# Linear Parameter-Varying Model Predictive Control of AUV for Docking Scenarios
###### Abstract
Model Predictive Control (MPC) is often used for the optimal control of industrial systems with hard constraints but this is a relatively nonlinear process that is faster than many applications. The solution proposed is, therefore, tailored to the application. The equations of motion are six degrees of freedom for the AUV. These are required for model predictive control. They have nonlinear characteristics for velocity and angular velocity given fluid dynamic and Coriolis forces. The actuator characteristics such as the fins and thrusters also have non-linear characteristics. If such a nonlinear and complex motion model is used directly for model predictive control the prediction stage results in an excessive computational load. It is not in general therefore suitable for real time control for a system such as an AUV. Different solutions have been proposed for facing the AUV control by MPC. For example, in Reference [7], the MPC is applied to the trajectory tracking of an AUV and the equation of motion is limited to the motion in the horizontal plane. It is also linearized around a constant forward speed to reduce the computational load. In [8], the MPC is applied to the trajectory tracking of an AUV, where motion is limited to the nonlinear motion in the horizontal plane. The three forces (moments) are used to control the three degrees of freedom (u, v, r) distributed models, and ways to reduce computational load are considered for nonlinear MPC problems. In both these cases, the control problem is limited to the horizontal plane. For the docking control problem there is a combination of a tracking/path following mode and finally a dynamic positioning control mode. In this latter case at the docking position the attitude in the vertical plane, pitch and the roll must be controlled. We therefore examined the transfer of position and attitude control, and then the dynamic positioning control for the six degrees of freedom model. To reduce the computational load, the basic configuration of the control system is divided into two modules: an MPC control module for outputting the virtual force requiredto follow a predetermined position, speed, and attitude, and a Thruster Allocation (TA) module for determining the command value to each actuator required to generate the virtual force [9]. The TA problem is also involved in the dynamic positioning control of a ship. The calculation load is reduced by dividing a complicated optimization problem into the two more manageable optimization problems. In addition, a Kalman filter is implemented to estimate states and disturbances, such as tidal currents. To reduce the computational load of the MPC control module, a Linear Parameter Varying (LPV) modelling approach was adopted [10; 11]. The LPV-MPC can be treated as a linear problem, although it can represent a good approximation of a nonlinear model and the system matrices are parameter dependent and change with time. As a result, a linear quadratic programming problem can be generated, so that predictive control can be performed in real-time with reasonable economy. A method to compensate for the prediction error caused by using locally linear models, representing the inherently nonlinear model, was introduced. The proposed control system has been tested in simulation considering different docking scenarios featured by several tidal current acting on the vehicle as an external unmeasured disturbance. The optimum control of the AUV for docking under the constraint conditions is a challenging problem. Furthermore, the critical hardware development items, such as the docking devices, were developed in parallel. Therefore, for the control system design, the control algorithm was developed for the concept model AUV, and was verified based on simulation. This paper reports the development and simulation verification of this control algorithm. The paper covers the modeling in Section 2, the control system in Section 3, the simulation results in Section 4, and the finally the conclusions in Section 5.