Robust control of an underactuated surface vessel with thruster dynamics

In this paper a continuous periodic time-varying feedback law is proposed that exponentially stabilizes both the position and orientation of a surface vessel having only two actuators. To this end, a stability result for a class of homogeneous time-periodic systems is presented. The exponential stability provided by the proposed feedback law does not depend on exact knowledge of the model parameters, and is thus robust to model parameter uncertainty. The surface vessel model considered is nonlinear and describes both the dynamics and the kinematics of the surface vessel. Furthermore the actuator dynamics is included in the control design. Simulation results are presented.