Exponential Stabilization of an Underactuated Surface Vessel

The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous nor discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessel is presented, and a continuous periodic timevarying feedback law is proposed. It is shown that this feedback law exponentially stabilizes the surface vessel to the origin, and this is illustrated by simulations. 1. Introduction Control of underactuated vehicles, i.e. vehicles where the control vector has lower dimension than the configuration vector, is a field of increasing interest. It has been studied by e.g. Byrnes and Isidori [1] who gave results on stabilizability of a class of underactuated vehicles. Leonard [4, 5] shows how open loop smallamplitude periodic time-varying forcing can be used to control both underactuated spacecraft and underwater vehicles. Morin et al. [8] present smooth time-varying feedb..