Integral Control on Lie Groups

TL;DR

This paper generalizes integral control to systems on Lie groups, enabling bias cancellation in nonlinear configuration spaces, with applications demonstrated in 3D motion control.

Contribution

It introduces a novel definition of integral action for Lie group systems, extending classical control techniques to nonlinear configuration spaces.

Findings

Integral control cancels constant bias in velocity and torque inputs.

The method is applicable to fully actuated systems on Lie groups.

Demonstrated effectiveness in 3D motion control applications.

Abstract

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.