This paper deals with numerical simulations using the nonlinear model predictive control (NMPC) for the route tracking problem of an autonomous underwater vehicle (AUV) in two-dimensional space. The NMPC algorithm minimizes the errors of the target heading angle or the target cruising speed. At the same time, the NMPC changes control signals in multiple constraints, such as maximum propeller speed and rudder angle. The Otsuka's continuation/generalized minimal residual (C/GMRES) algorithm, a kind of the NMPC, was introduced here to carry out the optimization calculation in short sampling period. Firstly, the computation speed of the NMPC was measured and it was verified that this algorithm is effective for the use of an on-board computer. Secondly, traveling routes and control signals using the NMPC and the PI control were compared. It was clarified that the AUV using the NMPC algorithm followed the target velocity with less fluctuation of the propeller thrust. In the numerical simulations, it was demonstrated that the NMPC method is useful for controlling AUVs.
