On quaternion-based attitude control and the unwinding phenomenon

• Published in: Proceedings of the 2011 American Control Conference pp. 299 - 304
• Main Authors: Mayhew, Christopher G., Sanfelice, Ricardo G., Teel, Andrew R.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.06.2011
• Subjects: Aerospace electronics; Asymptotic stability; Attitude control; Heuristic algorithms; Quaternions; Stability analysis; Trajectory
• ISBN: 1457700808; 9781457700804
• ISSN: 0743-1619
• DOI: 10.1109/ACC.2011.5991127

The unit quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, quaternion-based feedbacks require an additional mechanism that lifts a continuous attitude path to the unit quaternion space. When this mechanism is memoryless, it has a limited domain where it remains injective and leads to discontinuities when used globally. To remedy this limitation, we propose a hybrid-dynamic algorithm for lifting a continuous attitude path to the unit quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate quaternion-based controllers and their asymptotic stability properties (obtained in the unit-quaternion space) to the actual rigid-body-attitude space. We also show that when quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a unit-quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets.