Application of a new Lyapunov function to global adaptive attitude tracking

A new family of strict global Lyapunov functions for mechanical systems is applied to achieve an adaptive version of the inverse dynamics algorithm in the case when the inertial parameters of the rigid body are not known a priori. Specifically, the author considers the problem of tracking a desired signal on a non-Euclidean space-the Lie group SO(3)-via a completely actuated mechanical system with all states directly available. The resulting closed-loop adaptive system is shown to be stable, and the rigid-body phase errors are shown to converge to the limit trajectories of the nonadaptive algorithm