Nilpotent Approximation and Nilpotentization for Under-actuated Systems on Matrix Lie Groups 1

This paper develops a method for constructing nilpo-tent approximations for local representations of invariant systems on matrix Lie groups via a simple operation on the structure constants of the associated Lie algebra. The crucial role such nilpotent approximations play for the problem of feedback nilpotentization is discussed. The presented ideas are illustrated with an example modeling the kinematics of an under-actuated rigid body.