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Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups, Part II: A General Constructive Control Algorithm

dc.contributor.authorLeonard, Naomi E.en_US
dc.contributor.authorKrishnaprasad, Perinkulam S.en_US
dc.date.accessioned2007-05-23T09:56:08Z
dc.date.available2007-05-23T09:56:08Z
dc.date.issued1994en_US
dc.identifier.urihttp://hdl.handle.net/1903/5489
dc.description.abstractIn this paper we present a general algorithm for constructing open-loop controls to solve the complete constructive controllability problem for drift-free invariant systems on Lie groups that satisfy the Lie algebra controllability rank condition with up to ( p - 1) iterations of Lie brackets, p = 1,2,3. Specifically, given only the structure constants of the given system, an initial condition Xi, a final condition Xf and a final time tf, the algorithm specifies open-loop, small (e) amplitude sinusoidal controls such that the system starting from Xi, reaches Xf at t = tf, with O (ep) accuracy. The algorithm is based on the formulas and geometric interpretation of the average approximations to the solution given in Part I to this paper. To illustrate the effectiveness of the algorithms, we apply it to three problems: the spacecraft attitude control problem with only two controls available, the unicycle motion planning problem and the autonomous underwater vehicle motion control problem with only three controls available.en_US
dc.format.extent408314 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; TR 1994-9en_US
dc.subjectgeometric controlen_US
dc.subjectkinematicsen_US
dc.subjectnonlinear systemsen_US
dc.subjectroboticsen_US
dc.subjectIntelligent Servomechanismsen_US
dc.titleMotion Control of Drift-Free, Left-Invariant Systems on Lie Groups, Part II: A General Constructive Control Algorithmen_US
dc.typeTechnical Reporten_US
dc.contributor.departmentISRen_US


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