Modeling and control of an Odyssey III AUV through system identification tests

We address the issue of dynamic modeling and control of the Bluefin Odyssey III class vehicle “Caribou,” operated by the MIT Sea Grant AUV Laboratory. Focus is on demonstrating a simple forward design procedure for the flight control system, which can be carried out quickly and routinely to maximize vehicle effectiveness. In many situations, the control loops are tuned heuristically in the field; frequent retuning is necessitated by the inevitable changes in vehicle components, layout, and geometry. Our paradigm here is that 1) a prototype controller is developed, based on an initial model, 2) this controller is then used to perform a very compact set of runs designed to identify the vehicle dynamic response, and 3) a revised, precision controller based on this improved model is implemented for the ultimate mission. We first developed a hydrodynamic model of the vehicle from theory and benchtop laboratory tests; no data from prior field tests with this vehicle was used. Body added mass approximations were included as well as lift and hydrostatic forces and moments. Inertial properties were approximated by assuming the vehicle density was that of water. Caribou’s tailcone assembly consists of a double-gimbaled thrustvectoring duct, with significant positioning dynamics and a non-traditional hydrodynamics. We carefully tested this tailcone’s response behavior through laboratory tests, and created a low-order model. Using the tailcone model and the vehicle’s initial hydrodynamic model, we developed a conservative controller design from basic principles. The control system consisted of a heading controller, pitch controller, and depth controller; the pitch control loop was nested inside the depth control loop. This control system was successfully tested in the field: the vehicle was controllable within several degrees of heading and approximately one-half meter of depth, on the firstpass design. System identification tests were then completed with the preliminary controller to gain a better understanding of the complete hydrodynamics of the vehicle, and in order to develop a precision controller based on the improved model. The resulting data provided a full-system linear model of the vehicle, and led to a successful controller redesign, with significantly improved performance. Introduction Developments made in Autonomous Underwater Vehicle (AUV) related technologies have enabled AUVs to move out of the research laboratory and into the commercial environment. AUVs are also used by the military, and a large portion of the AUVs in use today are still used in a scientific setting. Improvement in the performance of AUVs is needed to enhance the developments made in long-range oceanographic surveys, shallow-water mine reconnaissance and countermeasures, and procedures in autonomous docking [1]. By improving the vehicle’s control system, maneuvering becomes more precise and battery power is conserved. In order to develop a precise control system a finely tuned dynamic model of the vehicle is needed for testing and research purposes. Previous work in dynamic modeling of AUVs includes simulation model verification done through field tests [2] as well as theoretical and empirical methods in addition to tow tank results [3]. Recent work done on AUV control has included gains obtained using partial model matching methods [4], as well as sliding mode control based on estimated coefficients [5], in addition to fuzzy sliding mode control systems [6]. Previous work in system identification of AUV systems has been done using neural network identifiers [7] and neurofuzzy identification techniques [8]. The work presented here focuses on development of dynamic models and control systems from first principles. The system identification tests and simulation process form a forward design process. Odyssey III Class AUV Caribou The platform for this research was a Bluefin Odyssey III class vehicle, Caribou, operated by the MIT Sea Grant AUV Laboratory. Since receiving this vehicle from Bluefin, the AUV Lab has used an in-house developed operating system, and made substantial modifications to the hull, including several large holes for sensors. We stress that the dynamic response of this vehicle, described in this paper, does not necessarily represent that of other Bluefin vehicles as delivered. Figure 1: The Caribou AUV in short configuration Caribou is highly maneuverable and has a variable configuration in length and payload. It can operate at a range of speeds, and it has a novel propulsor and control surface that consists of a double-gimbaled ring finned duct thruster, which allows for vectored thrusting. The duct thruster’s angle is limited at ±15degrees in both the yaw and pitch plane, known typically as the rudder and elevator angles, respectively. The propeller is confined to the duct for protection, as well as enhanced flow capabilities. The duct also acts as a control surface. Thus, the Odyssey III class AUV does not need fins to control the vehicle motion because the duct and vector thrusting capability is sufficient to impose directional control. Figure 2 shows the duct thruster arrangement. Figure 2: Caribou’s ring fin duct thruster The hull shape of the Odyssey III base vehicle is based on a Series 58, Model 4154 Gertler polynomial [9] with a length of 84in (2.13m) and a maximum diameter of 21in (0.53m). For this work, the body referenced coordinate frame is located along the symmetric axis of rotation at the midpoint of the AUV. In this body coordinate system the x-axis is along the symmetric line proceeding towards the nose of the vehicle. The yaxis extends towards the port side of the AUV, while the z-axis is directed upwards. Body referenced velocity in the x direction, surge, is denoted by u. Velocity in the body frame y and z directions is v, sway, and w, heave, respectively. Rotational velocity about the x-axis, roll velocity, is denoted as p. Rotational velocity about the y-axis and z-axis is q, pitch rate, and r, yaw rate, respectively. External body forces in the x, y and z direction are denoted as X, Y and Z respectively, while external body moments in the x, y and z direction are K, M and N respectively. The vehicle’s angular orientation is described in the inertial frame of reference with Euler angles, ! , ", and #. Nonlinear Model The external forces and moments resulting from the vehicle hydrostatics, hydrodynamic lift and drag, added mass, and the control input of the vehicle’s ducted thruster are all defined in terms of specific coefficients for this model. Nonlinear equations were used to determine the vehicle’s coefficients, and rigid-body dynamics. While the vehicle is inherently nonlinear, the nonlinear simulations provide more realistic simulations, but for control purposes, a linear model provides a sufficient platform, while maintaining less complexity. In order to simplify the challenge of completely modeling an autonomous underwater vehicle, the following assumptions about the vehicle and the environment were made for simulation purposes: • The vehicle is a rigid body of constant mass • The vehicle is deeply submerged in a homogenous, unbounded fluid • The vehicle does not experience memory effects • The vehicle does not experience underwater turbulence Overall Vehicle Modeling The vector transformation from an inertial frame of reference to the body frame is developed by using Euler angles (ψ,θ,φ), which describe the roll, pitch and yaw position of the vehicle in inertial space, as described by Crandall [10]. The general motion of the vehicle in six degrees of freedom is described by the following twelve states: [ ] z y x x = ! [ ] E φ θ ψ = ! [ ] w v u v = ! [ ] r q p = ω The locations of the vehicle centers of mass and volume (buoyancy) are defined in terms of the bodyfixed coordinate system. The vessel inertial dynamics were derived from the physics of the system and are written as follows in the body-referenced frame. X, Y and Z are the external body forces applied in the bodyreferenced directions of x, y and z respectively. [ ] [ ] [ ] CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM z q p r qy px x q y p qu pv w m Z y p r q px rz z p x r pw ru v m Y x r q p rz qy y r z q rv qw u m X ) ( ) ( ) ( ) ( ) ( ) (