Stabilizing feedback control for a nonholonomic underwater vehicle

A time varying stabilizing feedback controller is constructed for an autonomous underwater vehicle by employing a Lie bracket extension of the original system. The synthesis method is general, in that it applies to a large class of drift free, completely controllable systems, for which the associated controllability Lie algebra is finite dimensional. The approach does not rely on any specific choice of a Lyapunov function. The resulting feedback law is a composition of a standard stabilizing feedback control for the extended system and a periodic continuation of a parametrised solution to an open loop, finite horizon control problem stated in logarithmic coordinates.