The 3-dimension straight-line tracking control is proposed for an underactuated autonomous underwater vehicle
by using the cascaded approach of nonlinear systems. The 3-dimension straight-line tracking model is divided into the
vertical tracking model and horizontal tracking model which is perturbed by the former. The desired pitch angle and yaw
angle are designed, and the two planar tracking models are divided into the position tracking models and the euler angles
tracking models in the cascaded structures. The pitch and yaw angles tracking control laws are designed based on the pitch
and yaw angles tracking models respectively. The nonlinear cascaded system theory is used to strictly prove the global K-
exponential stability of the whole tracking system without any assumptions on the underactuated sway and heave motions
used by the former researches. Simulation results show the effectiveness of the proposed controller.