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dc.contributor.advisorCelledoni, Elenanb_NO
dc.contributor.authorKleivedalen, Anne Marinb_NO
dc.date.accessioned2014-12-19T13:19:25Z
dc.date.available2014-12-19T13:19:25Z
dc.date.created2014-05-21nb_NO
dc.date.issued2014nb_NO
dc.identifier718667nb_NO
dc.identifierntnudaim:10454nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/247225
dc.description.abstractGeometric numerical integration schemes have been studied for rigid body attitudecontrol problems. We consider symplectic integrators and present a Lie group varia-tional integrator and a discrete gradient method. The two methods preserve some ofthe geometric properties of rigid body dynamics, such as symplecticity, conservationof first integrals and the Lie group structure of the rotation matrices. We presentsome numerical experiments for an uncontrolled 3D pendulum where we investigatethe geometric properties of the two methods.The main part of this thesis concerns rigid body attitude control. We discuss theconcept of passivity and present a feedback control that rotates the rigid body froman initial state to a desired state. Passivity is a property that can be related to en-ergy conservation, and the feedback system presented in this paper is input-outputpassive. This means that the feedback system does not generate energy. Throughseveral numerical experiments, we investigate to which extent the Lie group varia-tional integrator and the discrete gradient method preserve the passivity condition.Our experiments indicate that the discrete gradient method preserves a discrete ver-sion of the passivity condition and for the Lie group variational integrator, the errorin the preservation of passivity is small. We compare our results with a Lie groupRunge-Kutta method and we observe that the method fails to preserve the discretepassivity condition for large step sizes.Lastly, we look at optimal attitude control. We present a time optimal attitudecontrol problem for a rigid body where the objective is to minimize the maneuvertime. The optimal control problem is formulated as a discrete-time optimizationproblem using a Lie group variational integrator. We present some numerical exper-iments to visualize the time optimal maneuver for a rigid body, where the controlinput is bounded.nb_NO
dc.languageengnb_NO
dc.publisherInstitutt for matematiske fagnb_NO
dc.titleRigid Body Attitude Controlnb_NO
dc.typeMaster thesisnb_NO
dc.source.pagenumber93nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for naturvitenskap og teknologi, Institutt for fysikknb_NO


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