International Journal of Control, Automation, and Systems (2015) 13(5):1212-1220 ISSN:1598-6446 eISSN:2005-4092 DOI 10.1007/s12555-014-0252-8 http://www.springer.com/12555 An Autonomous Underwater Vehicle as an Underwater Glider and Its Depth Control Moon G. Joo* and Zhihua Qu Abstract: To provide a conventional autonomous underwater vehicle with gliding capability, we as- sume a moving battery and a buoyancy bag installed in a torpedo shaped autonomous underwater ve- hicle. We develop a mathematical model for the underwater vehicle and derive a stable gliding condi- tion for it. Then an LQR controller is designed to control the zigzag depth of the vehicle, where the de- rived gliding condition is used as set-points of the control system. For control efforts in the gliding movement, the changes in the center of gravity and the net buoyancy are used, but neither thruster nor rudders are used. By using the gliding capability, the underwater vehicle can move to a farther location silently with less energy consumption and then start operating as a normal autonomous underwater ve- hicle. We show the feasibility of the proposed method by simulations using Matlab/Simulink. Keywords: Autonomous underwater vehicle, depth control, LQR controller, underwater glider. 1. INTRODUCTION winged airplane, and it performs a vertical zigzag movement to go forward by changing net buoyancy and Unmanned underwater vehicles have been developed the position of center of gravity [6-10]. UWG has been in many countries. They can be roughly categorized into developed as a moving device for measuring temperature, autonomous underwater vehicle (AUV) [1-4] and salinity, water currents, etc. Since a very small amount of remotely operated vehicle (ROV) depending on the energy is required to inflate/deflate buoyancy bag or to existence of tether that determines the autonomy level. push/pull the position of the battery position to change AUV has on-board power and an on-board navigation the center of gravity, UWG has a long operation time system free from a tether, whereas ROV needs a tether to that lasts over a month and thus offers a long range be supplied with power and steering control from the coverage wider than 1000 km. However, it has mother ship on the surface. A kind of hybrid AUV has disadvantages from the large turning radius which makes also been developed which has the appearance of a it difficult for precise position control. conventional ROV having several thrusters to move to Combining the good aspects of the conventional AUV any direction but having no tether to transport power and and UWG is so natural that some of the combined control signals from the mother ship [5]. underwater vehicles have been developed including an The conventional AUV has a torpedo shape. It has at UWG without wings [11-13], an UWG with thruster and least one thruster to go forward and rudders to change rudders [14], and an AUV with buoyancy bag and direction. The main area of application is military moving mass [15]. It can be another type of hybrid AUV operation such as mine detection, terrain search, in a sense that it can be used either as an AUV or as an surveillance mission, and so on. Its advantages include a UWG when necessary. rapid response and a small turning radius. Since propeller From the viewpoint of modeling for control purpose, a thrust needs much energy, however, its operating time is REMUS as a conventional AUV has been modeled in [1], limited to a few hours. On the other hand, the underwater where the AUV was assumed to be a rigid body and the glider (UWG) is a kind of AUV, which is shaped like a external forces were mathematically obtained by the mechanical shapes of the hull, rudder, and sterns. Then __________ the higher order terms of the external forces were Manuscript received June 23, 2014; revised September 26, ignored for simplification. Control inputs are the thruster 2014; accepted November 1, 2014. Recommended by Associate Editor Sung Jin Yoo under the direction of Editor Hyouk Ryeol velocity and the angle of sterns and rudders. There have Choi. been many control schemes reported such as PID, state This work was supported by Basic Science Research Program feedback, sliding mode controller, neuro-fuzzy system, through the National Research Foundation of Korea(NRF) funded and so on [16-20]. The modeling for UWG was also by the Ministry of Education, Science and Technology (2013 conducted in [21,22] assuming the vehicle as a multi R1A1A4A01005930). body system consisting of moving masses, a hull, and a Moon G. Joo is with the Department of Information and Communications Engineering, Pukyong National University, variable mass buoyancy. External forces are not modeled Busan 608-737, Korea (e-mail: [email protected]). directly, but obtained by the experiment or Zhihua Qu is with the Department of Electrical Engineering computational fluid dynamics software. They are and Computer Science, University of Central Florida, FL 32816, described as functions of lift and drag depending on the USA (e-mail: [email protected]). angle of attack. Control inputs are the position of moving © ICROS, KIEE and Springer 2015 An Autonomous Underwater Vehicle as an Underwater Glider and Its Depth Control 1213 mass and the mass of buoyancy. Some control schemes have been also reported [23-27]. In modeling of the hybrid AUV combining AUV and UWG, no unified modeling to handle both aspects of AUV and UWG has been reported yet to the best of our knowledge. We, thus, propose a method of developing a unified model in order to add a gliding capability to the conventional AUV with which it can travel a long distance to a far location as an UWG and then operate as a normal AUV. The REMUS model in [1] is applied basically to use the already developed AUV control scheme in the AUV mode, and the work in [21] is adopted to derive the stable gliding condition in glider Fig. 2. State variables represented in the body fixed mode. This kind of hybrid AUV is advantageous from coordinate system and the earth fixed coordinate the aspect of quietness and energy saving under low system. current since it makes neither the noise nor the turbulence which an AUV inevitably makes because of equations using 12 state variables, (,xyzuvw ,,,, ,,φθ , the propeller thruster. ψ ,,,)pqr as shown in Fig. 2 [28,29]. The NED Section 2 develops a dynamic model for an AUV as an coordinate is used as the earth fixed coordinate system. UWG. Section 3 derives the desired value of several Generally, the center of buoyancy is used as the origin necessary state variables for a stable gliding. Section 4 of the body fixed coordinate, i.e., xyz===0. The develops a linearized depth model to design a controller bbb center of gravity in each direction is denoted as (,x y , for vertical plane movement. Section 5 gives the gg z ). The mass of the vehicle is mmmm=++ simulation results using Matlab. A brief summary is g vh b where mh is the mass of hull and its static components, followed in Section 6. m m is the moving mass such as battery pack, and b is 2. MODELING OF AUV AS UWG the point mass buoyancy. The mass of the water m displaced by the vehicle is denoted as . Then the net mmm=−. Because the controllers of AUV such as REMUS have buoyancy mass is ov I been widely studied, this paper focuses on controlling an Now we have the following 12 dynamic equations. xx, I I AUV as UWG under the assumption that the AUV has a yy and zz are moments of inertia in the body fixed buoyancy bag and a moving battery pack in its hull as coordinate. Among them, equations (1)-(6) are labeled to shown in Fig. 1. The purpose of modification is to endow depict the vertical plane movement of the robot for later the AUV with gliding capability which does not use any use. propeller propulsion. m[() u −+ vr wq − x q22 + r It is worth to mention that unwinged UWGs in [11-13] vg (1) +−++=ypqr()()] zprq X, are supposed to be operated as underwater gliders only. g g ∑ ext UWG in [14] focused on the change of parameter values mv[() −+− wpury r22 + p due to the thruster and rudders from only the viewpoint vg (2) of underwater glider. AUV in [15] is most similar and +−++=z ()()]qr p x qp r Y , gg∑ ext has a buoyancy bag and a moving battery in its hull, but I pI+−()[() Iqrmywuqvp + −+ it uses the buoyancy bag and the moving battery to xx zz yy v g achieve zero angle of attack at neutral buoyancy, for −−+zvwpur(), ] = K g ∑ ext efficient propeller propulsion to minimize drag effect and I qI+−()[() Irpmzuvrwq + −+ thus to lengthen the operational time and range. In other yy xx zz v g (3) words, the AUV operates always as a propeller-driven −−+xwuqvp() ],= M g ∑ ext AUV, even though the vertical zigzag trajectory is used I rI+−()[() Ipqmxvwpur + −+ during its operation. zz yy xx v g −−+yuvrwq(), ] = N It is well known that an underwater robot with 6 g ∑ ext degrees of freedom is described by nonlinear differential xu =+cosψθ cos v (cos ψθφ sin sin − sin ψ cos φ) (4) ++w(cosψθφ sin sin sin ψφ sin ), yu =+sinψθ cos v (sin ψθφ sin sin + cos ψφ cos ) +−w(sinψθφ sin cos cos ψφ sin ), (5) zu =−sinθθφθφ + v cos sin + w cos sin , φφθφθ =+pqsin tan + r cos tan , θφφ =−qrcos sin , (6) Fig.