Modeling and Optimal Three-dimensional Trajectory Tracking for an Autonomous Underwater Vehicle

This paper introduces a new approach for designing a simplified control law, which controls an autonomous underwater vehicle (AUV) to track a given 3D trajectory. To get a Linear Time Variant (LTV) state space model, the 6 degrees of freedom (6DOF) dynamics and kinematics model of the AUV is linearized about the given desired 3D trajectory it needs to track. A linear quadratic regulator (LQR) is designed based on the linear model and is applied to the nonlinear model to track the desired trajectory. Simulation results show that the linear control law provides satisfactory results when applied to the nonlinear model for tracking basic trajectory maneuvers: helix, saw-tooth path, and 3D Dubin's path.