# Linear Parameter-Varying Model Predictive Control of AUV for Docking Scenarios
## 5 Conclusions  
The modelling and control of an Autonomous Underwater Vehicle (AUV) in a docking task was presented. The nonlinear dynamics model of the AUV was developed for the vehicle dynamics, actuators and sensor characteristics, and the effect of tidal currents acting on the vehicle was treated as an unmeasured disturbance. A control system based on an optimal predictive constrained control design approach was developed [16].  
The control system is composed of three major subsystems. A Thrust Allocation (TA) algorithm subsystem was based on the models of the actuators. A Model Predictive Control (MPC) block was designed using a Linear Parameter-Varying (LPV) model of the AUV derived from the nonlinear model of the vehicle. A time varying Kalman Filter (KF) was used to estimate the state of the system. The control system performance was tested by driving the AUV over a set of control scenarios featuring different tidal current disturbance conditions. The results illustrated that the proposed controller could control the vehicle effectively in the docking task. Further developments involve the integration of the proposed control system within an advanced path planning policy that can minimize energy while approaching the docking station.  
Mitsubishi Heavy Industries is also developing the AUV prototype for a docking technology demonstration based on the concept shown in Figure 1. This is in parallel with this study, which is called \"Naminow-D\". The \"Naminow-D\" study has the addition of side thrusters and docking devices to the existing mono-axial propulsion AUV \"Naminow\". The side thrusters and docking devices, including the underwater wireless power receiver, are installed externally to minimize the development cost. Figure 13 shows the \"Naminow-D\" under functional testing in the water tank.  
Future studies will require physical parameter modifications, changes to the control software for implementation into embedded computer systems, and the sea trials, including comparison with simulation results.  
Figure 12: Max current test: rear side thrusters’ control signals (blue plot) with respect to the saturation values (dashed red plot).  
**Author Contributions:** This study group consists of Japanese team and Scottish team. Japanese team mainly takes part of AUV and docking conceptualization and Scottish team takes part of development of control algorithm. And both team validated the results. In Japanese team, [PERSON] initiated and managed all of this study project, and contributed of AUV conceptualization and investigation of AUV and docking system. [PERSON] supervised AUV and docking system. [PERSON] contributed conceptualization of AUV. [PERSON], [PERSON] and [PERSON] contributed the validation, and [PERSON] supervised in Japanese side. In Scottish side, [PERSON] managed the Scottish team, and [PERSON] supervised development of control algorithm. [PERSON] and [PERSON] contributed the development of control algorithm, such as conceptualization, formal analysis, Investigation, Methodology and Software. [PERSON] also contributed validation of the all of analysis result. The original manuscript was written by [PERSON], [PERSON] and [PERSON]. And all of authors reviewed and edited the manuscript. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Nippon Foundation, Grant Number 2019524843.  
**Institutional Review Board Statement:** Not Applicable.  
**Informed Consent Statement:** Not Applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.