I. Introduction
It is a well known fact that because of Brocketts Theorem [1] the point stabilization problem of an underactuated 3D floating rigid body cannot be solved by time-invariant, smooth feedback. As for many other systems affected by Brocketts negative result, either time-varying or discontinuous solutions must be considered. Both approaches have advantages and disadvantages; while the convergence rate may be exponential in both frameworks, time-varying solutions are in general smooth and globally defined, but the resulting paths may exhibit cusps or very unnatural and perhaps practically unacceptable oscillations due to the trigonometric time dependence of the controller. On the other hand with discontinuous control solutions it may be much easier to satisfy “practical” constraints as driving in only one forward direction avoiding cusps and converging on the target on a null curvature path at the expense of isolated discontinuity points (including the target). Time-varying solutions for both the kinematic and dynamic model of an underactuated underwater vehicle have been proposed in [2] and [3].