Optimal attitude maneuvers in the presence of prohibited directions

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dc.date.accessioned2023-08-14T13:17:55Z
dc.date.available2023-08-14T13:17:55Z
dc.date.issued2023-05-31
dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.identifierdoi:10.17170/kobra-202307218446
dc.identifier.urihttp://hdl.handle.net/123456789/14987
dc.language.isoeng
dc.relation.doidoi:10.1002/pamm.202200179
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subject.ddc620
dc.subject.ddc660
dc.subject.swdWeltraumteleskopger
dc.subject.swdRichtungger
dc.subject.swdÄnderungger
dc.subject.swdGeschwindigkeitger
dc.titleOptimal attitude maneuvers in the presence of prohibited directionseng
dc.typeAufsatz
dc.type.versionpublishedVersion
dcterms.abstractWe consider the problem of realigning a space telescope from one observation target to the next in the presence of prohibited directions. More specifically, we want to steer the space telescope – modelled as a gyrostat – from an initial attitude at rest to a final attitude at rest within a fixed time interval. During the motion, the line of sight of the telescope must be kept away from forbidden directions towards bright objects like the sun, moon or earth due to power or thermal requirements. The kinematics of the spacecraft motion are governed by a differential equation on the rotation group SO(3). Treating the angular velocities as control variables, this equation takes the form of a controlled dynamical system. To ensure reorientation maneuvers satisfying these pointing constraints, we introduce a cost functional penalizing proximity of the line of sight of the telescope to any of the forbidden directions. Furthermore, we include penalty terms which provide a smooth motion of the satellite and ensure the execution of a rest-to-rest maneuver. The chosen cost functional is minimized over all possible trajectories of the controlled dynamical system between the prescribed initial and target attitudes, which leads to an optimal control problem on SO(3), which is solved by applying a version of Pontryagin's Maximum Principle tailor-made for optimal control problems on Lie groups. Parametrizing SO(3) in terms of Cardan angles, the solution is formulated as a boundary-value problem on Euclidean space and hence can be solved numerically by conventional methods. The existence of two first integrals is established and exploited to reduce the computational effort. The applicability of this approach is shown in concrete examples.eng
dcterms.accessRightsopen access
dcterms.creatorAilabouni, David
dcterms.creatorMeister, Andreas
dcterms.creatorSpindler, Karlheinz
dcterms.source.articlenumbere202200179
dcterms.source.identifiereissn:1617-7061
dcterms.source.issueIssue 1
dcterms.source.journalProceedings in Applied Mathematics and Mechanics (PAMM)eng
dcterms.source.volumeVolume 23
kup.iskupfalse

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