Nonlinearcontrollabilityandattitudestabilizationarestudiedfortheunderactuatednonholonomicdynamicsofarigidspacecraftwithonevariable-speedcontrolmomentgyro(VSCMG),whichsuppliesonlytwointernaltorques.Nonlinearcontrollabilitytheoryisusedtoshowthatthedynamicsarelocallycontrollablefromtheequilibriumpointandthuscanbeasymptoticallystabilizedtotheequilibriumpointviatime-invariantpiecewisecontinuousfeedbacklawsortime-periodiccontinuousfeedbacklaws.Specifically,whenthetotalangularmomentumofthespacecraft-VSCMGsystemiszero,anyorientationcanbeacontrollableequilibriumattitude.Inthiscase,theattitudestabilizationproblemisaddressedbydesigningakinematicstabilizinglaw,whichisimplementedthroughanonlinearproportionalandderivativecontroller,usingthegeneralizeddynamicinverse(GDI)method.Thesteady-stateinstabilityinherentintheGDIcontrolleriselegantlyavoidedbyappropriatelychoosingcontrolgains.Inordertoobtainthecommandgimbalrateandwheelaccelerationfromcontroltorques,asimplesteeringlogicisconstructedtoaccommodatetherequirementsofattitudestabilizationandsingularityavoidanceoftheVSCMG.Illustrativenumericalexamplesverifytheefcacyoftheproposedcontrolstrategy.
