# Linear Parameter-Varying Model Predictive Control of AUV for Docking Scenarios
###### Abstract  
A control system for driving an Autonomous Underwater Vehicle (AUV) performing docking operations in presence of tidal current disturbances is proposed. The nonlinear model of the vehicle has been modelled in a Linear Parameter-Varying (LPV) form. This is suitable for the design of the control system using a model-based approach. The LPV model was used for a Model Predictive Control (MPC) design for computing the set of forces and moments driving the nonlinear vehicle model. The LPV-MPC control action is mapped into the reference signals for the actuators by using a Thrust Allocation (TA) algorithm. This was based on the nonlinear models for the actuators and their position and orientation on the vehicle's hull. The structural decomposition of MPC and TA reduces the computational burden involved in computing the control law on-line on an embedded control board. Both MPC and TA algorithms use the vehicle's linear and angular positions, and velocities that are estimated by an LPV based Kalman Filter (KF). The proposed control system has been tested in different docking scenarios using various tidal current disturbances acting on the vehicle as an unmeasured disturbance. The simulation results show the controller is effective in controlling the AUV over the range of control scenarios meeting the constraints and specifications. Autonomous Underwater Vehicle; underwater docking; Model Predictive Control; Linear Parameter-Varying +
Footnote †: journal: Applied Sciences  
0000-0001-7227-330][PERSON] 0000-0001-7227-330][PERSON] 0000-0001-7227-330][PERSON] 0000-0002-0002-1991-1901][PERSON] 0000-0001-7227-3330][PERSON] 0000-0002-0002-1901-190 In Reference [4], the concept of underwater docking using AUV and ROV (Remotely Operated Vehicle) docking stations was proposed. The operation involves the AUV moving close to the standby ROV docking station, stopping and hovering in the vicinity of the ROV, and then the docking station on the ROV capturing the AUV with the docking device. When the AUV and the ROV docking station are in a separate positional relationship, the respective positions can be obtained from the surface ship, controlling the ROV docking station using an ultra-short baseline (USBL) acoustic positioning system. This transmits information to the AUV using underwater acoustic communications. However, when the AUV is close to the ROV docking station, it is important for the AUV to transition to the optimum position and orientation. The ROV docking station can then easily capture the AUV in the limited view of the underwater camera. The concept here is to install a 3D imaging sonar on the AUV to estimate the position and the attitude of the ROV docking station. The transfer can then be achieved to the optimum position and attitude using an advanced hovering control [5; 6]. In the following, we introduce new trajectory and attitude control for the AUV. After estimating the orientation of the ROV docking station with a 3D imaging sonar, the AUV transitions to a final hovering position where the ROV docking station can easily capture it. It then holds a fixed point in a predetermined orientation, and awaits capture by the ROV docking station. During cruising at a certain speed or higher, the AUV position and attitude are controlled by the main thruster and the rudder. However, during low speeds, or holding at a fixed point, the hydrodynamic action from the rudder is insufficient, so the AUV is controlled by a plurality of side thrusters that generate thrust in the vertical and horizontal directions. In this way, it is necessary to perform control by a number of actuators including a side thruster in order to shift the position and the attitude while decelerating the speed in a relatively short distance and finally holding a fixed target position. It is necessary to consider constraints for an actuator, such as a rudder, or side thruster, including limits on rudder angle and upper limits on thrust.