[Paper] The design of static output feedback control for vertical path tracking of autonomous underwater vehicle

Summary

A design of an output feedback controller for autonomous underwater robots is proposed to realize the path tracking task in the vertical plane. Using vehicle kinematics, a frame of reference is generated that provides the desired orientation of the vehicle along the path. The reference trajectory is then used to define the error space and linearize from it. Based on the linearization model, a static output feedback controller is designed and implemented on a nonlinear object. Computer simulation has been used to verify the design of the controller.

Introduction

In the past few decades, autonomous underwater robots have been an active area of ​​research because of their various applications in military, commercial, and scientific missions. The limitation of energy consumption and the use of sensor measurement make the control and guidance of underwater robots more challenging. The lack of suitable acoustic sensors and the limitations on the cost-effectiveness of underwater robots have resulted in physically achievable output feedback controllers. Due to nonlinearity, coupled dynamics and unknown hydrodynamic coefficients, underwater survey or maneuvering tasks are difficult to handle (Fosen, 1990). As a basic feedback control problem, output feedback controllers have been extensively reviewed in the literature. Refsnes et al. (2007) verified the effectiveness of the output feedback controller through experiments. The dynamic output feedback controller implemented by Silvestre et al. (2002) and Silvestre and Pascoal (2007) ensures the stability of the closed-loop dynamics. However, compared with static output feedback controllers, such dynamic controllers require higher design and calculation costs and more complex implementations.

Although the controller for underwater robots is easier to implement, moves faster, and is more suitable for underwater robot applications, there are problems with the design of such controllers because there are no sufficient and necessary conditions to solve the design problems of underwater robots (Syrmos et al., 1997). This led researchers to propose several iterative algorithms, using any of them to generate control for a given problem. Geromell et al. (1998) studied the stability and convexity of the self-organizing function controller, and gave sufficient conditions for the self-organizing function controller to be solvable. Yu (2004) proposed a convergence algorithm to solve the dual optimal output feedback regulator theory and ensure the stability of the SOF controller. Iwasaki et al. (1994) and Kucera and De Souza (1995) investigated various stabilization conditions and algorithms to determine the effectiveness of the s of controller. In this paper, the SOF controller is implemented in the error space defined by the Serret-Frenet framework, and the path tracking task in the vertical surface dynamics of the underwater robot is realized. The difference in speed and position between the body frame fBg and the desired body frame fCg is used to define the error space. Then the error space is linearized and used in the SOF design algorithm of (2004). It is observed that the algorithm successfully generates the controller gain, and the designed gain can stably meet a certain secondary performance system. Through the simulation of the underwater robot model, the obtained results are verified.

The second section reviews the kinematics and dynamics models of the underwater robot on the vertical plane. Section 3 introduces the error space, while Section 4 covers the linearization of the error space. The fifth section proposes the design of programmable controller. The simulations and conclusions in Section 6 verify the effectiveness of the designed controller under different reference conditions.

Underwater robot modeling

Reference System

Ship modeling involves the study of kinematics and dynamics. According to Fussen (1990), the model of the underwater robot on the vertical plane will be described in the following chapters.

The movement of the main body fixed frame is described relative to the inertial frame. The motion of the earth hardly affects low-speed craft, so the fixed reference frame of the earth can be regarded as an inertial reference frame. The position and direction of the vehicle are described in the inertial reference frame I, while the linear velocity and angular velocity are described in the body fixed coordinate system B relative to I. The forward movement of the underwater robot is controlled by the propeller, and the steering with the required direction is adjusted by the bow, stern and rudder control plane. Fig. 1 shows three linear velocities and three angular velocities expressed in a body-fixed coordinate frame relative to an inertial frame.

The dynamics of underwater robots contain nonlinear and coupled hydrodynamic parameters, which are difficult to control. According to Healey and Linard (1993), the six-degree-of-freedom model of an underwater vehicle can be subdivided into three non-interactive or slightly interacting subsystems for speed control, vertical plane mode and steering mode. In order to control the rise or fall of the vertical plane of the underwater robot, a sub-model can be used. Cristi et al. (1990), You Hechai (1998), Silvestre (2000) and Silvestre et al. (2009) chose to control the AUV in the vertical plane, ignoring the sway, roll and yaw velocity dynamics.

Vertical plane model

Ignoring the stable roll mode of the vehicle and considering the symmetry of the vehicle, the underwater robot model can be simplified into two interacting or non-interacting subsystems, namely the longitudinal subsystem and the lateral subsystem. The longitudinal subsystem or vertical plane model includes the wave, heave and pitch as its state and the kinematics model



. The vehicle kinematics equation in the inertial coordinate system I is given by the following equation,


where $m、\rho 、I_{and},L,WandB$ represent vehicle mass, water density, moment of inertia along the y axis, vehicle length, weight and buoyancy, respectively. The input of the vehicle is the stern plane deflection$d_s$And thrust $T$。