Global Exponential Attitude Tracking Controls on SO(3)

TL;DR

This paper develops robust, globally exponentially stable attitude tracking control systems on SO(3) for rigid bodies, avoiding singularities and ambiguities, with demonstrated numerical effectiveness.

Contribution

It introduces the first robust, globally exponentially stable attitude tracking controllers directly on SO(3), using hybrid schemes and integral terms for disturbance rejection.

Findings

Achieves almost semi-global exponential stability

Extends to global exponential stability with hybrid control

Demonstrates robustness against fixed disturbances

Abstract

This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. It is extended to achieve global exponential stability by using a hybrid control scheme based on multiple configuration error functions. They are further extended to obtain robustness with respect to a fixed disturbance using an integral term. The resulting robust, global exponential stability for attitude tracking is the unique contribution of this paper, and these are developed directly on the special orthogonal group to avoid singularities of local coordinates, or ambiguities associated with quaternions. The desirable features are illustrated by numerical examples.