Underactuated point stabilization using predictive models with application to marine vehicles

Point stabilization of an underactuated vehicle is most often accomplished using a periodic time-varying control law, resulting in oscillatory trajectories. We present a two-stage algorithm that achieves point stabilization without oscillatory behavior. A low-level controller regulates as many outputs as available control inputs. The unregulated states are generally nonzero when the regulated states have converged, but for certain initial conditions the vehicle arrives at the origin of the state space using only the low-level controller. This set of initial conditions forms a manifold in the state space. A separate Lyapunov-based manifold convergence controller drives the vehicle states to this manifold so that the low-level controller can bring the vehicle to the origin. We provide experimental results of this two-stage algorithm applied to a 1.25-meter ship model.