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dc.contributor.authorAmiss, David Scott Cameron
dc.contributor.otherQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))en
dc.date2012-12-18 20:53:43.272en
dc.date.accessioned2013-01-03T19:31:15Z
dc.date.issued2013-01-03
dc.identifier.urihttp://hdl.handle.net/1974/7703
dc.descriptionThesis (Ph.D, Chemical Engineering) -- Queen's University, 2012-12-18 20:53:43.272en
dc.description.abstractThe subject of this thesis is the motion planning algorithm known as the continuation method. To solve motion planning problems, the continuation method proceeds by lifting curves in state space to curves in control space; the lifted curves are the solutions of special initial value problems called path-lifting equations. To validate this procedure, three distinct obstructions must be overcome. The first obstruction is that the endpoint maps of the control system under study must be twice continuously differentiable. By extending a result of A. Margheri, we show that this differentiability property is satisfied by an inclusive class of time-varying fully nonlinear control systems. The second obstruction is the existence of singular controls, which are simply the singular points of a fixed endpoint map. Rather than attempting to completely characterize such controls, we demonstrate how to isolate control systems for which no controls are singular. To this end, we build on the work of S. A. Vakhrameev to obtain a necessary and sufficient condition. In particular, this result accommodates time-varying fully nonlinear control systems. The final obstruction is that the solutions of path-lifting equations may not exist globally. To study this problem, we work under the standing assumption that the control system under study is control-affine. By extending a result of Y. Chitour, we show that the question of global existence can be resolved by examining Lie bracket configurations and momentum functions. Finally, we show that if the control system under study is completely unobstructed with respect to a fixed motion planning problem, then its corresponding endpoint map is a fiber bundle. In this sense, we obtain a necessary condition for unobstructed motion planning by the continuation method.en_US
dc.languageenen
dc.language.isoenen_US
dc.relation.ispartofseriesCanadian thesesen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectgeometric control theoryen_US
dc.subjectmotion planningen_US
dc.subjectcontinuation methoden_US
dc.subjectpath-lifting equationsen_US
dc.subjectsingular controlsen_US
dc.subjectnonlinear control theoryen_US
dc.titleObstructions to Motion Planning by the Continuation Methoden_US
dc.typeThesisen_US
dc.description.restricted-thesisThe document contains original results which have not been published. We would like these results to appear in journal articles first, and on QSpace second.en
dc.description.degreePh.Den
dc.contributor.supervisorGuay, Martinen
dc.contributor.departmentChemical Engineeringen
dc.embargo.terms1825en
dc.embargo.liftdate2018-01-02


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