Flat systems, flat information and an application to attitude control

In this work we consider a class of nonlinear flat systems evolving on the tangent bundle TG of a Lie-Group G. For this class of systems every set of local coordinate functions is a local flat output. As a consequence, the canonical projection of TG on G acts as a global flat output, called flat information. It is shown that a stabilization control law for such a system induces canonically a control law for tracking assintotically any desired trajectory on G. It is show that ε(t) = g(t)h
⁻¹
(t) is a "global" tracking error information, where g(t) is the desired trajectory on G and g(t) is the actual position. An application of these results to attitude control is presented. Based on a robust (nonlinearizing) global stabilization strategy, a control law for tracking assintotically a desired trajectory on SO(3) is designed. Some computer simulations of the closed loop system are presented.