  In this paper, we extend the popular integral control technique to systems
evolving on Lie groups. More explicitly, we provide an alternative definition
of "integral action" for proportional(-derivative)-controlled systems whose
configuration evolves on a nonlinear space, where configuration errors cannot
be simply added up to compute a definite integral. We then prove that the
proposed integral control allows to cancel the drift induced by a constant bias
in both first order (velocity) and second order (torque) control inputs for
fully actuated systems evolving on abstract Lie groups. We illustrate the
approach by 3-dimensional motion control applications.
