The undersea environment is generally still a mystery for the human race, although it has been with us for a long time. To explore under the sea, the underwater glider is the efficient equipment capable of sustainable operation for several months. For faster and longer duration performance, a new design of underwater glider (UG) shaping ray type is proposed. To have the shortest settling time, a new design of time-optimal trajectory (TOT) for controlling the states of the ray-type hybrid underwater glider (RHUG) is proposed. And for the stable flight control, a robust adaptive controller is designed for the RHUG with unknown parameters and environmental disturbances. The heading dynamics of the RHUG is presented with linear and quadratic damping. A closed form solution of the heading dynamics is realized for designing the time-optimal trajectory. The conventional and super-twisting sliding mode control will be constructed for tracking this trajectory. The tracking performance considering the disturbance effect will be discussed in simulations. For identification of unknown parameters of the system, the adaptive control is designed and implemented by the heading experiment. The RHUG uses the net buoyancy force for gliding under the water, so the depth control is essential. In this dissertation, a robust control algorithm with TOT will be carried out for the heaving motion using a hybrid actuation of the buoyancy engine and the propeller. The net buoyancy force with a constant rate is generated by the buoyancy engine for both descending and ascending motion. And the second actuator for the depth control is the propeller with quick response in producing thrusting force. To apply the robust control with TOT, the control input is designed for the buoyancy engine and thruster individually. And finally, the robust control with TOT using the buoyancy engine and thruster is simulated with consideration of external disturbances. When the RHUG is the underactuated system, a robust adaptive control is designed for the RHUG dynamics based on Lyapunov’s direct method using the backstepping and sliding mode control techniques. The performance of this controller is simulated for gliding motion and depth control with unknown parameters and bounded disturbances.