Time-Optimal Trajectory Design for Heading Motion of the Underwater Vehicle

Underwater vehicles are a powerful tool that can assist oceanologists with measuring the state of oceans on a large scale. The heading control is essential for the underwater vehicle to follow a specific path. This study describes the general decoupled dynamics of underwater vehicles, which is a nonlinear second-order differential equation considering linear and quadratic damping hydrodynamics. A novel aspect of this study is the development of a new analytical solution for the second-order nonlinear differential equation, which involves the heading motion of the underwater vehicle. In this study, the time-optimal trajectory is formulated as the closed-form solution for the heading dynamics of the underwater vehicle. The concept of this trajectory is based on the shortest arrival time when the maximum force from the thrusters is applied to the underwater vehicle. Finally, a simulation of the time-optimal trajectory and evaluation of the robustness of the controller were demonstrated in order to verify the effectiveness of the proposed trajectory for controlling underwater vehicles.