Analytical Solution of Time-Optimal Trajectory for Heaving Dynamics of Hybrid Underwater Gliders

Abstract

Underwater vehicles have capacity limits for control inputs, within which their time-optimal trajectories (TOTs) can be formulated. In this study, the fastest trajectory for the depth control of a hybrid underwater glider (HUG) was found using buoyancy engines and propellers individually, and the decoupled heave dynamics of the HUG were defined using quadratic hydrodynamic damping. Because buoyancy engines always run at slow speeds, the buoyancy force was formulated based on the constant force rate of the engine. It was assumed that the nominal value of the heave dynamics parameters could be estimated; therefore, the analytical solution of heave dynamics could be formulated using the thrusting saturation and constant buoyancy force rate. Then, the shortest trajectory for depth control of the HUG could be established while considering the actuator saturation. To verify the effectiveness of the TOT in HUG heave dynamics, extensive tracking control simulations following the TOT were conducted. It was found that the proposed TOT helps the HUG reach the desired depth in the shortest arrival time, and its robust depth control showed good tracking performance in the presence of external bounded disturbances.