Geometric Tracking Control of the Attitude Dynamics of a Rigid Body on SO(3)

TL;DR

This paper introduces a globally valid geometric control method on SO(3) for rigid body attitude tracking, ensuring robust performance during large maneuvers without ambiguities of traditional representations.

Contribution

It develops a new attitude control approach on SO(3) that guarantees global tracking performance and stabilizes attitude without inertia knowledge in certain cases.

Findings

Guarantees uniform tracking performance for large initial errors

Achieves attitude stabilization without inertia matrix knowledge in fixed commands

Validated by numerical simulations demonstrating effectiveness

Abstract

This paper provides new results for a tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. By selecting an attitude error function carefully, we show that the proposed control system guarantees a desirable tracking performance uniformly for nontrivial rotational maneuvers involving a large initial attitude error. In a special case where the desired attitude command is fixed, we also show that the attitude dynamics can be stabilized without the knowledge of an inertia matrix. These are illustrated by numerical examples.