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State-dependent Riccati equation-based robust dive plane control of AUV with control constraints
Abstract
The paper treats the question of suboptimal dive plane control of autonomous underwater vehicles (AUVs) using the state-dependent Riccati equation (SDRE) technique. The SDRE method provides an effective mean of designing nonlinear control systems for minimum as well as nonminimum phase AUV models. It is assumed that the hydrodynamic parameters of the nonlinear vehicle model are imprecisely known, and in order to obtain a practical design, a hard constraint on control fin deflection is imposed. The problem of depth control is treated as a robust nonlinear output (depth) regulation problem with constant disturbance and reference exogenous signals. As such an internal model of first-order fed by the tracking error is constructed. A quadratic performance index is chosen for optimization and the algebraic Riccati equation is solved to obtain a suboptimal control law for the model with unconstrained input. For the design of model with fin angle constraints, a slack variable is introduced to transform the constrained control input problem into an unconstrained problem, and a suboptimal control law is designed for the augmented system using a modified performance index. Using the center manifold theorem, it is shown that in the closed-loop system, the system trajectories are regulated to a manifold (called output zeroing manifold) on which the depth tracking error is zero and the equilibrium state is asymptotically stable. Simulation results are presented which show that effective depth control is accomplished in spite of the uncertainties in the system parameters and control fin deflection constraints.
... developed based on the pseudo-linearization framework to solve different problems such as robust H ∞ filter design [10], suboptimal sliding mode control design for delayed systems [11], observer design for nonlinear delayed systems [12], and so on. These methods were effectively applied in a wide variety of applications, such as drug administration in cancer treatment [13] and dive plane control of autonomous underwater vehicles (AUVs) [14]. Two complete surveys of the SDRE techniques and the related theories can be found in [8] and [9]. ...
... The objective of this example lies in the design of a robust suboptimal tracking control system for the control of AUVs in the dive plane using the proposed method presented in Section II. For this purpose, the following SDC representation of the AUV model is used [14]: ...
... In the above equations, w, q, z, and θ are the heave velocity, the pitch velocity, the depth, and the pitch angle, respectively, and δ s denotes the fin angle, which is considered as the control input for the dive plane control of the AUV. The hydrodynamic parameters values of the AUV are reported in Table I [14]. Table II also represents the physical parameters values of the AUV [14], where (x B , z B ) and (x G , z G ) are the coordinates of the center of buoyancy and the coordinates of the center of gravity of the AUV with respect to the center of buoyancy, respectively. ...
... developed based on the pseudo-linearization framework to solve different problems such as robust H ∞ filter design [10], suboptimal sliding mode control design for delayed systems [11], observer design for nonlinear delayed systems [12], and so on. These methods were effectively applied in a wide variety of applications, such as drug administration in cancer treatment [13] and dive plane control of autonomous underwater vehicles (AUVs) [14]. Two complete surveys of the SDRE techniques and the related theories can be found in [8] and [9]. ...
... The objective of this example lies in the design of a robust suboptimal tracking control system for the control of AUVs in the dive plane using the proposed method presented in Section II. For this purpose, the following SDC representation of the AUV model is used [14]: ...
... In the above equations, w, q, z, and θ are the heave velocity, the pitch velocity, the depth, and the pitch angle, respectively, and δ s denotes the fin angle, which is considered as the control input for the dive plane control of the AUV. The hydrodynamic parameters values of the AUV are reported in Table I [14]. Table II also represents the physical parameters values of the AUV [14], where (x B , z B ) and (x G , z G ) are the coordinates of the center of buoyancy and the coordinates of the center of gravity of the AUV with respect to the center of buoyancy, respectively. ...
In this brief, a new technique for solving a suboptimal tracking problem for a class of nonlinear dynamical systems is presented. Toward this end, an optimal tracking problem using a discounted cost function is defined and a control law with a feedback-feedforward structure is designed. A state-dependent Riccati equation (SDRE) framework is used in order to find the gains of both the feedback and the feedforward parts, simultaneously. Due to the significant properties of the SDRE technique, the proposed method can handle the presence of input saturation and state constraint. It is also shown that the tracking error converges asymptotically to zero under mild conditions on the discount factor of the corresponding cost function and the desired trajectory. Two simulation and experimental case studies are also provided to illustrate and demonstrate the effectiveness of our proposed design methodology.
... We consider the vehicle's depth control for which we take a nonlinear continuous model of the vehicle at constant surge velocity as ground truth and for simulation purposes [31]. Around a trim point of purely horizontal movement the states and input of the system are ...
... parameters given in[31]. With constant surge velocity u 0 = 2m/s, we trim the model around w cos(Θ)+u 0 sin(Θ) = 0 and q = 0. ...
Gaussian process (GP) regression has been widely used in supervised machine learning for its flexibility and inherent ability to describe uncertainty in the function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal linear system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and the benefits of considering feedback in the prediction is demonstrated. We describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Efficient computation with state-of-the-art solvers is discussed and simulation examples demonstrate the feasibility of the approach for systems with sub-second sampling times.
... The control problem is solved using linear matrix inequality (LMI) techniques. In Naik and Singh (2007), a suboptimal diving control algorithm has been designed for AUVs using the state-dependent Riccati equation (SDRE) technique that can be used for both nonlinear minimum phase (in particular for heading dynamics) and nonminimum phase (for diving dynamics) AUV models. Another diving control algorithm using Lyapunov theory and backstepping techniques is explored in Lapierre (2009) that provides guaranteed robust performance in the presence of uncertainties. ...
... The comparison of the NHSF and NHOF control algorithms with the SDRE based control algorithm (Naik and Singh, 2007) is presented in Figure 5. Referring to Figure 5(a), it is observed that the tracking of the desired depth by the NHOF controller is better than the NHSF controller and SDRE based control. The synthesis ensures that the settling times for the controller are same whereas the overshoot is completely eliminated in the case of the NHOF control algorithm during the the tracking of the desired depth profile. ...
This paper addresses the development of a nonlinear ℋ∞ diving control algorithm for an autonomous underwater vehicle. It employs both state and output feedback control techniques in designing a nonlinear ℋ∞ controller such that the autonomous underwater vehicle tracks the desired depth profile. The diving control problem is formulated as a disturbance attenuation problem, in view of achieving the desired performance by attenuating the internal as well as the external disturbances by ensuring internal stability and robustness. Two Hamilton–Jacobi–Isaacs inequalities have been formulated in the form of a Taylor series technique to determine solutions to the control algorithms. The solution of the first Hamilton–Jacobi–Isaacs inequality renders a state feedback control law whereas the second inequality is exploited to design a nonlinear observer for estimating the autonomous underwater vehicle states in order to realize an output feedback controller. These control algorithms are implemented firstly using the MATLAB/Simulink environment and then, the experimental validation of the developed control algorithm has been performed in order to ensure the effectiveness of the control scheme.
... Presentation of advanced controllers for AUVs is one of the modern topics in the literature of marine control systems. Several methods are reportedly used to control AUVs [2][3][4][5][6][7][8]. Among them, those which consider the practical problems of the design have eventually attained more interests. ...
... This technique is also applied to a nonlinear model of REMUS AUV. Robust [2,3] and adaptive methods [7,8] are commonly used controllers in AUVs. Dealing with uncertain dynamics of these systems may be mostly investigated in the presence of actuator saturation [4]. ...
Input saturations and uncertain dynamics are among the practical challenges in control of autonomous vehicles. Adaptive control is known as a proper method to deal with the uncertain dynamics of these systems. Therefore, incorporating the ability to confront with input saturation in adaptive controllers can be valuable. In this paper, an adaptive autopilot is presented for the pitch and yaw channels of an autonomous underwater vehicle (AUV) in the presence of input saturations. This will be performed by combination of a model reference adaptive control (MRAC) with integral state feedback with a modern anti-windup (AW) compensator. MRAC with integral state feedback is commonly used in autonomous vehicles. However, some proper modifications need to be taken into account in order to cope with the saturation problem. To this end, a Riccati-based anti-windup (AW) compensator is employed. The presented technique is applied to the non-linear six degrees of freedom (DOF) model of an AUV and the obtained results are compared with that of its baseline method. Several simulation scenarios are executed in the pitch and yaw channels to evaluate the controller performance. Moreover, effectiveness of proposed adaptive controller is comprehensively investigated by implementing Monte Carlo simulations. The obtained results verify the performance of proposed method.
... We consider the depth control of an autonomous underwater vehicle (AUV). The vehicle is described by a nonlinear continuous-time model of the vehicle at constant surge velocity as ground truth and for simulation purposes [41]. Around a trim point of purely horizontal movement, the states and input of the system are . ...
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller.
... First, we assume that the pitch angle of the AUV is very small, and then we assume that the motion dynamics of the pitch angle can be expressed as a linear equation. Based on the above assumptions, the vertical motion model of the AUVs can be linearized [24][25][26][27]. ...
In order to improve the endurance of underwater vehicles and make it possible for the underwater vehicle to inspect long-distance water tunnels, a sliding mode control method based on event triggering is proposed for the depth control of underwater vehicles from the perspective of energy saving. Firstly, the kinematics and dynamics models of underwater vehicle dive surface are established. Secondly, an event-triggered sliding mode controller is designed. According to the Lyapunov function, the stability of the designed controller is proved by theoretical analysis, and Zeno phenomena will not appear in the closed-loop control system. Compared with other controllers, the simulation results show that this controller can effectively realize the depth control of AUV, has strong adaptability and robustness to unmodeled nonlinear dynamics and bounded disturbances, and has the effect of saving computing resources.
... Recently, work on a depth control based' on solving the algebraic Riccati equation [108] for an AUV has been developed. ...
p>This thesis is concerned with the guidance and control problem for autonomous hom- ing and docking tasks using an autonomous underwater vehicle. The tasks will play a key role in long-term underwater applications in the future. Current technology allows most vehicles capable of short-term operation. Because of limitations of energy stor- age and sensor capability, underwater vehicles considered in large networks are unable to operate continuously in completing a large task assignment for extended periods of time. To extend a large scope of the missions, autonomous homing and docking tasks are therefore required allowing a vehicle to automatically return to the docking station and then recharge its own battery and exchange data before continuing the operations. The thesis describes work towards guidance and control systems to enable a nonholo- nomic torpedo shaped underwater vehicle to perform automatic homing and docking preparation tasks. The artificial potential field and the vector field path generation methods construct the predefined trajectory by extracting position information from surrounding sensor nodes. Thus, the predefined path leads an AUV relatively close to the docking station with obstacle avoidance. With an enhanced model, the switching weighted vector field technique applies a set of varying weights. This technique shapes a trajectory which a docking preparation manoeuvre can improve.</p
... In fact, this inherent characteristic maybe cause performance degradation or even instability in the closed-loop response of tracking systems (Cui et al., 2017;Yu et al., 2020). To solve this problem, a slack variable is first introduced in Naik and Singh (2007) Chu et al. (2018), a new modified auxiliary system with time-varying nonlinear gains is proposed to compensate for the effects of input saturation in diving control of underwater vehicles as well as to remove the assumption regarding bounded auxiliary states. In Wu et al. (2018), augment 1 adaptive control with Riccati-based anti-windup compensator is utilized to modify the pitch tracking performance of REMUS in the presence of saturation. ...
Accurate depth tracking control is of great importance for an underwater vehicle that performs an underwater task such as seabed mapping and underwater docking. This paper addresses the problem of adaptive depth tracking control for an underwater vehicle, particularly in the presence of hydrodynamics uncertainty, thruster’s dead-zone and saturation. Before deriving an adaptive depth control law, an unified and continuous hydrodynamics model in heave is built, where the thruster’s characteristics composed of output time-delay, input dead-zone and saturation are taken into consideration. Subsequently, fuzzy universal approximation theorem is resorted to online approximate the unknown and complex hydrodynamics in heave, and then adaptive sliding mode control technique is utilized to compensate for the approximation residual. In order to reject inherent input saturation, gradient projection method is introduced into the above adaptive control law, resulting in an adaptive bounded depth control law. Furthermore, through obtaining two dead-zone breakpoints in advance and online translation compensation, the final control output can always change within the permitted range. Finally, three comparative experiments are performed to verify the outperformance of the designed adaptive bounded depth tracking controller.
... Tan et al. presented an integrated collision avoidance system for autonomous underwater vehicles [168]. Naik and Singh presented the robust design of the SDRE controller for an AUV in regulation problem [169]. Cimen presented development and validation of a mathematical model for control of constrained nonlinear oil tanker motion and then used the SDRE controller to control the model [94]. ...
This paper presents an extensive tutorial and a complete review on the state-dependent Riccati equation (SDRE). The review covers contributions from the beginning to (near the end of 2017) current trend and works, categorized according to theoretical and practical impact. The tutorial section presents the fundamental relations, derivation and necessary conditions of the SDRE as a controller, observer and estimator. The state-dependent Riccati equation serves as a continuous and discrete time controller, observer, filter and estimator in the field of control engineering. The nature of the SDRE is in non-linear optimal control domain; and nowadays it plays a vital role in aerospace, robotics, control of unmanned aerial vehicle, aircraft, autonomous underwater vehicle, surface vessel and other nonlinear plants. Optimality, robustness, asymptotic stability, flexibility in design and a systematic procedure are some of the advantages of this method. The capability to combine the SDRE with other methods (such as sliding mode control, fuzzy, genetic, neural network and etc.) is another important feature of the approach. The mentioned characteristics, advantages and combination of the SDRE with other techniques are reviewed comprehensively in this work.
... Ref. [83] optimized the system by using the quadratic performance index to solve the SDRE and obtain the sub-optimal control law of the input unconstrained model. Al-though the system parameters and control fin deflection constraint conditions are uncertain, effective depth control can still be achieved. ...
Autonomous underwater vehicles (AUVs) have been widely used to perform underwater tasks. Due to the environmental disturbances, underactuated problems, system constraints, and system coupling, AUV trajectory tracking control is challenging. Thus, further investigation of dynamic characteristics and trajectory tracking control methods of the AUV motion system will be of great importance to improve underwater task performance. An AUV controller must be able to cope with various challenges with the underwater vehicle, adaptively update the reference model, and overcome unexpected deviations. In order to identify modeling strategies and the best control practices, this paper presents an overview of the main factors of control-oriented models and control strategies for AUVs. In modeling, two fields are considered: (i) models that come from simplifications of Fossen’s equations; and (ii) system identification models. For each category, a brief description of the control-oriented modeling strategies is given. In the control field, three relevant aspects are considered: (i) significance of AUV trajectory tracking control, (ii) control strategies; and (iii) control performance. For each aspect, the most important features are explained. Furthermore, in the aspect of control strategies, mathematical modeling study and physical experiment study are introduced in detail. Finally, with the aim of establishing the acceptability of the reported modeling and control techniques, as well as challenges that remain open, a discussion and a case study are presented. The literature review shows the development of new control-oriented models, the research in the estimation of unknown inputs, and the development of more innovative control strategies for AUV trajectory tracking systems are still open problems that must be addressed in the short term.
... with τ = τ u , τ q and τ r . And τ max and τ min denote the upper and lower bounds of control forces respectively (Naik and Singh, 2007;Zheng et al., 2018). Let us define a parameterized reference path which is propagated based on the variable ϖ(t), and the virtual tracking point on the path in {NED} frame is denoted with O p (x p , y p , z p ). ...
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.
... The aim is to design a controller such that by applying the control signal u(t) to the ROV fins, the depth of the ROV tracks a desired time-varying trajectory. The hydrodynamic and physical parameters values of the ROV are represented in Tables I and II, respectively [43]. ...
In this paper, using a novel event-triggered method, a robust H ∞ depth tracking controller is designed for a remotely operated underwater vehicle (ROV). It is assumed that the desired trajectory of the ROV is determined by an operator outside of the vehicle based on its needed depth and obstacles in its path. It is also assumed that a wireless network is used to connect the user with the ROV. To decrease the communication rate between the controller and the ROV, a novel nonlinear event-triggered H ∞ controller is designed. The effects of the disturbance on the system performance are also attenuated. Stability of the ROV under the designed event-triggered controller is proved through a theorem. Simulation results demonstrate that the error between the depth of the ROV and its time-varying desired trajectory converges to zero using the proposed event-triggered H ∞ controller. It is also shown that the communication rate between the designed controller and the ROV is considerably reduced.
... The SDRE technique has been widely used in the literature since 1960s as a tool for suboptimal stabilization of nonlinear systems [27,3,33] and showed its effectiveness for many engineering applications such as aerial [7,1], spacial [30], marine [26], robotics [11,32,20], and electronics [9,10] systems to name a few. The suboptimal control scheme constructed by SDRE is appealing due to its simplicity and capability of online implementation without any need of solving two-point boundary value problems by direct implementation of the LQR scheme to nonlinear systems. ...
A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal solution by means of dynamic control gains, based on the estimated main and extended state variables obtained through a high-gain observer. Three numerical examples compare the performance of the proposed control scheme applied to linear and nonlinear systems with that of a fixed-gain conventional ADRC as well as several model-based optimal and suboptimal controllers.
... For marine vehicles, there exists inherent actuator saturation (Naik and Singh, 2007;Zheng et al., 2017). Therefore, the propeller thrust and rudder angles of the AUV discussed here should be bounded, viz. ...
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 addition, the author found it necessary to adjust a subset of the calculated coefficients derived using the strip integral method, and these adjustments were based on comparisons with the experimental data [9]. It is discovered that the more accurate nondimensional hydrodynamic coefficients [12] for torpedo-type AUVs can be obtained based on comparisons with those of the REMUS data [9], [13]. ...
This paper presents the detailed modeling and simulation of the dynamic coupling between an autonomous underwater vehicle (AUV) and a manipulator. The modeling processes are described with the incorporation of the most dominating hydrodynamic effects such as added mass, lift and drag forces. The hydrodynamic coefficients are derived using strip theory and are adjusted according to dynamical similarity. A fuzzy decoupling controller (FDC) is proposed for an autonomous underwater vehicle-manipulator system (UVMS) which consists of two subsystems, an underwater vehicle and a manipulator. The proposed controller uses a fuzzy algorithm (FA) to adaptively tune the gain matrix of the error function (EF). The EF is described by the integral sliding surface function. This technique allows the off-diagonal elements developed for decoupling the system to be incorporated in the gain matrix. Tracing the FA and EF back to the principle of feedback linearization, one further obtains evidence about the decoupling and stability of the system. Moreover, a desired trajectory with the consideration of the dynamic coupling of the AUV is designed to reduce the thruster forces and manipulator’s torques. This technique provides high performance in terms of tracking error norms and expended energy norms. A major contribution of this study is that it adopts the off-diagonal elements to exploit the dynamic coupling between the degrees of freedom of the subsystem and the dynamic coupling between the two subsystems. Simulation results demonstrate the effectiveness and robustness of the proposed technique in the presence of parameter uncertainties and external disturbances.
... Hence, control of AUVs is very challenging. Various control algorithms such as adaptive control [1], robust control [2], model predictive control [3], sliding mode control [1], neurocontrol [4] etc. have been proposed for successful control of AUVs. ...
The performance of a formation control algorithm for a group of autonomous underwater vehicles (AUVs) may be degraded due to communication constraints between the leader and the follower AUVs. Moreover, as the distance between the AUVs change due to ocean waves, the delay in communication also varies. In this study, a modified constrained adaptive controller (CAC) is proposed to resolve the issue of variable-delay as well as actuator saturation. Due to the on-line reduction of the cost function, the gains of the CAC are updated at each sampling time taking into account the effects of communication delay. This improves the path-following accuracy of the leader AUV as well as follower AUVs. The effectiveness of the proposed control algorithm is demonstrated by implementing it on a prototype AUV (ODRA-I) model. The obtained simulation and experimental results show that the follower AUVs maintain a desired distance from the leader AUV to avoid a collision. For the proposed algorithm, the desired path-following performance of the follower AUV is maintained even when the delay is changed from 0 to 5 s. Moreover, the proposed control algorithm is efficient in avoiding actuator saturation.
... The Remote Environmental Unit (REMUS) AUV 21 and its corresponding reference frames are illustrated in Figure 1. The inertial reference frame is considered a fixed frame, whose z-axis directed into the gravitational direction and the other two axes are perpendicular to the z-axis. ...
An adaptive fuzzy sliding mode controller is proposed for the depth control of an underactuated underwater vehicle based on the state-dependent Riccati equation. An adaptive fuzzy control algorithm is embedded into the sliding mode controller to solve the buffering and mismatched uncertain problems in the robust sliding mode variable structure controller, where an auxiliary fuzzy control unit is designed to automatically adjust the scale factor of the main fuzzy controller output. Based on Lyapunov stability theory and final value bounded theorem, the stability and convergence properties of the closed-loop system are demonstrated. Numerical simulations are carried out to validate the effectiveness of the proposed controller.
... Out of the 24 on unmanned vehicles design, 13 are dedicated to control systems and 11 are related to systems or algorithms for controlling these UV, both for underwater vehicles [11][12][13][14][15][16] as well as for surface ones [17][18][19][20][21]. The last two works on UV control systems are on the design of a non-linear control system [22] and a literature review on maritime mechatronics systems [23]. ...
Although maritime transport is the backbone of world commerce, its digitalization lags significantly behind when we consider some basic facts. This work verifies the state-of-the-art as it currently applies to eight digital domains: Autonomous vehicles and robotics; artificial intelligence; big data; virtual reality, augmented and mixed reality; internet of things; the cloud and edge computing; digital security; and 3D printing and additive engineering. It also provides insight into each of the three sectors into which this industry has been divided: Ship design and shipbuilding; shipping; and ports. The work, based on a systematic literature review, demonstrates that there are domains on which almost no formal study has been done thus far and concludes that there are major areas that require attention in terms of research. It also illustrates the increasing interest on the subject, arising from the necessity of raising the maritime transport industry to the same level of digitalization as other industries.
... Remark 3. For marine vehicles, there exists inherent actuator saturation (Naik and Singh, 2007;Zheng et al., 2017). Therefore, the propeller thrust and the yaw rudder angle of the AUV discussed here should be bounded, viz. ...
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.
... In fact, actuator saturation exists in the practical vehicle system and maybe cause performance degradation even instability in the closedloop response [24]- [26]. To solve the problem of actuator saturation, a slack variable was introduced to transform the saturated fin angle control problem into the unsaturated problem, and then a state-dependent Riccati equation-based robust controller was designed for fixed-depth tracking of the REMUS AUV [27]. In [28], a nonlinear model predictive control-based tracking controller was designed so that the entire AUV closed-loop stability can be guaranteed in the presence of actuator saturation. ...
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.
... Paying attention to these properties, several problems have been solved using the SDRE technique such as robust H 8 filter design Reif et al. (1999), suboptimal sliding mode control design for delayed systems Batmani & Khaloozadeh (2016), observer design for nonlinear delayed systems Batmani & Khaloozadeh (2014), and so on. These methods are effectively applied in a wide variety of applications, such as dive plane control of autonomous underwater vehicle (AUVs) Naik & Singh (2007) and drug administration in cancer treatment Batmani & Khaloozadeh (2013). 20 Due to the aforementioned properties of the SDRE technique, the method was also applied to the chaotic systems Jayaram & Tadi (2006). ...
In this paper, the problems of chaos control and chaos synchronization are solved using the state-dependent Riccati equation methods. In the former problem, a nonlinear suboptimal control law is found, which leads to a stable closed-loop system. In the latter, an optimal infinite-time horizon tracking problem is defined and solved using the state-dependent Riccati equation technique. It is shown that the synchronization error between the slave and the master systems converges asymptotically to zero under some mild conditions. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the methods.
... It is expected and desired that the AUV SFDIT system detects and isolates the occurrence of different types of faults f (t ) ∈ R 2 (corresponding to various fault severities and different locations of fault occurrences) in presence of disturbances d(t ) ∈ R 2 , w(t ) ∈ R 2 and reference inputs u r (t ) ∈ R 2 and should also simultaneously track the desired output y r (t ) ∈ R 2 . Note that the problem of tracking a set point for the Subzero II and REMUS AUVs is solved by using H Ý robust control and state-dependent Riccati equation (SDRE) methods in Feng and Allen (2002) and Naik and Singh (2007), respectively. Nevertheless, it is important for us to design a controller that makes the AUV track a desired time-varying trajectory, given complex missions and scenarios. ...
The problem of simultaneous fault detection, isolation and tracking (SFDIT) control design for linear systems subject to both bounded energy and bounded peak disturbances is considered in this work. A dynamic observer is proposed and implemented by using the H∞/H−/L1 formulation of the SFDIT problem. A single dynamic observer module is designed that generates the residuals as well as the control signals. The objective of the SFDIT module is to ensure that simultaneously the effects of disturbances and control signals on the residual signals are minimized (in order to accomplish the fault detection goal) subject to the constraint that the transfer matrix from the faults to the residuals is equal to a pre-assigned diagonal transfer matrix (in order to accomplish the fault isolation goal), while the effects of disturbances, reference inputs and faults on the specified control outputs are minimized (in order to accomplish the fault-tolerant and tracking control goals). A set of linear matrix inequality (LMI) feasibility conditions are derived to ensure solvability of the problem. The extended LMI approach is employed for reducing the conservativeness in the problem solution by introducing additional matrix variables to eliminate the couplings of the Lyapunov matrices with the system matrices. In order to illustrate and demonstrate the effectiveness of our proposed design methodology, the developed and proposed schemes are applied to an autonomous unmanned underwater vehicle (AUV).
... Since then several methods have been developed based on the pseudo linearization framework to solve different problems such as robust H ∞ filter design [11], suboptimal sliding mode control design for delayed systems [12], observer design for nonlinear delayed systems [13], and so on. These methods are effectively applied in a wide variety of applications, such as drug administration in cancer treatment [14] and dive plane control of AUVs [15]. Consider the nonlinear system (1). ...
The state-dependent Riccati equation (SDRE) technique can be used to solve optimal control problems for a wide class of nonlinear dynamical systems. In this method, instead of solving a complicated Hamilton-Jacobi-Bellman (HJB) equation, a state-dependent Riccati equation is solved which leads to a suboptimal control law. However, a priori model of the system must be available to apply this technique to the optimal control problem. In this paper, to solve the SDRE without using a priori model of the system, a direct adaptive suboptimal algorithm is proposed. The algorithm, named state-dependent Riccati equation adaptive dynamic programming (SDRE-ADP), is based on a reinforcement learning approach which can be implemented in an online fashion. Like the SDRE technique, the proposed SDRE-ADP can locally asymptotically stabilize the closed-loop system provided that some conditions are satisfied. Application of the proposed algorithm to an autonomous unmanned underwater vehicle (AUV) and a numerical example shows that it can be effectively applied for nonlinear systems.
The path-following control design for an autonomous underwater vehicle (AUV) requires prior full or partial knowledge about the mathematical model defined through Newton’s second law based on a geometrical investigation. AUV dynamics are highly nonlinear and time-varying, facing unpredictable disturbances due to AUVs operating in deep, hazardous oceanic environments. Consequently, navigation guidance and control systems for AUVs must learn and adapt to the time-varying dynamics of the nonlinear fully coupled vehicle model in the presence of highly unstructured underwater operating conditions. Many control engineers focus on the application of robust model-free adaptive control techniques in AUV maneuvers. Hence, the main goal is to design a novel salp swarm optimization of super twisting algorithm-based secondorder sliding mode controller for the planar path-following control of an AUV through regulation of the heading angle parameter. The finite time for tracking error convergence in the horizontal plane is provided through the control structure architecture, particularly for lateral deviations from the desired path. The proposed control law is designed such that it steers a robotic vehicle to track a predefined planar path at a constant speed determined by an end-user, without any temporal specification. Finally, the efficacy and tracking accuracy are evaluated through comparative analysis based on simulation and experimental hardware-in-loop assessment without violating the input constraints. Moreover, the proposed control law can handle parametric uncertainties and unpredictable disturbances such as ocean currents, wind, and measurement noise.
In this paper, a control system is designed for a path following problem of a flight-type underactuated autonomous underwater vehicle (AUV) operating in a vertical plane. Initially, a guidance law is formulated based on a desired path tangential angle and vertical cross-track error. The guidance law generates the pitch angle reference for the pitching motion of the vehicle such that the cross-track converges to zero. A pitching control system is constructed based on the extended state observer-based controller (ESO) for the AUV to track the commanded pitch angle value with stern deflection angle as a control input. The resulting diving motion drives the AUV to reach and follow the reference path. For the purpose of evaluating the effectiveness of the control system design, numerical simulations are conducted.
This paper deals with a novel direct state-dependent Riccati equation (SDRE) controller designed for trajectory tracking of underactuated autonomous underwater vehicles (AUVs) in the presence of parameter perturbation. Despite the traditional SDRE regulator control, the proposed closed-loop SDRE controller design chiefly consists of two parts. First, by selecting a virtual reference point in front of the AUV system as the tracking output, the error variable control model in the earth-fixed reference frame is described. Second, the position errors are driven to the origin by introducing an integral model of first-order fed by the tracking error. The main advantage of the proposed control scheme is that the controller has a unified structure. Moreover, the algorithm is able to provide robustness with parameter perturbation because of its intrinsic robustness capability. Within the SDRE framework, the asymptotic stability of the closed-loop tracking system is also guaranteed. The robustness and effectiveness of the proposed methodology are verified by performing simulation experiments on an underactuated AUV.
The flapping-wing technology has emerged recently in the application of unmanned aerial robotics for autonomous flight, control, inspection, monitoring, and manipulation. Despite the advances in applications and outdoor manual flights (open-loop control), closed-loop control is yet to be investigated. This work presents a nonlinear optimal closed-loop control design via the state-dependent Riccati equation (SDRE) for a flapping-wing flying robot (FWFR). Considering that the dynamic modeling of the flapping-wing robot is complex, a proper model for the implementation of nonlinear control methods is demanded. This work proposes an alternative approach to deliver an equivalent dynamic for the translation of the system and a simplified model for orientation, to find equivalent dynamics for the whole system. The objective is to see the effect of flapping (periodic oscillation) on behavior through a simple model in simulation. Then the SDRE controller is applied to the derived model and implemented in simulations and experiments. The robot bird is a 1.6 m wingspan flapping-wing system (six-degree-of-freedom robot) with four actuators, three in the tail, and one as the flapping input. The underactuated system has been controlled successfully in position and orientation. The control loop is closed by the motion capture system in the indoor test bed where the experiments of flight have been successfully done.
To improve the anti-disturbance stability of the autonomous underwater vehicles (AUVs) under bounded disturbances in amplitude, we develop a robust controller based on the estimated signals generated by the filter. The AUV studied has the characteristics of time-varying delay, under-actuated, and switched linear parameter varying (LPV) dynamics. Both the filter and the control strategies, we proposed are based on the robust performance criterion, which is suitable for the amplitude-bounded disturbances in the ocean environment. In the filter and controller design, the corresponding Lyapunov–Krasovskii functional is established to verify the stability of the systems. As there exist couplings between the designed functional and the system parameter matrices, slack matrices are constructed for decouplings after validating the stability of the under-actuated AUV filtering error system and closed-loop control system. The filter and the controller are obtained in the form of parameter linear matrix inequalities (PLMIs), whose solution is infinite-dimensional matrix inequalities. The approximate basis function and gridding technique are applied to transform the filter and the controller into that of finite dimensional LMIs. The simulation has verified the effectiveness of the robust filter and anti-disturbance depth robust controller.
In this paper, a novel dynamic surface control is developed by employing the nonlinear continuous predictive approach. The tracking error in the last subsystem is predicted by a functional expansion. To minimize the difference between the predicted and desired response, a control law for the continuous-time system is developed. The stability of the individual controller for the switching phases is discussed. Furthermore, the tracking error is proven to converge to the origin. The continuous predictive control approach based on dynamic surface control is applied to the tracking control of marine vehicles. The actual control in the corresponding subsystems is proposed based on the optimal cost function. By adjusting the weight matrix contained in the optimization performance index, control input in the initial stage can be guaranteed to meet the propelling capability. The proposed method is further applied to the marine vessel in the presence of unknown ocean current disturbance. Simulation studies demonstrate that the proposed control structures show outstanding performance and feasibility.
This paper presents a study of depth tracking controller design for a hybrid AUV in the presence of model uncertainty and propeller torque's effect. Firstly, the six degrees of freedom (6-DOF) nonlinear equations of motion, as well as the operating mechanisms and specific characteristics of the hybrid AUV, are described. Subsequently, the model for depth-plane is extracted by decoupling and linearizing the 6-DOF AUV model. Furthermore, a nonlinear disturbance observer (NDO) is constructed to deal with the linearization errors and uncertain components in the depth-plane model. A depth tracking controller is then designed based on the backstepping technique to guarantee the tracking error converges to an arbitrarily small neighborhood of zero. Besides, the robust stability of the proposed controller concerning the propeller torque's effect and the model uncertainty is analyzed. To ensure the objectivity and feasibility of the proposed method, the depth controller is applied to the 6-DOF model of AUV so that it maintains the coupling between roll, yaw, and pitch motion. Finally, the numerical simulation is carried out via MATLAB/SIMULINK to verify the controller's effectiveness, feasibility, and stability.
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شبکه کاهش می یابد. همگرایی تخمین حاصل از رویتگر به حالت سیستم از قالب یک قضیه بررسی و کارایی روش پیشنهادی از طریق دو مثال
)نوسان ساز وندرپل و سیستم سه تانک( ارزیابی شده است
A new adaptive robust control scheme combining the disturbance-observer-based control (DOBC) with fuzzy adapted S-Surface control is proposed for trajectory tracking control of autonomous underwater vehicle. The main contribution of the proposed method is that control configuration does not require the bounds of uncertainty of the vehicle to be known and disturbances effect can be estimated and rejected. The proposed control law is mainly composed of three parts: a feed forward control along with disturbance estimator, S-Surface control and single input adaptive fuzzy proportional-integral (PI) compensator. The nominal feed forward controller specifies desired closed loop dynamics with extravagance from known preferred acceleration vector. Meanwhile, the disturbance observer and adaptive fuzzy PI control term to compensate the unknown effects that are disturbances and unmodeled dynamics. An additional term as S-Surface control assures fast convergence due to a nonlinear expression in to surface and also enhance stability of the underwater vehicle in oceanic environment. Moreover, the disturbance observer enhances the robustness performance of the adaptive fuzzy system for disturbances that cannot be modeled by fuzzy logic. The stability of closed loop controlled system is proven to be guaranteed according to Lyapunov theory. Finally, numerical simulation results illustrate the effectiveness and robustness of the proposed control method.
In this paper, using a novel event-triggered method, a robust H
∞
depth tracking controller is designed for a remotely operated underwater vehicle (ROV). It is assumed that the desired trajectory of the ROV is determined by an operator outside of the vehicle based on its needed depth and obstacles in its path. It is also assumed that a wireless network is used to connect the user with the ROV. To decrease the communication rate between the controller and the ROV, a novel nonlinear event-triggered H
∞
controller is designed. The effects of the disturbance on the system performance are also attenuated. Stability of the ROV under the designed event-triggered controller is proved through a theorem. Simulation results demonstrate that the error between the depth of the ROV and its time-varying desired trajectory converges to zero using the proposed eventtriggered H
∞
controller. It is also shown that the communication rate between the designed controller and the ROV is considerably reduced.
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 focuses on the development of a nonlinear H∞ control (NHC) algorithm for an autonomous underwater vehicle (AUV) in the vertical plane. A three-degree-of-freedom AUV depth model is developed in terms of a nonlinear affine form which is used to design the control algorithm. The depth is controlled using a backstepping technique which generates a desired pitch angle for the NHC algorithm. The nonlinear control is designed using the L2-gain analysis which is transformed into a Hamilton–Jacobi–Isaacs (HJI) inequality. Further, the HJI inequality is presented in terms of a nonlinear matrix inequality structure in order to find a solution for the NHC problem using the concept of convex optimization. Hence, we desire to test the convex property of the nonlinear system before the realization of the control algorithm. The robust behaviour of the NHC algorithm is realized by ensuring the performance of the proposed control algorithm in the face of model and parameter uncertainties. A comparison between the NHC algorithm and the state-dependent Riccati equation is made in order to show the efficacy of the developed control algorithm. Furthermore, an experimental study of the proposed control scheme has been pursued to analyse the effectiveness of the developed control algorithm.
This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles (AUVs) in the presence of wave disturbances. An approximate optimal tracking control (AOTC) approach is proposed. Firstly, a six-degrees-of-freedom (six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV’s system is represented by the exosystem. Then, the coupled two-point boundary value (TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit (REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.
A full envelope missile output feedback pitch autopilot is designed using the state-dependent Riccati equation (SDRE) approach presented in [1]. The particular SDRE design methodology chosen for this paper is referred to as SDRE HZ- The SDRE HI design structure is the same as that of linear HZ, except that the two Riccati equations are state-dependent. Hence, SDRE HZ design is a nonlinear extension of linear HZ design. A full envelope missile model using the same aerodynamics as an earlier work [5] is used to demonstrate the usefulness of the SDRE method for full envelope design. In this paper the SDRE Hz method is breifly discussed. The full envelope model is described and the state dependent coefficient (SDC) parameterization is presented. Finally the SDRE Hz design and design results are presented.
The theoretical control of low-speed maneuvering of small underwater vehicles in the dive plane using dorsal and caudal fin-based control surfaces is considered. The two dorsal fins are long and are actually mounted in the horizontal plane. The caudal fin is also horizontal and is akin to the fluke of a whale. Dorsal-like fins mounted on a flow aligned vehicle produce a normal force when they are cambered. Using such a device, depth control can be accomplished. A flapping foil device mounted at the end of the tailcone of the vehicle produces vehicle motion that is somewhat similar to the motion produced by the caudal fins of fish. The moment produced by the flapping foils is used here for pitch angle control. A continuous adaptive sliding mode control law is derived for depth control via the dorsal fins in the presence of surface waves. The flapping foils have periodic motion and they can produce only periodic forces. A discrete adaptive predictive control law is designed for varying the maximum tip excursion of the foils in each cycle for the pitch angle control and for the attenuation of disturbance caused by waves. Strouhal number of the foils is the key control variable. The derivation of control laws requires only imprecise knowledge of the hydrodynamic parameters and large uncertainty in system parameters is allowed. In the closed-loop system, depth trajectory tracking and pitch angle control are accomplished using caudal and dorsal fin-based control surfaces in the presence of system parameter uncertainty and surface waves. A control law for the trajectory control of depth and regulation of the pitch angle is also presented, which uses only the dorsal fins and simulation results are presented to show the controller performance.
This paper treats the question of control of a biorobotic autonomous undersea vehicle (BAUV) in the yaw plane using a biomimetic mechanism resembling the pectoral fins of fish. These fins are assumed to undergo a combined sway-yaw motion and the bias angle is treated as a control input, which is varied in time to accomplish the maneuver in the yaw-plane. The forces and moments produced by the flapping foil are parametrized using computational fluid dynamics. A finite-difference-based, Cartesian grid immersed bound-ary solver is used to simulate flow past the flapping foils. The periodic forces and mo-ments are expanded as a Fourier series and a discrete-time model of the BAUV is developed for the purpose of control. An optimal control system for the set point control of the yaw angle and an inverse control law for the tracking of time-varying yaw angle trajectories are designed. Simulation results show that in the closed-loop system, the yaw angle follows commanded sinusoidal trajectories and the segments of the intersample yaw trajectory remain close to the discrete-time reference trajectory. It is also found that the fins suitably located near the center of mass of the vehicle provide better maneuverability.
This paper presents an adaptive nonlinear controller for diving control of an autonomous underwater vehicle (AUV). So far, diving dynamics of an AUV has often been derived under various assumptions on the motion of the vehicle. Typically, the pitch angle of AUV has been assumed to be small in the diving plane. However, these kinds of assumptions may induce large modeling errors and further may cause severe problems in many practical applications. In this paper, through a certain simple modification, we break the above restricting condition on the vehicle's pitch angle in diving motion so that the vehicle could take free pitch motion. Proposed adaptive nonlinear controller is designed by using a traditional backstepping method. Finally, certain numerical studies are presented to illustrate the effectiveness of proposed control scheme, and some practical features of the control law are also discussed.
In this paper, a controller design method for underwater vehicles is presented, which is based on re-configuration of a sliding-mode controller in case of disturbances caused by shallow water conditions. The disturbance distribution information can be obtained and used to update the corrective gain vector of the sliding-mode controller. This increases the robustness of the controller and, hence, keeps the system performance within acceptable limits. Proposed method is validated with simulations on a submarine model.
The emergence of biorobotic autonomous undersea vehicle (AUV) as a focus for discipline-integrated research in the context of underwater propulsion and maneuvering is considered within the confines of the Biorobotics Program in the Office of Naval Research. The significant advances in three disciplines, namely the biology-inspired high-lift unsteady hydrodynamics, artificial muscle technology and neuroscience-based control, are discussed in an effort to integrate them into viable products. The understanding of the mechanisms of delayed stall, molecular design of artificial muscles and the neural approaches to the actuation of control surfaces is reviewed in the context of devices based on the pectoral fins of fish, while remaining focused on their integrated implementation in biorobotic AUVs. A mechanistic understanding of the balance between cruising and maneuvering in swimming animals and undersea vehicles is given. All aquatic platforms, in both nature and engineering, except during short duration burst speeds that are observed in a few species, appear to lie within the condition where their natural period of oscillation equals the time taken by them to travel the distance of their own lengths. Progress in the development of small underwater experimental biorobotic vehicles is considered where the three aforementioned disciplines are integrated into one novel maneuvering device or propulsor. The potential in maneuvering and silencing is discussed.
A neural network based control system “Self-Organizing
Neural-Net-Controller System: SONCS” has been developed as an
adaptive control system for Autonomous Underwater Vehicles (AUVs). In
this paper, an on-line adaptation method “Imaginary
Training” is proposed to improve the time-consuming adaptation
process of the original SONCS. The Imaginary Training can be realized by
a parallel structure which enables the SONCS to adjust the controller
network independently of actual operation of the controlled object. The
SONCS is divided into two separate parts: the Real-World Part where the
controlled object is operated according to the objective, and the
Imaginary-World Part where the Imaginary Training is carried out. In
order to adjust the controller network by the Imaginary Training, it is
necessary to introduce a forward model network which can generate
simulated state variables without involving actual data. A neural
network “Identification Network” which has a specific
structure to simulate the behavior of dynamical systems is proposed as
the forward model network. The effectiveness of the Imaginary Training
is demonstrated by applying to the heading keeping control of an AUV
“Twin-Burger”. It is shown that the SONCS adjusts the
controller network-through on-line processes in parallel with the actual
operation
A recent extension of sliding model control is shown to handle the problems in underwater-vehicle control-system design associated with nonlinear dynamics, uncertain models, and the presence of disturbances that are difficult to measure or estimate. The method deals directly with nonlinearities, is highly robust to imprecise models, explicitly accounts for the presence of high-frequency unmodeled dynamics, and produces designs that are easy to understand. Using a nonlinear vehicle simulation, the relationship between model uncertainty and performance is examined. The results show that adequate controllers can be designed using simple nonlinear models, but that performance improves as model uncertainty is decreased. The improvements can be predicted quantitatively.
A nonlinear control problem has been posed by Bupp et al.1 to provide a benchmark for evaluating various nonlinear control design techniques. In this paper, the capabilities of the state-dependent Riccati equation (SDRE) technique are illustrated in producing two control designs for the benchmark problem. The SDRE technique represents a systematic way of designing nonlinear regulators. The design procedure consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = - R-1(x)BT(x)P(x)x, where P(x) is the solution of the SDRE. Analysis of the first design shows that in the absence of disturbances and uncertainties, the SDRE nonlinear feedback solution compares very favorably to the optimal open-loop solution of the posed nonlinear regulator problem, the latter being obtained via numerical optimization. It is also shown via simulation that the closed-loop system has stability robustness against parametric variations and attenuates sinusoidal disturbances. In the second design it is demonstrated how a hard bound can be imposed on the control magnitude to avoid actuator saturation.
Preface 1. Linear output regulation 2. Introduction to nonlinear systems 3. Nonlinear output regulation 4. Approximation method for the nonlinear output regulation 5. Nonlinear robust output regulation 6. From output regulation to stabilization 7. Global robust output regulation 8. Output regulation for singular nonlinear systems 9. Output regulation for discrete-time nonlinear systems Notes and references Appendices Bibliography Index.
A nonlinear control problem has been posed by Bupp et al. to provide a benchmark for evaluating various nonlinear control design techniques. In this paper, the capabilities of the state-dependent Riccati equation (SDRE) technique are illustrated in producing two control designs for the benchmark problem. The SDRE technique represents a systematic way of designing nonlinear regulators. The design procedure consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u=−R-1(x)BT(x)P(x)x, where P(x) is the solution of the SDRE. Analysis of the first design shows that in the absence of disturbances and uncertainties, the SDRE nonlinear feedback solution compares very favorably to the optimal open-loop solution of the posed nonlinear regulator problem, the latter being obtained via numerical optimization. It is also shown via simulation that the closed-loop system has stability robustness against parametric variations and attenuates sinusoidal disturbances. In the second design it is demonstrated how a hard bound can be imposed on the control magnitude to avoid actuator saturation. © 1998 John Wiley & Sons, Ltd.
A comprehensive and extensive study of the latest research in control systems for marine vehicles. Demonstrates how the implementation of mathematical models and modern control theory can reduce fuel consumption and improve reliability and performance. Coverage includes ocean vehicle modeling, environmental disturbances, the dynamics and stability of ships, sensor and navigation systems. Numerous examples and exercises facilitate understanding.
A full-envelope, hybrid bank-to-turn (BTT)/skid-to-turn (STT) autopilot design for an air-breathing air-to-air missile is carried out using the state-dependent Riccati equation (SDRE) technique of nonlinear control. Hybrid BTT/STT autopilot command logic is used to convert the guidance law's commanded acceleration to angle of attack, side-slip, and bank angle reference commands for the autopilot. In the midcourse and terminal phases of flight, BTT control is employed to prevent engine flameout. In the endgame, STT control is employed to increase response time. As the missile approaches the endgame phase and passes a preset time-to-go threshold, STT commands are ramped into the BTT commands over a preselected time interval to attenuate transient responses. During this interval, the missile is flying hybrid BTT/STT. An SDRE nonlinear outer-loop controller converts the angle-of-attack, sideslip, and bank angle commands to body rates commands for the inner loop. An inner-loop SDRE nonlinear controller converts the body rate commands to fin commands. Hard bounds on the fin deflections are embedded within the inner-loop controller dynamics ensuring that the autopilot only commands deflections that are achievable. The nonlinear design is evaluated using a detailed six-degrees-of-freedom simulation.
This paper presents the design of an adaptive input–output feedback linearizing dorsal fin control system for the yaw plane control of low-speed bio-robotic autonomous underwater vehicles (BAUVs). The control forces are generated by cambering two dorsal fins mounted in the vertical plane on either side of the vehicle. The BAUV model includes nonlinear hydrodynamics, and it is assumed that its hydrodynamic coefficients as well as the physical parameters are not known. For the purpose of design, a linear combination of the yaw angle tracking error and its derivative and integral is chosen as the controlled output variable. An adaptive input–output feedback linearizing control law is derived for the trajectory control of the yaw angle. Unlike indirect adaptive control, here the controller gains are directly tuned. The stability of the zero dynamics is examined. Simulation results are presented for tracking exponential and sinusoidal yaw angle trajectories and for turning maneuvers, and it is shown that the adaptive control system accomplishes precise yaw angle control of the BAUV using dorsal fins in spite of the nonlinearity and large uncertainties in the system parameters.
This paper proposes a nonlinear robust adaptive control strategy to force a six degrees of freedom underactuated underwater vehicle with only four actuators to follow a predefined path at a desired speed despite of the presence of environmental disturbances and vehicle’s unknown physical parameters. The proposed controller is designed using Lyapunov’s direct method, the popular backstepping and parameter projection techniques. The closed loop path following errors can be made arbitrarily small. Interestingly, it is shown that our developed control strategy is easily extendible to situations of practical importance such as parking and point-to-point navigation. Numerical simulations are provided to illustrate the effectiveness of the proposed methodology.
In this paper, adaptive control of low speed bio-robotic autonomous underwater vehicles (BAUVs) in the dive plane using dorsal fins is considered. It is assumed that the model parameters are completely unknown and only the depth of the vehicle is measured for feedback. Two dorsal fins are mounted in the horizontal plane on either side of the BAUV. The normal force produced by the fins, when cambered, is used for the maneuvering. The BAUV model considered here is non-minimum phase. An indirect adaptive control system is designed for the depth control using the dorsal fins. The control system consists of a gradient based identifier for online parameter estimation, an observer for state estimation, and an optimal controller. Simulation results are presented which show that the adaptive control system accomplishes precise depth control of the BAUV using dorsal fins in spite of large uncertainties in the system parameters.
This work demonstrates the feasibility of applying a sliding mode fuzzy controller to motion control and line of sight guidance of an autonomous underwater vehicle. The design method of the sliding mode fuzzy controller offers a systematical means of constructing a set of shrinking-span and dilating-span membership functions for the controller. Stability and robustness of the control system are guaranteed by properly selecting the shrinking and dilating factors of the fuzzy membership functions. Control parameters selected for a testbed vehicle, AUV-HM1, are evaluated through tank and field experiments. Experimental results indicate the effectiveness of the proposed controller in dealing with model uncertainties, non-linearities of the vehicle dynamics, and environmental disturbances caused by ocean currents and waves.
The self-organizing neural-net-controller system (SONCS) has been
developed as an adaptive control system for autonomous underwater
vehicles (AUVs). In this paper, a quick adaptation method of the
controller, called imaginary training (IT), is proposed to improve the
time-consuming adaptation process of the original SONCS. IT can be
realized by a new parallel structure which enables the SONCS to adjust
the controller network independently of the actual operation of the
controlled object. In the proposed structure, the SONCS is divided into
two separate parts: the real-world part, where the controlled object is
operated according to the objective of the controller, and the imaginary
world part, where the IT is carried out. A forward model network which
can generate the simulated state variables without measuring actual data
is introduced. A neural network, called “Identification
Network”, which has a specific structure for simulation of
dynamical systems is proposed as the forward model network in the
imaginary-world part. The effectiveness of the IT is demonstrated by
applying it to the heading control of an AUV called “The
Twin-Burger”
Biologically inspired maneuvering of autonomous undersea vehicles (AUVs) in the dive plane using pectoral-like oscillating fins is considered. Computational fluid dynamics are used to parameterize the forces generated by a mechanical flapping foil, which attempts to mimic the pectoral fin of a fish. Since the oscillating fins produce periodic force and moment of a variety of wave shapes, the essential characteristics of these signals are captured in their Fourier expansions. Maneuvering of the biorobotic AUV in the dive plane is accomplished by periodically altering the bias angle of the oscillating fin. Based on a discrete-time AUV model, an inverse control system for the dive-plane control is derived. It is shown that, in the closed-loop system, the inverse control system accomplishes accurate tracking of the prescribed time-varying depth trajectories and the segments of the intersample depth trajectory remain close to the discrete-time reference trajectory. The results show that the fins located away from the center of mass toward the nose of the vehicle provide better maneuverability.
underwater vehicles present difficult control-system design problems due to their nonlinear dynamics, uncertain models, and the presence of disturbances that are difficult to measure or estimate. In this paper, a recent extension of sliding mode control is shown to handle these problems effectively. The method deals directly with nonlinearities, is highly robust to imprecise models, explicitly accounts for the presence of high-frequency unmodeled dynamics, and produces designs that are easy to understand. Using a nonlinear vehicle simulation, the relationship between model uncertainty and performance is examined. The results show that adequate controllers can be designed using simple nonlinear models, but that performance improves as model uncertainty is decreased and the improvements can be predicted quantitatively.
A position and attitude tracking control law for autonomous
underwater vehicles (AUV's) in 6 degrees of freedom (DOF) is derived.
The 4-parameter unit quaternion (Euler parameters) is used in a
singularity-free representation of attitude. Global convergence of the
closed-loop system is proven. In addition, several 3-parameter
representations in terms of the Euler parameters are discussed with
application to the same control law. These schemes contain
singularities, and only local convergence can therefore be proven. The
proposed control scheme is simulated with Euler parameters and Euler
angles
The flight control system of an autonomous underwater vehicle
(AUV) developed at the Norwegian Defence Research Establishment (NDRE)
is presented. A mathematical model of the vehicle is derived and
discussed. The system is separated into lightly interacting subsystems,
and three autopilots are designed for steering, diving, and speed
control. The design of the separate controllers is based on PID
techniques. Results from extensive sea testing show robust performance
and stability for the autopilot
A six-degree-of-freedom model for the maneuvering of an underwater
vehicle is used and a sliding-mode autopilot is designed for the
combined steering, diving, and speed control functions. In flight
control applications of this kind, difficulties arise because the system
to be controlled is highly nonlinear and coupled, and there is a good
deal of parameter uncertainty and variation with operational conditions.
The development of variable-structure control in the form of sliding
modes has been shown to provide robustness that is expected to be quite
remarkable for AUV autopilot design. It is shown that a multivariable
sliding-mode autopilot based on state feedback, designed assuming
decoupled modeling, is quite satisfactory for the combined speed,
steering, and diving response of a slow AUV. The influence of speed,
modeling nonlinearity, uncertainty, and disturbances, can be effectively
compensated, even for complex maneuvering. Waypoint acquisition based on
line-of-sight guidance is used to achieve path tracking
With the increased utilization of remotely operated vehicles in
subsea applications, the development of autonomous vehicles becomes
highly desirable to enhance operator efficiency. The dynamic model of an
untethered remotely operated underwater vehicle is presented, and an
adaptive control strategy for such vehicles is described. The robustness
of the control system with respect to nonlinear dynamic behavior and
parameter uncertainties is investigated by computer simulation. The
results show that the use of the adaptive control system can provide
high performance of the vehicle in the presence of unpredictable changes
in the dynamics of the vehicle and its environment
A position and attitude tracking control law for autonomous underwater vehicles (AUVs) in 6 degrees of freedom (DOF) is derived. The 4-parameter unit quaternion (Euler parameters) is used in a singularity-free representation of attitude. Global convergence of the closed-loop system is proven. In addition several 3-parameter representations in terms of the Euler parameters are discussed with application to the same control law. These schemes contain singularities and only local convergence can therefore be proven. The proposed control scheme is simulated with Euler parameters and Euler angles. 1 Introduction For rigid-bodies in 6 DOF the nonlinear dynamic equations of motion have a systematic structure which becomes apparent when applying vector notation. This is exploited in the control literature, particularly in the control of robot manipulators. A convergent nonlinear adaptive tracking control law exploiting the passivity properties of robot manipulators was derived in [19]. Late...
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