Quay walls are important structures that keep the water in harbours and canals within their bounds, and accommodate large infrastructure like roads or ship-handling structures on top of them. Due to their importance it is critical that they do not fail or collapse. Inspections are done to prevent this, as a better knowledge of the state of quay walls can help in predicting future behaviour of the quay walls. However, current inspection methods are not satisfactory and can be improved upon. This thesis proposes the Raybot. This is an Autonomous Underwater Vehicle that can move along the quay walls like rays swim along the walls of their aquariums. The design of the Raybot is presented, which keeps in mind the requirements that follow logically from the quay wall inspection mission. This resulted in a rectangular robot with an outward modular frame. The thrusters, on-board computers, and sensors can be mounted on the inside. Next, a Model Predictive Controller is proposed for the motion control of the Raybot. For this, the extensive kinematics and kinetics of the Fossen model are explained. The parameters of this Fossen model are estimated for the Raybot using various methods. A Model Predictive Controller is formulated for Autonomous Underwater Vehicles and implemented in the Robot Operating System 2. A physical and visual representative simulation environment is set up, which can simulate the motion of the Raybot. This is used to assess the path tracking behaviour of the Raybot. The Model Predictive Controller is compared to a cascaded PID controller by path tracking of a zig-zag path along the quay wall. An analysis of the tuning parameters of the Model Predictive Controller is presented. The Model Predictive Controller outperforms the cascaded PID controller on both the Mean Squared Error of the path tracking error and the completion time of the inspection mission, whilst adhering to constraints set by the minimum and maximum velocity of the Raybot and the minimum and maximum thruster inputs. This improved performance leads to a higher quality of the inspections, as they can be done more up-close, as well as a higher quantity of the inspections, as more inspections can be done in the same time. For future work it is recommended to estimate some parameters of the model on a real robot, as well as testing the Model Predictive Controller on a real robot in a tank. This will showcase the performance of the motion controller in an even more realistic scenario.