV data. The primary applications are i) submarine volcanism and hydrothermal vent studies, ii) mapping and monitoring of low-temperature fluid escape features and chemosynthetic ecosystems, iii) benthic habitat mapping in shallow- and deep-water environments, and iv) mapping of seafloor morphological features (e.g. bedforms generated beneath ice or sediment-gravity flows). A series of new datasets are presented that highlight the growing versatility of AUVs for marine geoscience studies, including i) multi-frequency acoustic imaging of trawling impacts on deep-water coral mounds, iii) collection of high-resolution seafloor photomosaics at abyssal depths, and iii) velocity measurements of active submarine density flows. Future developments in AUV technology of potential relevance to marine geoscience include new vehicles with enhanced hovering, long endurance, extreme depth, or rapid response capabilities, while development of new sensors will further expand the range of geochemical parameters that can be measured.
There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units.
This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.
This paper addresses a dual closed-loop fast integral terminal sliding mode control method of a multi-underactuated AUV formation system with uncertain model parameters and environmental disturbances. Different from the traditional sliding mode control method, this technique can not only keep the formation stable, but also significantly overcomes the problem that the formation tracking errors of the traditional method may not converge to zero in finite time. Then, an adaptive radial basis function (RBF) neural network controller is incorporated with a conditional integrator to deal with the uncertain model parameters, approximation errors and environmental disturbances in practical multi-AUV systems. And also the proposed controller is continuous with the property of chattering restraining. A virtual leader is adopted on the basis of the leader-following strategy to improve the robustness of the formation system and prevent the problem of formation collapse caused by the failure of the leader AUV. Moreover, the rigorous stability analysis based on Lyapunov method and numerical simulations demonstrate tracking errors converge to 0 in finite time. Finally, simulation results demonstrate the effectiveness of the proposed formation controller: the AUV formation can track the desired trajectory accurately with ±10% model parameter perturbation.
In this paper an approach-angle-based three-dimensional path-following control scheme has been proposed for underactuated Autonomous Underwater Vehicle (AUV) which experiences unknown actuator saturation and environmental disturbance. First, the path-following error dynamic model is derived based on the principle of relative motion which was followed by the design of approach-angle-based guidance law in both horizontal and vertical profiles of AUV to transform the three-dimensional tracking errors into heading angle and elevation angle tracking errors. The kinematic control law is designed based on the Lyapunov theory and backstepping technique. Second, the kinetic controller is designed based on the Lyapunov theory, backstepping technique and fuzzy logic system approximation method. The indirect adaptive fuzzy logic system is applied to approximate unknown smooth functions which are composed of coupled AUV hydrodynamics and complex differentials of desired pitch and yaw velocities. Moreover, the application of fuzzy control completely free from dependence on accurate AUV kinetic model. Considering a disturbance-like term, which is comprised of fuzzy logic system approximation error and bounded ocean disturbance, an adaptive law is designed to estimate the bound of it. Finally, two sets of comparative numerical simulations, including straight path following with different initial posture and spatial helix path following with sudden disturbance, are studied to illustrate the effectiveness and robustness of the proposed control scheme.
This paper addresses the surge speed tracking of an unmanned surface vehicle (USV) subject to unknown surge and propeller dynamics. A two-phase on-line identification and control strategy is proposed for designing a speed tracking controller without any a priori knowledge of the model parameters in surge dynamics, propeller and drive motor. In the identification phase, an adaptive parameter estimation law is used for identifying the unknown parameters in the surge speed control system. Two-layer filters are employed to assure the convergence of estimation errors in the first learning phase. In the control phase, a pulse-width-modulation-driven (PWM-driven) adaptive model predictive speed control law is proposed where neural predictors are used to estimate the identification errors and unknown sea loads based on input-output data. The stability analysis of two neural predictors is proved on the basis of input-to-state stability. Simulation results are provided to demonstrate the efficacy of the proposed end-to-end surge speed tracking of the USV without any a priori knowledge of the surge and propeller dynamics.
This paper focuses on motion controller design for x-rudder underwater vehicles with four independent stern rudders where the conventional ganging method for maneuvering is not applicable. To realize the cooperation of the stern rudders, motion controller of an x-rudder underwater vehicle is divided into two parts, a dynamics controller and a control allocator. The controller design is conducted under both scenarios that model parameters are known and unknown. For known models, the desired maneuvering moments are generated by model based sliding mode control method. For unknown models, non-model based iterative sliding mode control method is utilized to calculate virtual steering rudder commands. The control allocator of both methods are based on sequential quadratic programming to solve the mixed minimum problem, with varied evaluation criterions and constraints. By conducting numerical simulations under various conditions, the functionality of the two proposed control methods are verified, and comparison in terms of accuracy, energy saving, and computation consumption are also discussed in detail.
An investigation is conducted into thruster fault tolerant control for autonomous underwater vehicle (AUV) in this paper. In order to reduce the steady error caused by thruster faults in the use of a traditional sliding mode controller, a fault tolerant control method integrated with thrust allocation is proposed based on the sliding mode theory. According to the proposed method, a thruster weighted matrix is introduced, whose value varies depending on the fault magnitude of the thruster. Then, the proposed controller is applied to compensate for the insufficient thrust of the fault thruster. In order to mitigate the chattering phenomenon in the sliding process, the adaptive law that applies to switching gain and the thickness of boundary layer is developed for the proposed controller. The stability of the system is demonstrated by the frame of Lyapunov theory. Finally, a series of pool-experiments on AUV prototype are conducted to validate the proposed method.
This paper presents an optimal robust control method for trajectory tracking of a X-rudder autonomous underwater vehicle (AUV) subjects to velocity sensor failures and uncertainties. Two reduced-order extended state observers (ESOs) are designed to estimate the surge and heave velocities, and the estimated values are used to replace all the linear velocity-related parameters in controller design, which helps releasing the requirements of linear velocities measurement and makes the controller robust against linear velocity sensor failures. In kinematics control loop, line-of-sight (LOS) guidance law and Lyapunov-based control are employed, and the unknown attack angle is calculated based on the estimated linear velocities. In dynamics control loop, a robust disturbance rejection control law is constructed using disturbance observers and modified terminal sliding mode control. Moreover, a multi-objective optimization method is proposed to achieve X-rudder allocation, which is not only energy efficient but also robust against rudder failures, and helps tackling the rudder input saturation problem at the same time. Finally, comparative numerical simulations are provided to demonstrate the robustness and effectiveness of the proposed approach.
In this paper, a modified proximate time-optimal control (PTOC) is proposed based on reduced order extended state observer (RESO) and controller scaling method, for the heading control of underactuated autonomous underwater vehicles (AUV) with input nonlinearities. First, a simple and practical modified ADRC is proposed for heading control with input nonlinearities. The non-symmetric dead-zone with unknown parameters is modeled as a combination of linear input and bounded disturbances, and the RESO is designed to estimate and compensate it. The influence of actuator saturation constraint is reduced by limiting the control signal before it goes into the RESO. Then, a parameter self-tuning strategy is proposed for the feedback controller with the changed control gain by the controller scaling method. The control gain is quadratic respect to the velocity of AUV, the active disturbance rejection control (ADRC) controller parameters can be adjusted based on the AUV velocity using the strategy. And finally, the modified PTOC, based on RESO and with an updating strategy for the limit of linear region, is proposed to improve the control performance. Several simulation experiments are carried out, the effectiveness of self-tuning modified ADRC is verified, and the proposed modified PTOC shows better performance.
This paper addresses the design of an improved line-of-sight (LOS) based adaptive trajectory tracking controller for an under-actuated AUV subjects to highly coupled nonlinearities, ocean currents-induced uncertainties, and input saturation. The influences of ocean currents on the AUV are expressed in a comprehensive way such that both the kinematic and dynamic models of AUV are established with ocean currents. Extended disturbance observers (EDO) are utilized to estimate the ocean currents-induced uncertainties as well as their time-derivatives. An improved LOS guidance law is designed by introducing an auxiliary variable to the conventional LOS, and utilizing extended disturbance observers to estimate the ocean current-induced disturbances in the kinematic model. EDO-based adaptive terminal sliding mode control method is employed for dynamic control to improve the tracking performance and converging rate. In addition, the influence of actuator saturation is weakened by anti-windup compensator. Rigorous theoretical analysis and extensive simulation studies demonstrate that the proposed approach has good tracking accuracy, stability, and anti-jamming ability, thus leading to satisfying trajectory tracking control.
This paper addresses the problem of robust bottom following control for a flight-style autonomous underwater vehicle (AUV) subject to system uncertainties, actuator dynamics, and input saturation. First, the actuator dynamics that is approximated by a first-order differential equation is inserted into the AUV dynamics model, which renders a high-order nonlinear dynamics analysis and design in the model-based backstepping controller by utilizing guidance errors. Second, to overcome the shaking control behavior resulted by the model-based high-order derivative calculation, a fuzzy approximator-based model-free controller is proposed, in order to online approximate the unknown part of the ideal backstepping architecture. In addition, the adaptive error estimation technology is resorted to compensate the system approximation error, ensuring that all the position and orientation errors of robust bottom following control tend to zero. Third, to further tackle the potential unstable control behavior from inherent saturation of control surfaces driven by rudders, an additional adaptive fuzzy compensator is introduced, in order to compensate control truncation between the unsaturated and saturation inputs. Subsequently, Lyapunov theory and Barbalat lemma are adopted to synthesize asymptotic stability of the entire bottom following control system. Finally, comparative numerical simulations with different controllers, environmental disturbances and initial states are provided to illustrate adaptability and robustness of the proposed bottom following controller for a flight-style AUV with saturated actuator dynamics.
A design method is presented for pathfollowing control of under-actuated autonomous underwater vehicles subject to velocity and input constraints as well as internal and external disturbances. In the guidance loop, a kinematic control law of desired surge speed and pitch rate is derived based on a backstepping technique and a line-of-sight guidance principle. In the control loop, an extended state observer is developed to estimate the extended state composed of unknown internal dynamics and external disturbances. Then, a disturbance rejection control law is constructed using the extended state observer. To bridge the guidance loop and control loop, a reference governor is proposed for computing optimal guidance signals within the velocity and input constraints. The reference governor is formulated as a quadratically constrained optimization problem. A projection neural network is employed for solving the optimization problem in real-time. Simulation results illustrate the effectiveness of the proposed method for path-following control of autonomous underwater vehicles subject to constraints and disturbances simultaneously in the vertical plane.
This paper investigates the finite-time extended state observer-based distributed formation control for marine surface vehicles with input saturation and external disturbances. Initially, a novel finite-time extended state observer is proposed to estimate the unavailable velocity measurements and external disturbances simultaneously. No longer regarding the time derivative of external disturbances as zero, the proposed finite-time extended state observer is designed by transforming the disturbances as an extended state of the system to be estimated. Then, based on the estimated values, a distributed finite-time formation controller is designed for a group of marine surface vehicles to track a time-varying virtual leader. The position state of virtual leader only can be accessed by a subset of the group members. Furthermore, a saturation function is incorporated into the controller to solve the input saturation problem. Finally, a rigorous Proof demonstrates that the finite-time stability of the proposed extended state observer and formation controller can be guaranteed by using homogeneous method and Lyapunov theory. Numerical simulations illustrate the effectiveness of the proposed formation control scheme.
Accurate path following control plays an important role for autonomous underwater vehicles (AUV) in the oceanic surveys and exploration. In the consideration with nonlinearity and external disturbance, the dynamic model of a portable AUV has been established on the basis of its actuation and control characteristics. An adaptive nonlinear second order sliding mode controller has been deduced to eliminate the chattering motion through a sliding surface during the path following control. On the uncertainties of external disturbances, an adaptive tuning law has been selected to estimate the upper bound of disturbance. In the lake experiments, the proposed controller not only provides better response with faster convergence and smaller overshoot, but also eliminates the chattering effect of control output, in compare with the controller with linear and PID second order sliding mode surface.
To inspect subsea cables, an autonomous underwater vehicle (AUV) with two triaxial magnetometers is usually assigned to track the cable route. In this paper, a novel two-layer framework synthesizing antinoise cable localization and robust tracking algorithm is proposed to guide an AUV to track subsea cables in the presence of sensor noise and ocean currents. First, an analytic formulation for the cable localization using two magnetometers is derived, and then a dedicated magnetic line-of-sight (LOS) guidance is built based on the horizontal offset between the AUV and the cable. Second, a novel antinoise method by estimating the horizontal offset is integrated into the LOS guidance law to reduce the negative effects of magnetic noise in the kinematic layer. Subsequently, in the dynamic layer, a simplified yet robust feedback controller with reduced implementation complexity is designed to track the desired guidance profiles, such that the AUV is able to track subsea cables in the presence of sensor noise and ocean currents. In addition, the capability of dynamic control laws accounting for ocean currents is analyzed in the amplitude–frequency domain. Finally, numerical studies illustrate the antinoise and robust performance of the proposed two-layer framework for subsea cable tracking.
This paper addresses the problem of motion control for autonomous underwater vehicles (AUVs) equipped with X rudder, in which all of the rudders can be operated independently. In order to offer accurate and reliable control ability, with the X rudder's character taken into consideration, one anti-normalization method based on virtual rudders and one rudder allocation including double-rudder, triple-rudder and quadruple-rudder modes are designed. Besides that, one new control ability judgment combined with traditional method and resistance energy is offered to find out the best control method. The simulations with different kinds of controllers under instantaneous and random disturbance are performed. In one simulation, one comparison with a cross-rudder AUV transformed from the test X-rudder AUV is also made. The results show that all of the designed X-rudder AUV motion control methods can complete the mission and the quadruple-rudder allocation has the best control ability.
In this paper, we investigate the trajectory tracking problem for a fully actuated autonomous underwater vehicle (AUV) that moves in the horizontal plane. External disturbances, control input nonlinearities and model uncertainties are considered in our control design. Based on the dynamics model derived in the discrete-time domain, two neural networks (NNs), including a critic and an action NN, are integrated into our adaptive control design. The critic NN is introduced to evaluate the long-time performance of the designed control in the current time step, and the action NN is used to compensate for the unknown dynamics. To eliminate the AUV's control input nonlinearities, a compensation item is also designed in the adaptive control. Rigorous theoretical analysis is performed to prove the stability and performance of the proposed control law. Moreover, the robustness and effectiveness of the proposed control method are tested and validated through extensive numerical simulation results.
This paper investigates the path following control problem for an unmanned airship in the presence of unknown wind and uncertainties. The backstepping technique augmented by a robust adaptive radial basis function neural network (RBFNN) is employed as the main control framework. Based on the horizontal dynamic model of the airship, an improved adaptive integral line-of-sight (LOS) guidance law is first proposed, which suits any parametric paths. The guidance law calculates the desired yaw angle and estimates the wind. Then the controller is extended to cope with the airship yaw tracking and velocity control by resorting to the augmented backstepping technique. The uncertainties of the dynamics are compensated by using the robust RBFNNs. Each robust RBFNN utilizes an nth-order smooth switching function to combine a conventional RBFNN with a robust control. The conventional RBFNN dominates in the neural active region, while the robust control retrieves the transient outside the active region, so that the stability range can be widened. Stability analysis shows that the controlled closed-loop system is globally uniformly ultimately bounded. Simulations are provided to validate the effectiveness of the proposed control approach.
In this paper, we consider attitude control for autonomous underwater vehicles (AUVs) with input nonlinearities and unknown disturbances taken into account. The dynamics model in the 3D space of an AUV is simplified to a second-order dynamics with unknown model parameters and disturbances for the yaw and pitch control. Based on this simplification, a sliding-mode-based adaptive control is proposed for the case without any input nonlinearities. For the dead-zone nonlinearity and unknown disturbances, a sliding-mode-based adaptive control combined with a nonlinear disturbance observer is employed, in which the non-symmetric dead-zone with unknown parameters is modeled as a time-varying disturbance-like term rather than constructing a smooth dead-zone inverse. For rudder saturation, the control is further designed by introducing an auxiliary dynamic compensator. The mathematical proof of the proposed algorithms is presented. Extensive simulation results are presented to illustrate the effectiveness of the proposed control. In addition, experimental results on an AUV whose attitude is controlled by cross-type rudders are also provided to show the effectiveness of the proposed algorithms.
The cooperative control of marine vehicles finds wide applications in many marine missions and tasks. This paper investigates the receding horizon formation tracking control problem of a fleet of underactuated autonomous underwater vehicles (AUVs), in which the follower AUVs are required to track the leader with prescribed formation pattern, and the control inputs of the follower AUVs are subject to practical constraints. An auxiliary stabilizable control law is first designed, based on which a novel optimization problem is proposed and a new receding horizon control (RHC) algorithm is designed to generate control inputs. The theoretical feasibility conditions of the RHC-based tracking algorithm and the stability conditions of the closed-loop systems are provided. Simulation studies are conducted, and the simulation results verify the effectiveness of the proposed algorithm and theoretical results.
This paper investigates the path following control problem for an unmanned marine surface vessel (MSV) in the presence of uncertainties and input saturation. The backstepping technique augmented by a robust adaptive radial basis function neural network (RBFNN) and an auxiliary design system is employed as the main control framework. Based on the dynamic model of the MSV, an improved adaptive integral line-of-sight (LOS) guidance law is first proposed, which is suitable for any parametric paths and can deal with time-varying ocean currents. The guidance law calculates the desired yaw angle and estimates the currents. Then the controller is extended to cope with the MSV yaw tracking and velocity control by resorting to the augmented backstepping technique. The uncertainties of dynamics are compensated by the robust RBFNNs. Each robust RBFNN utilizes an nth-order smooth switching function to combine a conventional RBFNN with a robust control. The auxiliary design system is presented to analyze the effect of input saturation, and states of the auxiliary design system are used to develop the controller. This systematic design methodology is proved to achieve ultimate boundedness of the closed-loop MSV system. Simulations validate the effectiveness of the proposed control approach.
This paper proposes a hierarchical image-based visual servoing (IBVS) strategy for dynamic positioning of a fully actuated underwater vehicle. In the kinematic loop, the desired velocity is generated by a nonlinear model predictive controller, which optimizes a cost function of the predicted image trajectories under the constraints of visibility and velocity. A velocity reference model, representing the desired closed-loop vehicle dynamics, is integrated with an IBVS kinematic model to predict the future trajectories. In the dynamic velocity tracking loop, a neural-network-based model reference adaptive controller is designed to ensure the convergence of the velocity tracking error in the presence of uncertainties associated with vehicle dynamic parameters, water velocity, and thrust forces. Comparative simulations with different control and system configurations are performed to verify the effectiveness of the proposed scheme and to illustrate the influences of the prediction horizon, cost function, closed-loop vehicle dynamics, and predictive velocity reference model on the IBVS system performance.
This paper addresses on a horizontal waypoint tracking problem for a class of nonlinear autonomous underwater vehicles (AUVs) with actuator saturations while keeping its constant surge speed. The concerned problem is formulated as an exponential stabilization of the error dynamics with respect to the desired surge speed and the desired yaw angle determined from the line of sight. It is shown that the feedback linearization technique makes the separate design of the available control inputs, the propeller thrust and the rudder angle, possible. By using the sector nonlinearity, the error dynamics is modeled as a polytopic linear parameter varying (LPV) system. Then, sufficient linear matrix inequality (LMI) conditions for its regional exponential stabilizability are derived in the sense of Lyapunov stability criterion. An example is provided to illustrate the effectiveness of the proposed methodology.
We propose the use of a second-order sliding-mode controller (2-SMC) to stabilize an autonomous underwater vehicle (AUV) which is subject to modeling errors and often suffers from unknown environmental disturbances. The 2-SMC is effective in compensating for the uncertainties in the hydrodynamic and hydrostatic parameters of the vehicle and rejecting the unpredictable disturbance effects due to ocean waves, tides, and currents. The 2-SMC is comprised of an equivalent controller and a switching controller to suppress the parameter uncertainties and external disturbances, and its closed-loop system is exponentially stable in the presence of parameter uncertainties and unknown disturbances. We performed numerical simulations to validate the proposed control approach, and experimental tests using Cyclops AUV were conducted to demonstrate its practical feasibility. The proposed controller increased the accuracy of trajectory tracking for an AUV in the presence of uncertain hydrodynamics and unknown disturbances.
This paper addresses two interrelated problems concerning the planar three degree-of-freedom motion of a vehicle, namely, the path planning problem and the guidance problem. The monotone cubic Hermite spline interpolation (CHSI) technique by Fritsch and Carlson is employed to design paths that provide the user with better shape control and avoid wiggles and zigzags between the two successive waypoints. The conventional line-of-sight (LOS) guidance law is modified by proposing a time-varying equation for the lookahead distance, which is a function of the cross-track error. This results in a more flexible maneuvering behavior that can contribute to reaching the desired path faster as well as obtaining a diminished oscillatory behavior around the desired path. The guidance system along with a heading controller form a cascaded structure, which is shown to be κ-exponentially stable when the control task is to converge to the path produced by the aforementioned CHSI method. In addition, the issue of compensating for the sideslip angle β is discussed and a new κ-exponentially stable integral LOS guidance law, capable of eliminating the effect of constant external disturbances for straight-line path following, is derived.
This paper considers the problem of adaptive neural tracking control for a class of nonlinear stochastic pure-feedback systems with unknown dead zone. Based on the radial basis function neural networks' online approximation capability, a novel adaptive neural controller is presented via backstepping technique. It is shown that the proposed controller guarantees that all the signals of the closed-loop system are semi-globally, uniformly bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the suggested control scheme. Copyright © 2012 John Wiley & Sons, Ltd.
The trajectory tracking control problem of underwater robot is addressed in this paper. In general, an accurate thrust modeling is very difficult to establish for underwater robot in practice. Hence, the control voltage of thruster is designed directly as the input of system by the controller in this article. First, Taylor's polynomial is used to transform the form of trajectory tracking error system of underwater robot to the form of affine nonlinear systems, whose input is the control voltage of thruster. Then, according to the principle of sliding mode control, and using the local recurrent neural network to estimate the unknown item of affine system online, an adaptive sliding mode control is proposed. Aiming at the chattering problem which is caused by sliding mode control item, we propose a switch gain adjust method based on exponential function. It was proved that the trajectory tracking error of the underwater robot control system is uniformly ultimately bounded through Lyapunov theory. The feasibility and effectiveness of the proposed approach is demonstrated with trajectory tracking experiments of the experimental prototype of underwater robot.