Exact solutions to the closed loop kinematics of an almost globally stabilizing feedback law on SO(3)
2012 (English)In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, 2274-2279 p.Conference paper (Refereed)
We propose a kinematic control law that solves the problem of stabilizing the attitude of a fully actuated rigid body to a desired rest attitude. The control law is designed on the special orthogonal group SO(3), thereby avoiding complications due to the representational singularities of local parametrizations and the unwinding phenomenon associated with global many-to-one parametrizations. We prove almost global stability, i.e. asymptotical stability from all initial conditions except for a set of zero measure. The proposed control law decouples the closed loop kinematics, allowing us to solve the state equations exactly for the rigid body attitude as a function of time, the initial conditions, and two gain parameters. The exact solutions provide an understanding of the transient behaviour of the system and can e.g. be used to tune the gain parameters. The geometric flavor of these ideas is illustrated by simulation.
Place, publisher, year, edition, pages
IEEE , 2012. 2274-2279 p.
, Proceedings of the IEEE Conference on Decision and Control, ISSN 0191-2216
Rigid-Body Attitude, Fixed Torques, Axial Torque, Tracking, Subject
IdentifiersURN: urn:nbn:se:kth:diva-118907DOI: 10.1109/CDC.2012.6426678ISI: 000327200402106ScopusID: 2-s2.0-84874274479ISBN: 978-1-4673-2066-5OAI: oai:DiVA.org:kth-118907DiVA: diva2:609058
51st IEEE Conference on Decision and Control, CDC 2012; Maui, HI; United States; 10 December 2012 through 13 December 2012
QC 201303042013-03-042013-03-042013-12-19Bibliographically approved