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Depth control of the INFANTE AUV using gain-scheduled reduced order output feedback
Abstract
The paper addresses the problem of autonomous underwater vehicle (AUV) control in the absence of full state information. An application is made to the control of a prototype AUV in the vertical plane. The methodology adopted for controller design is nonlinear gain-scheduling control, whereby a set of linear, dynamic, reduced order output feedback controllers are designed and scheduled on the vehicle's forward speed. The paper summarizes the controller design steps, describes a technique for its practical implementation, and presents experimental results obtained with the INFANTE AUV during tests at sea.
... Over the past three decades, substantial research efforts have been dedicated to AUV position stabilization and tracking control. These studies have taken into account the nonlinearities, uncertainties, underactuation, and underwater disturbances that AUVs encounter (Silvestre and Pascoal, 2007;Fossen, 2011;Li and Lee, 2005;Lapierre, 2009;Lou and Zhao, 2019;Mahapatra and Subudhi, 2017;Qi et al., 2022;Tran et al., 2021;Maurya et al., 2006Maurya et al., , 2022Zhang et al., 2022;Zhong et al., 2022;Zhou et al., 2022;Lakhekar et al., 2020;Mahapatra and Subudhi, 2021;Lei, 2020;Liu et al., 2022;Londhe et al., 2017;Lin et al., 2023). Among these motions, pitch and yaw control have ...
... Over the past three decades, substantial research efforts have been dedicated to AUV position stabilization and tracking control. These studies have taken into account the nonlinearities, uncertainties, underactuation, and underwater disturbances that AUVs encounter (Silvestre and Pascoal, 2007;Fossen, 2011;Li and Lee, 2005 . Among these motions, pitch and yaw control have garnered significant attention due to their pivotal roles in AUV diving and steering manoeuvres. ...
... Over the past three decades, substantial research efforts have been dedicated to AUV position stabilization and tracking control. These studies have taken into account the nonlinearities, uncertainties, underactuation, and underwater disturbances that AUVs encounter (Silvestre and Pascoal, 2007;Fossen, 2011;Li and Lee, 2005;Lapierre, 2009;Lou and Zhao, 2019;Mahapatra and Subudhi, 2017;Qi et al., 2022;Tran et al., 2021;Maurya et al., 2006Maurya et al., , 2022Zhang et al., 2022;Zhong et al., 2022;Zhou et al., 2022;Lakhekar et al., 2020;Mahapatra and Subudhi, 2021;Lei, 2020;Liu et al., 2022;Londhe et al., 2017;Lin et al., 2023). Among these motions, pitch and yaw control have garnered significant attention due to their pivotal roles in AUV diving and steering manoeuvres. ...
... An alternative is the work of Silvestre and Pascoal [26], where they design linear controllers for different forward velocities and thereafter use a gain scheduling controller to integrate them. Other works focused on using the advantages of gain scheduling controllers, but applying a fuzzy framework to manage them (e.g., [27,28]). ...
... In situations such as navigation in harbors or canals, the variation of the forward velocity becomes relevant, and so, it is important to be able to vary the controller's working point to adjust the paths to the desired ones. To solve this problem, Silvestre and Pascoal [26] use a set of linear controllers adjusted for different forward velocities and then use a gain scheduling controller to integrate them. Here, the same methodology has been followed, but a fuzzy controller has been applied to integrate the different linear controllers. ...
... However, the decision to change between one controller to the other one is not trivial. To solve this problem, Silvestre and Pascoal [26] use a set of linear controllers adjusted for different forward velocities and then use a gain scheduling controller to integrate them. Here, the same methodology has been followed, but innovatively applying a fuzzy controller, to integrate the different linear controllers. ...
Autonomous Underwater Vehicles (AUV) are proving to be a promising platform design for multidisciplinary autonomous operability with a wide range of applications in marine ecology and geoscience. Here, two novel contributions towards increasing the autonomous navigation capability of a new AUV prototype (the Guanay II) as a mix between a propelled vehicle and a glider are presented. Firstly, a vectorial propulsion system has been designed to provide full vehicle maneuverability in both horizontal and vertical planes. Furthermore, two controllers have been designed, based on fuzzy controls, to provide the vehicle with autonomous navigation capabilities. Due to the decoupled system propriety, the controllers in the horizontal plane have been designed separately from the vertical plane. This class of non-linear controllers has been used to interpret linguistic laws into different zones of functionality. This method provided good performance, used as interpolation between different rules or linear controls. Both improvements have been validated through simulations and field tests, displaying good performance results. Finally, the conclusion of this work is that the Guanay II AUV has a solid controller to perform autonomous navigation and carry out vertical immersions.
... They are nonlinear systems, and due to the uncertainties and disturbances, their good tracking performance always is an important control task. In the past years, several control techniques have been developed for the underwater vehicles [1][2][3][4][5][6][7][8][9][10][11][12][13]. ...
... (4) By the sensorless control of the actuator thrusters, it seems that the implementation of the proposed method is simpler and production cost is less. (5) In order to improve the approximation of uncertainties by adaptive fuzzy algorithm, and also to reduce the number of fuzzy sets and rules, in this paper we employ a CAF control method that uses the modified modeling error signals instead of the state variables as input in the CAF. Note that the basic idea of the CAF method for a good estimation of uncertainties is introduced by authors in [14]. ...
... In Sect. 5, simulation examples are provided to demonstrate the performance and feasibility of the proposed scheme. Sect. ...
In this paper, based on a proposed MIMO hybrid dynamical system of underwater vehicle and its actuators, a robust composite adaptive fuzzy controller is presented. The proposed method employs voltage control effort, which is more efficient than the torque control strategy. Also it is very simple, efficient and robust. Based on adaptive fuzzy method and the prediction error between the system states and the serial–parallel estimation model, a composite adaptive fuzzy law that uses the modeling error as input is constructed to adaptively compensate the unknown uncertainties and disturbances of the system. In addition, the proposed scheme is able to estimate the lumped uncertainties with large amplitude and high frequency. Stability of the proposed method is shown based on Lyapunov approach. The proposed control scheme is not limited only to control of the underwater vehicles, but can be applied for a class of nonlinear MIMO systems with square and non-square control gains.
... The AUV model is a 6-degree of freedom nonlinear structure as shown in Fig. 1. The parameters of the model in the Dive Plane is considered from [13]. Thus, the state and disturbance vector are considered as ...
... is the weight of the AUV, is the buoyancy and ( * ) are the hydrodynamic coefficients as reported in [13]. ...
... By assigning = 1 in (10a), the first order nonlinear ∞ control law is derived. [2] is realized by assigning = 2. From (9), a second order HJI equation can be derived as (13) and the unknown coefficients , = 1, 2, ⋅ ⋅ ⋅ 20, can also be evaluated by solving a set of 20 equations obtained by equating the equal power terms in (13). ...
A nonlinear H∞ measurement feedback control algorithm is exploited for the control of Autonomous Underwater Vehicle in the Dive Plane. Here, the control algorithm is designed with the combination of a nonlinear H∞ state feedback law along with a nonlinear observer. The control problem of measurement feedback is formulated in terms of two Hamilton-Jacobi-Isaacs inequality by using the dissipative theory. The solution of the control law is obtained by solving both the inequalities. The controller is intended to track different desired depth values by attenuating the external disturbance. The simulation results are realized using MATLAB/Simulink which suggest that the controller is effective in tracking by ensuring the internal stability and robustness.
... The modelling of AUV is reported in Fossen (1994), Silvestre (2000). In this, the mathematical model of AUV is considered from Silvestre and Pascoal (2007). The usage of Taylor's series based robust control technique on AUV control is a unique feature, which has not been addressed in the AUV literature to date. ...
... where C ( * ) are the hydrodynamic coefficients as reported in Silvestre and Pascoal (2007) and C 1 and C 2 are the coefficients of disturbances in heave and pitch motion respectively. The penalty and measurement vectors are presented as ...
... The reference path considered here is a sinusoidal path as shown in Fig. 3(a) and is represented as z d = 10 sin(0.01t). The simulation is being carried out with a constant forward speed and the parameters of AUV is considered from Silvestre and Pascoal (2007). The performance of the nonlinear H ∞ controller is better in disturbance attenuation and tracking of the desired depth that is observed from Fig. 3. ...
In this paper, a nonlinear path following control algorithm has been illustrated for Autonomous Underwater Vehicle (AUV) in the Vertical Plane. The nonlinear H∞ state feedback control technique has been adopted to track the desired path in the dive plane. The design of the control algorithm is obtained by solving a Hamilton-Jacobi-Isaacs inequality with a Taylor's series approach for the control of AUV. The developed algorithm provides a significant performance in robustness and internal stability by attenuating the disturbance. The performance of the developed control scheme has been reported by carrying out the simulation using MATLAB/Simulink environment.
... Their ability to regulate their depth is often imperative to their missions. There are many methods for producing the vertical forces required for regulating depth, including vertical/tunnel thrusters [2]- [4], control surfaces [5], [6], and variable buoyancy systems (VBSs) [7] that can use external bladders [8], [9], internal ballast tanks [10], [11], or internal bladders [12]. ...
... However, the majority of this research appears to be focused on vehicles with either vertical thrusters or forward thrusters combined with control surfaces (requiring control strategies similar to aerial vehicles). These controllers range from classical techniques, such as PID controllers [27], [28], to linear techniques, such as gain-scheduled output feedback [6], to nonlinear controllers, such as sliding-mode controllers [29], [30], adaptive controllers [3], [5] and RISE controllers [2]. In contrast, the controllers developed for VBSs seem to focus primarily on classical techniques such as bang-bang [31], PID, or modified PID controllers, e.g., a bang-zero-bang controller combined with a PID controller [19]. ...
This article presents a variable buoyancy system that uses cephalopod-inspired, fiber-reinforced elastomer membranes as bladders to enable model-based depth and pitch control of an autonomous underwater vehicle. The fiber reinforcement allows for a single measurement of each membrane to fully define the geometry of the membrane, regardless of the membrane’s orientation or level of inflation. This allows for precise control of each bladder’s enclosed water mass and center of mass by adjusting the differential pressure between the inside of the bladder and the vehicle’s cabin using water from the environment as the working fluid. Positioning bladders at the fore and aft of the vehicle enables control of both the vehicle’s density and center of mass while minimizing center of mass disturbances due to sloshing in and gravitational loads on the membranes. A nonlinear, adaptive, backstepping, trajectory-tracking controller is presented and proven to be asymptotically stable with Lyapunov stability analysis. The advantages of the proposed variable buoyancy system and controller are demonstrated through simulation and validated with 2 degree of freedom depth and pitch step and trajectory-tracking experiments in a large water tank. We evaluate the performance of the bladders and controller on the CephaloBot, an autonomous underwater vehicle designed and built by our group.
... Various dynamical models and control approaches have been developed for these systems, which are mainly employed for thrust control effort schemes. For example, in [3][4][5][6][7][8][9][10], some thrust control approaches are applied. Also, in some works, depth control of underwaters is applied [10][11][12][13][14][15]. ...
In this paper, a control method is presented for the six degrees of freedom (6-DoF) underwater systems. First, the proposed thruster voltage mapping control strategy of underwaters is proposed by combining the general model of the 6-DoF motion and the thruster dynamical model. Indeed, a novel control strategy is designed to be used for the 6-DoF underwater vehicle with various numbers of thrusters. The suggested technique is computationally simple by using only one control loop, and it overcomes problems arising from conventional methods. Second, an observer-based robust adaptive fuzzy estimator is presented to compensate for disturbance and uncertainties.
... While control strategies for underwater vehicles range from direct position tracking, see Silvestre and Pascoal (2007), to multi-layer path-following methodologies (Rober, Cichella, Ezequiel Martin, Kim and Carrica (2021)), each strategy employs a vehicle autopilot which is tasked with controlling vehicle dynamics to track a desired reference. Some of the early work on autopilot design for underwater vehicles used sliding-mode control methods to confine the vehicle's behavior to a set of sliding surfaces with desired properties (see, for example, Yoerger and Slotine (1985); Cristi, Papoulias and Healey (1990); Healey and Lienard (1993)). ...
This paper addresses the problem of guidance and control of underwater vehicles. A multi-level control strategy is used to determine (1) outer-loop path-following commands and (2) inner-loop actuation commands. Specifically, a line-of-sight path-following algorithm is used to guide the vehicle along a three-dimensional path, and an adaptive control algorithm is used to determine the low-level rudder commands to accomplish path following. The performance bounds of these outer- and inner-loop control algorithms are presented. Numerical results obtained using a physics-based Simulink model are used to aid in visualization of the control algorithm's performance.
... Among depth control strategies, the approaches based on Takagi-Sugeno models [5], have been largely utilized [6,7], either parallel distributed compensation (PDC) or static output feedback (SOF) controllers. In any case, T-S-based approaches have many advantages; especially have facilitated maneuvering in control by the implementation of dedicated techniques for linear systems. ...
This paper investigates the depth control of unmanned underwater vehicle (UUV) in the presence of external disturbances, time delay, and actuator saturation. Firstly, a Takagi–Sugeno model is elaborated based on the speed variation. Then, using the polyquadratic representation with Lyapunov-Krasovskii function, an H∞ criteria is applied to design a new LMI based stabilization to calculate PDC controller gains taking into consideration the input limitation. Finally, simulation results demonstrate the superiority of the proposed approach.
... We also point to a recent development within numerical solvers for DREs where the state space system is reduced prior to performing the time-integration of the differential Riccati equation [29,31]. These methods are also related to the concept of reduced controllers [52] or reduced order feedback [45]. These methods could be modified to perform an a-priori projection to then be combined with our methodology and we view them as complementary rather than competitors. ...
... At present, the research works of depth control for underwater vessels are mainly focused on AUVs and remotely operated vehicles (ROVs). For example, [15] use gainscheduled reduced order output feedback and [16] use reinforcement learning to achieve the depth control of AUVs; [17] use fuzzy PID and [18] use neural network predictive control to provide solutions for the depth control of ROVs. The optimized finite time stabilized attitude control approach with fault-tolerant capability can be also adapted to ROVs and other under water vessels [19], [20]. ...
The submarine drifter is a novel Lagrangian-based observation platform to explore the ocean, but its precise and rapid depth control system design is still an open issue. The major challenge would be the complex hybrid actuation system, which contains anisotropic characteristics and switching issues. In this paper, we proposed an modified complementary constrained model predictive control (MCCMPC) scheme to meet the metrics. The scheme reformulates complex drifter and hybrid actuation system dynamics into a solvable system with complementary constraints. The nonlinear component inside the system is approximated by applying a sgn-sigmoid approximation function for the sake of linearization and computation. Then the customized online optimizer predicts the system dynamics with complementary constraints and computes the optimal control outputs in the finite horizon in an iterative loop. The validation results prove that the proposed controller can effectively control the submarine drifter to achieve the desired depth and the key metrics are 10x, 4x, and 2x better than conventional PID control, disturbance observerbased control, and conventional MPC methods, respectively.
... y k = h (x k ; k) + v k (12) w 19 |Uwo O}iU R} wv |=y|r=wD v 2 R m w 2 R p ' w 2 R n u; QO xm |O}Q@}y |xDi=}xaUwD utr=m QDr}i s=o "CU= |r}tmD Cr=L Q=OQ@ x 2 R n+p u}vJ 'T = t k t k 1 CN=wvm} |Q=OQ@xvwtv u=tR R= xO=iDU= =@ 'q=@ sDU}U |= Q@ [31] %OwW|t u=}@ %|v=tR |v=UQRwQ x@ x k+1 ( ) = f (x k (+) ; k) (13) _ P = A P A T + LQL T (14) %|Q}oxR=Ov= |v=UQRwQ x@ ; L = @f (x ; k) @w ...
In the present study, a novel method has been introduced to estimate the hydrodynamic coefficients of an axisymmetric submersible prolate spheroid. In this heuristic procedure which is based on combination of the nonlinear Hybrid Extended Kalman Filter (HEKF) observer and Computational Fluid Dynamics (CFD), all of the hydrodynamic derivatives of a prolate spheroid in horizontal plane are estimated to simulate the Three Degrees of Freedom (3DoF) equations of motion. For this purpose, first, a CFD-based numerical model has been developed for an axisymmetric prolate spheroid by the commercial code ANSYS CFX software using the remeshing algorithm in dynamic mesh method. In this algorithm, the grid around objects deform locally using the Arbitrary Lagrangian-Eulerian (ALE) form of the governing fluid equations. When this deformation reduces the mesh resolution, significantly, the grid is re-meshes and improved. By performing the corresponding calculations along with the simulation, some hydrodynamic derivatives were obtained. Then, utilizing the hybrid kalman filter simulation code based on the parameter identification, other unknown derivatives was estimated in the MATLAB software environment by applying the equations of motion governing an ellipsoidal body shape. It should be noted that, for deriving the remaining hydrodynamic coefficients of the mentioned prolate spheroid using HEKF, positions and velocities of the object in each time step is needed. So, the dynamic motion of the vehicle in the fluid is simulated using the transient tool of the ANSYS CFX software while benefiting from the remeshing algorithm. Furthermore, the hybrid form of the Extended Kalman Filter (EKF) is chosen as the equations governing the 3DoF motion of the ellipsoid is continuous and the measurements are discrete. Results obtained from the proposed method indicate a good agreement for estimated added mass derivatives in comparison with the available analytical ones. The following study is an effort made to introduce an innovative strategy to investigate the hydrodynamic coefficients of submersible platforms like submarines, torpedoes and AUVs.
... An LQR control scheme is being explored in this paper. Nonlinear control theories are also used to control AUVs, mostly relying on lyapunov's stability criterion [20][21][22]. Other famous control algorithms are also implemented but are less popular in AUV control applications such as fuzzy controllers [23] [24]. ...
... For the reason of its sim- plicity, ease of implementation in practice, the static output feedback (SOF) controller provides a great solution in this sit- uation. The SOF control strategy has been used by many authors for different control applications, such as Benton and Smith (2005), Silvestre and Pascoal (2005) and Subudhi et al. (2013). Particularly, in Chang et al. (2015), the H N SOF con- trol design is investigated for linear systems, and in Hu et al. (2016) and Wang G et al. (2017) for nonlinear systems. ...
This paper presents an H ∞ static output-feedback control of electrical power steering (EPS) subject to actuator saturation. It deals with different practical problems in designing control of EPS systems, such as unavailability for measurement of the sideslip angle, friction effect, disturbances and the assist motor input current optimization. In order to guarantee good and stable driving, the nonlinear model of the EPS combined with bicycle model of electrical vehicles is used. Firstly, a new Takagi-Sugeno model is established, then using a fuzzy Lyapunov function, an H ∞ static output-feedback is designed in terms of linear matrix inequalities. Finally, the proposed control schemes are applied to an EPS system. Simulation results and comparison with previous works show the effectiveness of the proposed control methods.
... As explained above, this changing of parameters is attractive mainly because our system works in a highly nonlinear environment that needs a different strategy at each situation of wind. So, following the success of gainscheduling control strategies in other types of mobile robots [11][12][13][14][25][26][27][28][29] , we propose to use such approach in this work for the development of the sailboat control system. The proposed method uses experimental data obtained in simulation to decide which controller parameters satisfy specific constraints. ...
The development of a navigation system for autonomous robotic sailing is a particularly challenging task since the sailboat robot uses unpredictable wind forces for its propulsion besides working in a highly nonlinear and harsh environment, the water. Toward solving the problems that appear in this kind of environment, we propose a navigation system which allows the sailboat to reach any desired target points in its working environment. This navigation system consists of a low-level heading controller and a short-term path planner for situations against the wind. For the low-level heading controller, a gain-scheduling proportional-integral (GS-PI) controller is shown to better describe the nonlinearities inherent to the sailboat movement. The gain-scheduling-PI consists of a table that contains the best control parameters that are learned/defined for a particular maneuver and perform the scheduling according to each situation. The idea is to design specialized controllers which meet the specific control objectives of each application. For achieving short-term path-planned targets, a new approach for optimization of the tacking maneuvering to reach targets against the wind is also proposed. This method takes into account two tacking parameters: the side distance available for the maneuvering and the desired sailboat heading when tacking. An optimization method based on genetic algorithm is used in order to find satisfactory upwind paths. Results of various experiments verify the validity and robustness of the developed methods and navigation system.
... As explained above, this changing of parameters is attractive mainly because the sailboat works in a highly nonlinear environment that requires a different strategy at each situation of wind. So, following the success of Gain Scheduling control strategies in other types of mobile robots [16], [17], [18], [19], [20], we propose in this work a similar approach for the development of the sailboat control system. The proposed method uses experimental data obtained in simulation to decide which controller parameters satisfies specific constraints. ...
... Depth control is one of important control issues for unmanned underwater vehicles (UUVs). Various design techniques, including the sliding mode control [1], the reduced order output feedback [2], the adaptive nonlinear control [3], the adaptive sliding mode control [4], the robust control [5], and the gain-scheduled output feedback [6] are introduced on this issue. Recently, one of the powerful design approach, a linear matrix inequality (LMI)-based design has been applied in the control problems of UUVs [7], [8]. ...
This paper deals with the depth and speed controls of a class of nonlinear large diameter unmanned underwater vehicles (LDUUVs), while maintaining its attitude. The concerned control problem can be viewed as an asymptotic stabilization of the error model in terms of its desired depth, surge speed and attitude. To tackle its nonlinearities, the linear parameter varying (LPV) model is employed. Sufficient linear matrix inequality (LMI) conditions are provided for its asymptotic stabilization. A numerical simulation is provided to demonstrate the effectiveness of the proposed design methodology.
... However, due to highly nonlinear behaviour of AUV dynamics and significant variations in hydrodynamic coefficients, it is necessary to design control algorithms using nonlinear models. In Silvestre and Pascoal (2007), an adaptive control scheme is adopted for the design of a nonlinear gainscheduling control using a reduced order output feedback technique which is scheduled on nominal forward velocities of an INFANTE AUV. The control problem is solved using linear matrix inequality (LMI) techniques. ...
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.
... It has been shown in several different applications, e.g. vapor compres-sion (Yang, Pollock & Wen, 2015), wind turbine control (Jafarnejadsani and Pieper, 2015), air-fuel ratio of engines (Postma and Nagamune, 2012) and autonomous underwater vehicles (Silvestre and Pascoal, 2007) that this method works well in practice. In addition to gain scheduling, state-dependent (SD) system models are a common practice in the modeling of hydraulic systems in this community. ...
In this paper, a velocity tracking controller for hydrostatic drive transmissions is developed. The solution is based on a state-dependent model that incorporates nonlinear characteristics of the system. A full state feedback controller is devised and the gains are scheduled on measured speed and pressures, together with approximated volumetric flow. The effects of uncertainties, especially those related to equilibrium values of pressures, are eliminated by utilizing so-called D-implementation. This technique eliminates the need for equilibrium values, which are model based and thus uncertain.
To demonstrate the efficacy of the controller, the solution is implemented on a 4.5-ton wheel loader. For comparison purposes, a constant gain state feedback controller with integral action is devised, and also a linear PID controller is tuned. The results show that the benefits of the devised controller are significant when it is compared to these two controllers. Moreover, the controllability of the machine is maintained in every situation.
... The equivalent control law can be obtained by solving the equation 1 0 S without the parameters perturbations, which can guarantee the performance of the surge velocity subsystem when its states are on the sliding hyper-plane Eq. (16). Thus, the equivalent control law can be written as (18) where "^" is used to represent the nominal hydrodynamic coefficients of the underactuated UUV. The nominal model parameters can be estimated by semi-analytic and empirical methods or model's experiments in hydrodynamic tanks. ...
The problem of diving control for an underactuated unmanned undersea vehicle (UUV) considering the presence of parameters perturbations and wave disturbances was addressesed. The vertical motion of an UUV was divided into two noninteracting subsystems for surge velocity control and diving. To stabilize the vertical motion system, the surge velocity and the depth control controllers were proposed using backstepping technology and an integral-fast terminal sliding mode control (IFTSMC). It is proven that the proposed control scheme can guarantee that all the error signals in the whole closed-loop system globally converge to the sliding surface in finite time and asymptotically converge to the origin along the sliding surface. With a unified control parameters for different motion states, a series of numerical simulation results illustrate the effectiveness of the above designed control scheme, which also shows strong robustness against parameters perturbations and wave disturbances.
... A way to tackle a poor representation of a mathematical model is through robust control. Well known approaches of robust control (LQG/LTR, H 2 , H ∞ , µ − synthesis, LMI, etc) were already applied for controlling autonomous underwater vehicles (Roberts and Sutton, 2006;Donha and Luque, 2006;Silvestre and Pascoal, 2007). It is also well known that the performance and stability properties of a controlled system are improved when models are more precise. ...
An extended Kalman filter is used to tackle the problem of parameter identification of an autonomous underwater vehicle (AUV). Since a large number of parameters must be identified, two alternative sub-approaches are investigated. A classical approach seems to have a better performance in cases where a specific parameter will be identified. However, a modified approach guarantees a better identification when dealing with multiple parameters. A sway/yaw mathematical model for an AUV is obtained considering motions in the horizontal plane. Circular and zig-zag maneuvers are tested to assess the identification approaches employed. Results are presented and analysed.
This paper addresses the tracking control challenge in the diving motion system of a specific class of autonomous underwater vehicles (AUVs) characterized by a torpedo-like shape. A decoupled and reduced-order three degrees-of-freedom linearized diving motion model is employed for depth position control. A control law is synthesized using the immersion and invariance (I&I) technique to achieve the control objectives. The primary aim is to attain tracking by immersing a stable, lower-order target (second-order) dynamic system into a three-dimensional manifold, upon which the closed-loop system evolves. We address the regulation problem as a specialized instance of the tracking problem, with the reference input set as a predetermined known depth that requires regulation. The efficacy of the proposed control law is evaluated through simulation studies involving various scenarios. Robustness tests are conducted to assess the control law’s performance under modeling uncertainties and underwater disturbances. The computer simulation employs an AUV named MAYA, utilizing experimentally validated diving motion parameters. A comparative analysis is performed between the proposed control law and other benchmark controllers to gauge its performance. Additionally, the effectiveness of the proposed control law is confirmed by validating its application to the nonlinear model of the diving motion system.
This paper addresses the tracking control problem associated with the diving motion system of a torpedo-like shape autonomous underwater vehicle (AUV). A decoupled and reduced-order three degrees-of-freedom (3-DOF) nonlinear model is employed to represent the dynamics of the diving motion system for depth position control. The control objective is to track the demanded depth position in the presence of uncertainties and disturbances. A control law based on the immersion and invariance (I &I) technique is synthesized to achieve the control objectives. The proposed control law effectively tracks a stable, lower-order target dynamic system immersed within a three-dimensional manifold. Additionally, the regulation problem is treated as a specialized case of tracking, with a known depth serving as the reference input to be regulated. The performance of the proposed control law is assessed through simulation studies that consider various scenarios. The simulation study evaluates the robustness of the proposed control law resilience against modelling uncertainties and underwater disturbances. The simulations utilize the MAYA AUV, incorporating experimentally validated diving motion parameters. The proposed control law’s quantitative analysis and computational performance show better performance against the benchmark controller.
AUV play an important role in the exploration and utilization of the ocean. Underactuated autonomous underwater vehicles (AUVs) are widely used in these missions due to the associated low manufacturing costs, low power consumption, and high reliability. Among many control problems of underactuated AUVs, the research of trajectory tracking and formation control methods has become a hot topic in recent years. In order to obtain superior control performance, research on trajectory tracking and formation control of underactuated AUVs based on intelligent control methods should be further advanced and deepened. In this context, we present a survey of intelligent trajectory tracking and formation control of underactuated AUVs, which is beneficial to researchers in this field. To facilitate a comprehensive understanding of the subject matter, we review some preliminary knowledge in trajectory tracking and formation control of underactuated AUVs. We also highlight research problems and challenges, including external disturbances, system characteristics, and system faults. We review recent advances in intelligent trajectory tracking and formation control of underactuated AUVs and analyze and discuss their characteristics. Moreover, we put forward some prospects of advanced control techniques, especially AI-based techniques for underactuated AUVs.
This paper addresses the problem of guidance and control of underwater vehicles. A multi-level control strategy is used to determine (1) outer-loop path-following commands and (2) inner-loop actuation commands. Specifically, a line-of-sight path-following algorithm is used to guide the vehicle along a three-dimensional path, and an L1 adaptive control algorithm is used to determine the low-level rudder commands to accomplish path following. The performance bounds of these outer- and inner-loop control algorithms are presented. Numerical results obtained using a physics-based Simulink model are used to aid in visualization of the control algorithm’s performance.
A path planning algorithm for an Autonomous Underwater Vehicle (AUV) performing docking operations in the presence of tidal current disturbances is presented. The path planner is composed a way-point generator (WPG), an Model Predictive Control based optimal planner (OP), and a tidal current estimator (TCE). The WPG defines the next way-point with respect to the vehicle position and the OP iteratively generates the trajectory over a prescribed future horizon whilst satisfying certain physical and logical constraints. The TCE estimates the tidal current disturbance speed enabling to adapt the AUV trajectory for reducing actuators power consumption. The proposed path planning policy has been evaluated in a set of simulation scenarios to illustrate the ability of the policy to drive the AUV by satisfying specifications and limiting power consumption.
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.
This article proposes a model predictive control (MPC)-based depth control system for the gliding motion of a gliding robotic dolphin. An injector-based buoyancy-driven mechanism is employed to achieve more precise control of net buoyancy. In the system, a novel framework of depth control is proposed on the basis of a simplified model, including a depth controller with improved MPC, a heading controller with velocity-based proportional-integral-derivative, and a sliding mode observer. Extensive simulation and experimental results demonstrate the effectiveness of the proposed control methods. In particular, a variety of slider-based experiments are also conducted to explore the performance of a movable slider in the depth control so as to better govern the gliding angle. The results obtained reveal that it is feasible to realize regular gliding angles via regulating the slider, which offers promising prospects for bio-inspired gliding robots playing a key role in ocean exploration.
This paper studies the controller design for an autonomous underwater vehicle (AUV) with the target tracking task. Considering the uncertainty the nonlinear longitudinal model, a sliding mode controller is designed. Meanwhile the neural networks (NNs) are used to approximate the unknown nonlinear function in the model. To improve the NNs learning rapidity, the prediction error which reflect the learning performance is constructed, further the updating law is designed utilizing the composite learning technique. The system stability is guaranteed through the Lyapunov approach. The simulation results verify that the designed method could force the AUV to track the target until rendezvous, and the model uncertainty is addressed better via the composite learning algorithm.
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.
The use of Autonomous Underwater Vehicles (AUVs) is now widespread among the underwater observation and survey. Because AUVs are not restricted by an umbilical cable, we think that AUVs have the most suitable form to collect ocean data or work depending on subjects of survey efficiently in the same way as the sea lives with various forms. For example, form to collect ocean data while cruising in a huge range, form to collect the topography data of the seafloor and under the bottom of the sea while cruising with following seafloor, form to work such as the collection of the rock of the seafloor or the setting of the sensor on the seafloor, form to collect ocean data slowly and carefully without moving the investigation spot against the current and so on.
In general, the diving dynamics of an autonomous underwater vehicle (AUV) has been derived under various assumptions on the motion of the vehicle in vertical plane. Usually, pitch angle of AUV is assumed to be small in maneuvering, so that the nonlinear dynamics in the depth motion of the vehicle could be linearized. However, a small-pitch-angle is a somewhat strong restricting condition and may cause serious modeling inaccuracies of AUV’s dynamics. For this reason, many researchers concentrated their interests on the applications of adaptive control methodology to the motion control of underwater vehicle. In this chapter, we directly resolve the nonlinear equation of the AUV’s diving motion without any restricting assumption on the pitch angle in diving model. The proposed adaptive neuro-fuzzy sliding mode controller (ANFSMC) with a proportional + integral + derivative (PID) sliding surface is derived so that the actual depth position tracks the desired trajectory despite uncertainty, nonlinear dynamics and external disturbances. In the proposed control structure, the corrective term is approximated by a continuous fuzzy logic control and the equivalent control is determined by a feedforward neural network. The weights of the neural network are updated such that the corrective control term of the ANFSMC goes to zero. The adaptive laws are employed to adjust the output scaling factor and to compute PID sliding surface coefficients. Finally, the lyapunov theory is employed to prove the stability of the ANFSMC for trajectory tracking of diving behaviors. Simulation results show that this control strategy can attain excellent control performance.
The depth control of an Autonomous Underwater Vehicle (AUV) is addressed. The vehicle is equipped with two separate actuation systems for the heave axis: a ballast tank system and a set of four jet motors generating vertical forces in the bow and stern of the vehicle. These two actuation systems have different time constants: the ballast tank system is rather slow, while the jet actuators have a much faster dynamics. The proposed control systems is inspired by the theory of complementary filtering in estimation where the output of slow sensors (low pass filters) is combined with the output of faster sensors (or the very plant model, i.e. high pass filters) to generate an estimate. In the given setting a heave controller is designed generating a desired force command. This signal is partitioned in a lower and higher frequency component: the former is sent to the ballast tank system and the latter to the jet thruster actuators. As a result, the depth force command is seemingly executed concurrently by the two actuation systems each working in its most natural frequency domain. The control design methodology is outlined and simulation results are reported illustrating the overall performance.
In order to realize the bottom following control for underactuated autonomous underwater vehicle (AUV) accurately, an adaptive neural network controller is designed. In order to deal with the parameter variations and uncertainties due to time-varying hydrodynamic dampings, the radial basis function (RBF) neural network (NN) is adopted to estimate unknown terms where an adaptive law is chosen to guarantee optimal estimation of the weight of NN. The stability of the tracking control system is analyzed based on the Lyapunov stability theorem, and the closed error system is asymptotical stable and the system states are bounded by the designed controller. Bottom profile with real measured data is used to evaluate the performance of the bottom following controller. Simulation results demonstrate that the proposed controller is effective to eliminate the disturbances caused by vehicle's nonlinear and uncertainty, and has higher tracking accuracy for engineering application.
The depth control of an Autonomous Underwater Vehicle (AUV) is addressed. The vehicle is equipped with two separate actuation systems for the heave axis: a ballast tank system and a set of four jet motors generating vertical forces in the bow and stern of the vehicle. These two actuation systems have different time constants: the ballast tank system is rather slow, while the jet actuators have a much faster dynamics. The proposed control systems is inspired by the theory of complementary filtering in estimation where the output of slow sensors (low pass filters) is combined with the output of faster sensors (or the very plant model, i.e. high pass filters) to generate an estimate. In the given setting a heave controller is designed generating a desired force command. This signal is partitioned in a lower and higher frequency component: the former is sent to the ballast tank system and the latter to the jet thruster actuators. As a result, the depth force command is seemingly executed concurrently by the two actuation systems each working in its most natural frequency domain. The control design methodology is outlined and simulation results are reported illustrating the overall performance.
For the specific needs of the underwater unmanned vehicle (UUV) in the working environment, the autonomous suspending control method for UUV based on amendment of fuzzy control rules is advanced. According to the traditional fuzzy controller, this method based on particle swarm optimization (PSO) for online search strategies adjusts the amendment of fuzzy control rules in time. This online optimization of fuzzy control method has a faster convergence speed, and can effectively adaptive adjust the motion state of UUV, which carries out the autonomous suspending control within the scope of predetermined depth for the accuracy and robustness . It is illuminated by simulation experiments that this autonomous suspending control method for UUV based on amendment of fuzzy control rules is more effective against uncertain disturbance and serious nonlinear, time change process.
In order to implement precise diving control of the autonomous underwater vehicle (AUV), according to the kinematic and nonlinear dynamic model of AUV, an adaptive iterative backstepping method based on neural network is proposed, and a kinematic and dynamic controller is designed. In the investigation, considering the existence of attack angle and the uncertainties of hydrodynamic damping parameters of the nonlinear model of AUV, a neural network-based controller is designed to on-line estimate the nonlinear hydrodynamic damping terms existing in the pitch motion together with external ocean current disturbances. Then, the adaptive law of the network weights is presented based on the Lyapunov stability theory to guarantee the uniform ultimate bounding of all signals in the closed-loop system. Finally, two groups of simulation experiments are carried out to compare the system response of the designed controller at a certain control gain and the diving control performance in the presence of disturbances. The results show that the designed controller is of smaller static error and higher tracking precision.
We develop nonsmooth optimization techniques to solve \Hinf synthesis problems under additional structural constraints on the controller. Our approach avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems. The proposed framework is very versatile and can accommodate a number of challenging design problems including static, fixed-order, fixed-structure, decentralized control, design of PID controllers and simultaneous design and stabilization
problems. Our algorithmic strategy uses generalized gradients and bundling techniques suited for the \Hinf-norm and other nonsmooth performance criteria. Convergence to a critical point from an arbitrary starting point is proved (full version) and numerical tests are included to validate our methods.
This paper focuses on the static output feedback stabilization problem for a class of SISO systems in the case of multiple delay controllers. We are interested in giving necessary condi-tions for the existence of such stabilizing controllers. Illustra-tive examples (a chain of integrators, or a chain of oscillators) are presented and discussed.
MARIUS (Marine Utility Vehicle System) is an autonomous underwater
vehicle for environmental surveying in coastal waters. This paper
describes the design, construction and hydrodynamic testing of the
vehicle and analyzes its expected performance in terms of mission
duration and range
Using a moment interpretation of recent results on sum-of-squares decompositions of nonnegative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve nonconvex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to the global optimum. Results from the theory of moments are used to detect whether the global optimum is reached at a given LMI relaxation, and if so, to extract global minimizers that satisfy the PMI. The approach is successfully applied to PMIs arising from static output feedback design problems.
This note presents a new sufficient condition for the static output feedback stabilization of linear discrete-time systems. This new condition is expressed as a linear matrix inequality feasibility problem and hence easily tractable numerically. An extension of this condition is given in order to incorporate H∞ performance objectives. The applicability of the proposed approach is shown through numerical examples and compared to some recent methods.
This note focuses on the static output feedback stabilization problem for a class of single-input-single-output systems when the control law includes multiple (distinct) delays. We are interested in giving necessary conditions for the existence of such stabilizing controllers. Illustrative examples (second-order system, chain of integrators, or chain of oscillators) are presented, and discussed.
This paper describes a linear matrix inequality (LMI)-based
algorithm for the static and reduced-order output-feedback synthesis
problems of nth-order linear time-invariant (LTI) systems with n<sub>u
</sub> (respectively, ny) independent inputs (respectively,
outputs). The algorithm is based on a “cone complementarity”
formulation of the problem and is guaranteed to produce a stabilizing
controller of order m⩽n-max(nu,ny), matching a
generic stabilizability result of Davison and Chatterjee (1971).
Extensive numerical experiments indicate that the algorithm finds a
controller with order less than or equal to that predicted by Kimura's
generic stabilizability result (m⩽n-nu-ny+1).
A similar algorithm can be applied to a variety of control problems,
including robust control synthesis
This paper addresses the design of state- or output-feedback
H∞ controllers that satisfy additional constraints on
the closed-loop pole location. Sufficient conditions for feasibility are
derived for a general class of convex regions of the complex plane.
These conditions are expressed in terms of linear matrix inequalities
(LMIs), and the authors' formulation is therefore numerically tractable
via LMI optimization. In the state-feedback case, mixed H2/H
∞ synthesis with regional pole placement is also
discussed. Finally, the validity and applicability of this approach are
illustrated by a benchmark example
The parametric linear quadratic (PLQ) control problem is considered for discrete-time stochastic systems. The control problem consists of a non-linear optimization problem in the parameters of a linear regulator. Results on global convergence and on rate of convergence are given for the linear-descent mapping method for solving the optimal regulator parameter values. Furthermore a non-linear mapping method based on the solution of a generalized discrete Riccati equation is given. The PLQ control problem is a useful extension of the optimal output feedback problem with applications to the design of low-order regulators, decentralized control and adaptive control.
Preface Notation Part I. Introduction. Robust Decision Problems in Engineering: A linear matrix inequality approach L. El Ghaoui and S.-I. Niculescu Part II. Algorithms and Software: Mixed Semidefinite-Quadratic-Linear Programs J.-P. A. Haeberly, M. V. Nayakkankuppam and M. L. Overton Nonsmooth algorithms to solve semidefinite programs C. Lemarechal and F. Oustry sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure S.-P. Wu and S. Boyd Part III. Analysis: Parametric Lyapunov Functions for Uncertain Systems: The Multiplier Approach M. Fu and S. Dasgupta Optimization of Integral Quadratic Constraints U. Jonsson and A. Rantzer Linear Matrix Inequality Methods for Robust H2 Analysis: A Survey with Comparisons F. Paganini and E. Feron Part IV. Synthesis. Robust H2 Control K. Y. Yang, S. R. Hall and E. Feron Linear Matrix Inequality Approach to the Design of Robust H2 Filters C. E. de Souza and A. Trofino Robust Mixed Control and Linear Parameter-Varying Control with Full Block Scalings C. W. Scherer Advanced Gain-Scheduling Techniques for Uncertain Systems P. Apkarian and R. J. Adams Control Synthesis for Well-Posedness of Feedback Systems T. Iwasaki Part V. Nonconvex Problems. Alternating Projection Algorithms for Linear Matrix Inequalities Problems with Rank Constraints K. M. Grigoriadis and E. B. Beran Bilinearity and Complementarity in Robust Control M. Mesbahi, M. G. Safonov and G. P. Papavassilopoulos Part VI. Applications:Linear Controller Design for the NEC Laser Bonder via Linear Matrix Inequality Optimization J. Oishi and V. Balakrishnan Multiobjective Robust Control Toolbox for LMI-Based Control S. Dussy Multiobjective Control for Robot Telemanipulators J. P. Folcher and C. Andriot Bibliography Index.
We consider the problem of designing a suboptimal H2/H∞ feedback control law for a linear time-invariant control system when a complete set of state variables is not available. This problem can be necessarily restated as a nonconvex optimization problem with a bilinear, multiobjective functional under suitably chosen linear matrix inequality (LMI) constraints. To solve such a problem, we propose an LMI-based procedure which is a sequential linearization programming approach. The properties and the convergence of the algorithm are discussed in detail. Finally, several numerical examples for static H2/H∞ output feedback problems demonstrate the applicability of the considered algorithm and also verify the theoretical results numerically.
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.
This paper considers the design of a stabilizing static output feedback gain which keeps linear quadratic (LQ) performance index less than a specified number (we call this an ‘LQ suboptimal controller’). Existence of such a controller is shown to be equivalent to the existence of a positive-definite matrix P such that P satisfies two linear matrix inequalities (LMIs) while P−1 satisfies another LMI. All LQ suboptimal controllers are explicitly parametrized by the freedom in the choice of the positive-definite matrix P satisfying the LMIs, and an arbitrary positive scalar and an arbitrary matrix of fixed dimension with a norm bound. A modified version of the min/max algorithm is given to find a positive-definite solution P to the LMIs.
A new method is proposed to implement gain-scheduled controllers for nonlinear plants. Given a family of linear feedback controllers designed for linearizations of a nonlinear plant about constant operating points, a nonlinear gain-scheduled controller is derived that preserves the input-output properties of the linear closed loop systems locally, about each equilibrium point. The key procedures in the proposed method are to provide integral action at the inputs to the plant and differentiate some of the measured outputs before they are fed back to the scheduled controller. For a fairly general class of systems, the nonlinear gain-scheduled controllers are easy to obtain, and their structure is similar to that of the original linear controllers.
Computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities (LMIs). In particular, we concentrate on the stabilization and the suboptimal H∞ output feedback control design problems. These problems can be described by a pair of LMIs and an additional coupling condition. This coupling condition is convex for the full-order control design problem, but convexity is lost for the control problem of order strictly less than the plant order. We formulate these problems as feasibility problems with matrix constraint sets of simple geometry, and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets. Full-order and low-order controllers are designed using alternating projection methods. For the full-order controller case, global convergence of the alternating projection methods to a feasible solution is guaranteed. However, for the low-order control case, only local convergence is guaranteed. An example is provided to illustrate the use of these methods for the full-order and the low-order controller design.
A linear matrix inequality (LMI)-based procedure for the design of robust static-output-feedback controllers is demonstrated on the problem of emergency lateral control of a highway vehicle with bounded time-varying uncertainties. A linear time-varying (LTV) tire model is used with a yaw-plane model of a highway vehicle to express the problem of emergency lateral control. The vehicle system is parameterized for variation in speed between (15 m/s and 30 m/s) and independent variation of front and rear effective lateral tire stiffnesses (between 30 kN/rad and 60 kN/rad) to form a polytope of linear systems. A stabilizing static-output-feedback controller is designed and its gains are reduced while guaranteeing robust stability.
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Multi-objective optimization theory with applications to the integrated design of controllers/plants for autonomous vehicles
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Design, construction and hydrodynamic testing of the AUV MARIUS. In Proceedings of the AUV 94, Cambridge, MA, USA. El Ghaoui, L., & Niculescu, S. I. (1999) (Eds.). Advances in linear matrix inequality methods in control. Society for Industrial and Applied Mathematics, Philadelphia: SIAM. El Ghaoui, L., Oustry, F., & AitRami, M. (1997). A cone complementary linearization algorithm for static output-feedback and related pro-blems. IEEE Transactions on Automatic Control, 42(8), 1171–1176.
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