Stabilization of a nonlinear underactuated hovercraft

We consider the control of a hovercraft, having only two control inputs with three degrees of freedom. The model is obtained from equations of a simplified ship which is nonlinear and underactuated. Using a coordinate transformation the model is given by polynomial equations which describe its kinematics and dynamics. Two control laws are proposed. The first one controls the velocity of the hovercraft. The other one stabilizes both its position and the (underactuated) side velocity and provides global convergence to the origin. The convergence analysis is based on a Lyapunov approach.