Integral control on nonlinear spaces: two extensions

TL;DR

This paper extends integral control on nonlinear spaces to handle state-dependent biases and non-holonomic systems, enabling robust stabilization and steering in more complex scenarios.

Contribution

It introduces two novel extensions: robustness to state-dependent actuation bias and integral control for non-holonomic systems.

Findings

Robust stabilization of a pendulum at arbitrary angles.

Effective integral control for non-holonomic rigid body steering.

Demonstrated robustness against nonlinear and velocity biases.

Abstract

This paper applies the recently developed framework for integral control on nonlinear spaces to two non-standard cases. First, we show that the property of perfect target stabilization in presence of actuation bias holds also if this bias is state dependent. This might not be surprising, but for practical purposes it provides an easy way to robustly cancel nonlinear dynamics of the uncontrolled plant. We specifically illustrate this for robust stabilization of a pendulum at arbitrary angle, a problem posed as non-trivial by some colleagues. Second, as previous work has been restricted to systems with as many control inputs as configuration dimensions, we here provide results for integral control of a non-holonomic system. More precisely, we design robust steering control of a rigid body under velocity bias.