[Thesis] Model-based output feedback control of underactuated underwater vehicle with slender body: theory and experiment
Summary
This paper introduces the design and experimental results of a new type of slender underwater vehicle output feedback controller. The controller is obtained using model-based design techniques. Two independent control device models are used: a 3-degree-of-freedom (DOF) current-sensing ship model that takes into account the current load on the vehicle, and a 5-degree-of-freedom model that describes vehicle dynamics. The main design goal behind this strategy is to include vehicle dynamics when assessing the current impact on the vehicle. In addition, the transportation model is based on the concept of constant propeller speed, resulting in a partially linearized model, which leads to a clear and achievable controller and observer structure. The controller is obtained by using observer backstepping technology, and the closed-loop system is asymptotically stable by using Lyapunov and cascade system theory. The control objective is to track the desired pitch and heading angles generated by the line-of-sight guidance system while maintaining a constant forward thrust. The experimental results prove the successful performance of the output feedback controller implemented on the MkII underwater robot.
Index term-Autonomous Underwater Vehicle (AUV), experimental results, output feedback control based on nonlinear models.
Introduction
The underwater robot moves at a certain forward speed, and its dynamics are highly nonlinear and coupled. This brings about control challenges, which have aroused great interest in the design of nonlinear observers and controllers for underwater vehicles in the past few decades. However, there are relatively few reported results of model-based control (MBC) design of underwater vehicles including experimental tests. The main reason for this situation may be that it is difficult to obtain an accurate model of the ship. In addition, unpredictable current loads and poor position measurements can pose challenges when using MBC, which can have a significant impact on the controller.
For these reasons, in addition to issues related to actual implementation, optimization and debugging, non-model-based solutions are usually preferred. However, hiring MBC has some important benefits. Based on this model, the motion of the vehicle can be predicted by using controller actuator inputs and available state measurements. In addition, model-based observers can provide estimates of unmeasured states in addition to filtering noise signals. This article introduces the successful results of the MBC system of the slender underwater vehicle, and demonstrates azimuth tracking, estimation of unmeasurable states, filtering and dead reckoning. In this article, we refer to the model designed for the purpose of control design as the control device model (CPM). According to [31], CPM is defined as a model that captures the main characteristics of a physical system. Unfortunately, a poorly designed CPM that fails to capture important features of a dynamic system can lead to performance degradation and stability issues. Therefore, when deriving CPM, in addition to simplifying the model to make the analysis feasible, the stability and robustness issues related to the system should also be emphasized. Therefore, in this article, we will describe the development of the dynamic model and explain the most important hydrodynamic characteristics of the Slender Autonomous Underwater Vehicle (AUV). The more complex process plant model (PPM) is a comprehensive description of the actual process and should be as detailed as necessary. The main purpose of this model is to simulate real equipment and test the controller and observer based on the corresponding CPM design.
background
There are some research results on underwater robot MBC in the literature. In literature [16], a state feedback controller is proposed for the tracking of underwater robots. The model is linearized at a constant forward speed and decoupled into three independent systems: surge, horizontal steering (sway and yaw) and diving system (heave and pitch). A sliding mode controller and observer [9] are proposed to solve the tracking problem. The experimental results reported in [22] demonstrate the successful controller performance. NPS ARIES is an under-actuated slender underwater robot designed to track direction while maintaining a certain forward speed. This streamlined underwater robot should be distinguished from an open box-framed vehicle. These are low-speed vehicles, usually fully driven, fluid power and stability can vary greatly. n [30], a model-based robot vehicle positioning system is proposed, in which experimental evaluation of different controllers is performed on JHRUROV vehicles. The proposed model is completely decoupled, and the fluid mechanics is controlled by linear and nonlinear damping, that is, the Coriolis force is not explicitly included in the model. The conclusion of this paper is that the controller based on the fixed model is better than the partial discharge controller. However, according to [30], when incorrect model parameters are used, the performance will be greatly reduced. In the literature [34], the tracking of the open frame aircraft ODIN was studied experimentally. Although the non-linear model of the Odin vehicle is adopted, the reported controller is a linear PID controller. Therefore, it is not model-based because it does not dynamically incorporate the model into the controller. However, the controller provides good tracking results. In [30] and [34], speed measurement can be used for feedback. Literature [2] gives the successful tracking results of MBC derived from the inverse theory. The aircraft is an open-frame hovercraft, described by a three-degree-of-freedom horizontal model without nonlinear damping. All these mentioned results have one thing in common, that is speed can be used for feedback, and except [2], all the results assume that the unstable Coriolis force is controlled by hydrodynamic damping in some sense. Compared with low-speed applications of ships, such as dynamic positioning [21], this is a common method for modeling control equipment. In addition, the hydrodynamic characteristics of the box-shaped vehicle indicate that damping is dominant, and the hydrodynamic Coriolis force is negligible. However, for slender vehicles with some forward speeds, this assumption is unrealistic.
The work described in this article is driven by the mine serpenter MkII developed by Kongsberg NASA. The underwater robot is a low-cost torpedo-shaped underwater robot. Compared with the nominal speed, the weight is relatively small, which means that the dynamics dominate the speed, and the nonlinear characteristics of fluid dynamics become the decisive factor. In addition, due to cost reasons, this generation of mine sniper does not carry any speed or inertial measurement unit (IMU). The position is measured by using a short baseline acoustic measurement system. The sensor kit also provides heading, pitch, roll and depth measurements. This limitation of the instrument increases the difficulty of accurate tracking. Therefore, in order to improve performance, we propose an observer that provides position and velocity estimates. For underwater vehicles, the speed can be measured by using Doppler Velocity Logging (DVL) [19] Or obtained by integrating the acceleration measured by the inertial measurement unit. However, DVL can only produce accurate speed measurements, provided that the distance to the seabed is within a certain boundary. In addition, when erroneous acceleration measurements are integrated, the inertial measurement unit will drift in the derived velocity. Therefore, the output feedback controller proposed in this paper can also improve the performance of slender aircraft with more complex sensor groups, because the proposed observer and controller can work independently of these speed measurements, thereby providing analysis for the measurement values. Redundancy improves the reliability of the control system. This makes the system more tolerant of failures. In underwater applications, ocean currents have a serious impact on the performance of aircraft, and even if the speed of the aircraft and water can be measured, the impact of ocean currents is difficult to predict. Therefore, a common approach is to model the disturbance as a constant or slowly varying deviation, see for example [34] and [14]. One disadvantage of this method is that when modeling the current load, the hydrodynamic characteristics of the vehicle are not properly considered. Other reported methods include the use of kinematics and filtering techniques to obtain an estimate of the current speed. Examples of this can be seen in, for example, [5], [3] and [4], which all require some kind of speed feedback. In this article, we will adopt the modeling method first introduced in [26] and more fully described in [29]. A three-degree-of-freedom model is derived as the basis for the current observer design. This is a current-induced blood vessel model, which can be interpreted as a third-order filter whose constants are obtained based on vehicle parameters. The goal is to provide an estimate of the current speed so as to estimate the impact of the current load on the vehicle. In this way, when estimating the impact of environmental disturbances, key hydrodynamic characteristics are taken into account, because the estimated current velocity is explicitly used to calculate nonlinear hydrodynamic damping and Coriolis forces. In addition, since only the azimuth is measured, especially locations that may be heavily noise-contaminated, a high-order model is preferred to avoid large jumps and oscillations in current estimation. The successful experimental results of this observer concept can be found in [27], which reports the design of a three-degree-of-freedom current-sensing ship model that works with a fully nonlinear six-degree-of-freedom aircraft model. The output controller has not been tested with the observer in [27]. This article supplements the results of output feedback control given in [29], because we have considered the situation where speed measurement is not available in this article. In addition, this article gives the experimental test on a full-scale aircraft in the ocean. result. Locations that may be heavily noise-polluted, so higher-order models are preferred to avoid large jumps and oscillations in current estimation. The successful experimental results of this observer concept can be found in [27], which reports the design of a three-degree-of-freedom current-sensing ship model that works with a fully nonlinear six-degree-of-freedom aircraft model. The output controller has not been tested with the observer in [27]. This article supplements the results of output feedback control given in [29], because we have considered the situation where speed measurement is not available in this article. In addition, this article gives the experimental test on a full-scale aircraft in the ocean. result. Locations that may be heavily noise-polluted, so higher-order models are preferred to avoid large jumps and oscillations in current estimation. The successful experimental results of this observer concept can be found in [27], which reports the design of a three-degree-of-freedom current-sensing ship model that works with a fully nonlinear six-degree-of-freedom aircraft model. The output controller has not been tested with the observer in [27]. This article supplements the results of output feedback control given in [29], because we have considered the situation where speed measurement is not available in this article. In addition, this article gives the experimental test on a full-scale aircraft in the ocean. result.
In this article, we consider under-actuated underwater robots, which is a vehicle attribute that often complicates the overall analysis. In [10] and [3], the guidance kinematics algorithm is included in the controller derivation. This makes it possible to demonstrate convergence to the desired path, despite the lack of control actuators. In this article, we use a slightly different approach, treating the desired trajectory as an external, time-varying, and bounded signal. This contributes to a relatively simple solution for observer-controller design. Then, by analyzing the inherent dynamics of the proposed controller, we proved that the unactuated state is bounded due to hydrodynamic damping. This method was first introduced in [13], and it is a convenient tool derived from the use of the reverse method [20]. The three-dimensional guidance system is based on the line-of-sight method and has been fully described and analyzed in the literature; for example, see [7] and [8].
Main contributions and thesis outline
The main contributions of this paper are as follows. The design and results of the guidance and control system of an under-actuated underwater robot with a slender body that only measures position, depth and direction. The control goal is to track the desired pitch and heading angle while maintaining a constant forward thrust. The output feedback controller is composed of a pair of non-linear Luenberger observers working together to provide filtering and estimation of position, Euler angle, vehicle and current speed. The proposed vehicle CPM is semi-linear; when a constant propeller rotation is applied, unstable Coriolis forces and moments are linearized near the relative forward speed. However, nonlinear damping is also included. The experimental results show that the proposed observer and controller have satisfactory performance. The cascade system theory is used to prove the asymptotic stability of the closed-loop system. Neither high gain nor bounded controller feedback is required. Observer and controller gains can be tuned separately. These features facilitate practical implementation. This article is an extension of the literature [28], showing all the evidence, and expounding the modeling of the guidance system and actuators in detail. An important goal of this work is to develop an easy-to-implement observer-controller system. Due to the nonlinear coupling between the three-degree-of-freedom current-sensing ship model and the five-degree-of-freedom vehicle model, the stability analysis becomes quite complicated, but the obtained observer and controller are easy to implement.
This article is organized as follows: The description of mathematical modeling is given in the second part. The third and fourth sections respectively give the design and analysis of the observer and the controller. In addition, in the fifth section, a case study on Minesniper MkII is introduced, which describes the actuator modeling and guidance system, and finally gives the experimental results. Section VI gives some conclusions.
To be continued
Conclusion and future work
Aiming at the under-actuated underwater robot with a slender body, an output feedback controller is proposed. The continuous production management system includes two separate models: a five-degree-of-freedom vehicle model and a three-degree-of-freedom current-sensing ship model considering the main current load. A part of the vehicle CPM is linearized based on the relative surge speed. Using Lyapunov function and cascade system theory, it is proved that the nonlinear Luenberger observer and the controller designed with observer backstepping technology are UGAS. One advantage of the method used is that it does not require any high gains, nor does it require a bounded feedback controller gain. In addition, the observer and controller gains can be adjusted separately. A sea test was carried out on Minesniper MkII and showed satisfactory observation and tracking performance. Further work includes obtaining more accurate vehicle parameters and optimal adjustment of controller feedback gains in an attempt to optimize vehicle performance.
Paper link