High-Order Averaging on Lie Groups and Control of an Autonomous Underwater Vehicle

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dc.contributor.authorLeonard, Naomi E.en_US
dc.contributor.authorKrishnaprasad, Perinkulam S.en_US
dc.contributor.departmentISRen_US
dc.date.accessioned2007-05-23T09:54:28Z
dc.date.available2007-05-23T09:54:28Z
dc.date.issued1993en_US
dc.description.abstractIn this paper we extend our earlier results on the use of periodic forcing and averaging to solve the constructive controllability problem for drift-free left-invariant systems on Lie groups with fewer controls than state variables. In particular, we prove a third-order averaging theorem applicable to systems evolving on general matrix Lie groups and show how to use the resulting approximations to construct open loop controls for complete controllability of systems that require up to depth- two Lie brackets to satisfy the Lie algebra controllability rank condition. The motion control problem for an autonomous underwater vehicle is modeled as a drift-free left-invariant system on the matrix Lie group SE (3). In the general case, when only one translational and two angular control inputs are available, this system satisfies the controllability rank condition using depth-two Lie brackets. We use the third-order averaging result and its geometric interpretation to construct open loop controls to arbitrarily translate and orient an autonomous underwater vehicle.en_US
dc.format.extent1103553 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/5415
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; TR 1993-70en_US
dc.subjectgeometric controlen_US
dc.subjectkinematicsen_US
dc.subjectnonlinear systemsen_US
dc.subjectroboticsen_US
dc.subjectIntelligent Servomechanismsen_US
dc.titleHigh-Order Averaging on Lie Groups and Control of an Autonomous Underwater Vehicleen_US
dc.typeTechnical Reporten_US

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