High-order averaging on lie groups and control of an autonomous underwater vehicle

Naomi Ehrich Leonard, P. S. Krishnaprasad

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations


In this paper, extending our previous work on averaging on Lie groups, we present a third-order averaging theorem for periodically forced, drift-free, left-invariant systems on Lie groups and use it to demonstrate constructive controllability for a class of problems. Specifically, this class includes the case for which depth-two Lie brackets are needed for complete controllability. We illustrate this via an example on the group SE(3), appropriate as a model of kinematic control of an underwater vehicle.

Original languageEnglish (US)
Pages (from-to)157-162
Number of pages6
JournalProceedings of the American Control Conference
StatePublished - Dec 1 1994
Externally publishedYes
EventProceedings of the 1994 American Control Conference. Part 1 (of 3) - Baltimore, MD, USA
Duration: Jun 29 1994Jul 1 1994

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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