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Exact solutions to the closed loop kinematics of an almost globally stabilizing feedback law on SO(3)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.ORCID iD: 0000-0003-0177-1993
2012 (English)In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, 2274-2279 p.Conference paper, Published paper (Refereed)
Abstract [en]

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.
Series
Proceedings of the IEEE Conference on Decision and Control, ISSN 0191-2216
Keyword [en]
Rigid-Body Attitude, Fixed Torques, Axial Torque, Tracking, Subject
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-118907DOI: 10.1109/CDC.2012.6426678ISI: 000327200402106Scopus ID: 2-s2.0-84874274479ISBN: 978-1-4673-2066-5 (print)OAI: oai:DiVA.org:kth-118907DiVA: diva2:609058
Conference
51st IEEE Conference on Decision and Control, CDC 2012; Maui, HI; United States; 10 December 2012 through 13 December 2012
Note

QC 20130304

Available from: 2013-03-04 Created: 2013-03-04 Last updated: 2013-12-19Bibliographically approved

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Hu, Xiaoming

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