Practical stabilization of driftless systems on Lie groups

A general control design approach for the stabilization of controllable driftless nonlinear systems on Lie groups is presented. The approach is based on the concept of transverse functions, the existence of which is equivalent to the system's controllability. Its outcome is the practical stabilization of any trajectory, i.e., not necessarily a solution of the control system in the state space. The approach can be used for an arbitrary controllable driftless system, via homogeneous approximation and lifting of the control vector fields.