Averaging for attitude control and motion planning

Naomi Ehrich Leonard, P. S. Krishnaprasad

Research output: Chapter in Book/Report/Conference proceedingConference contribution

30 Scopus citations


In this paper we show how to use periodic forcing to solve the constructive controllability problem for drift-free, left-invariant systems on matrix Lie groups with fewer controls than states. In particular, we prove a second-order averaging theorem applicable to systems evolving on general matrix Lie groups. Using this theorem, we show how to construct open loop controls for complete controllability of systems that require up to depth-one Lie brackets to satisfy the Lie algebra controllability rank condition. We apply these results to the attitude control problem with only two controls available and to the unicycle motion planning problem.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherPubl by IEEE
Number of pages7
ISBN (Print)0780312988
StatePublished - Dec 1 1993
Externally publishedYes
EventProceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4) - San Antonio, TX, USA
Duration: Dec 15 1993Dec 17 1993


OtherProceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4)
CitySan Antonio, TX, USA

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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