# Integral Control on Lie Groups

arXiv: https://arxiv.org/abs/1410.7614 · HTML: https://mlsanity.com/paper/1410.7614/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2014.

## Built on by (most cited first, 1 of 1)

- [Geometric Fault-Tolerant Neural Network Tracking Control of Unknown Systems on Matrix Lie Groups](https://mlsanity.com/paper/2505.04725/) (2025)

## Abstract (arXiv)

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.