Abstract: Traditionalformationkeepingorbitdesignisbasedonlinearrelativemotionmodelwhichwillleadtomorefuelconsumptionduringlongtermspacecraftformationflying.Firstly,theperiodicconditionandperiodicsolutionwereobtainedbysolvingtheellipticalorbitrelativemotionmodelconsideringthesecondordernonlineartermswithperturbationapproach.TheperiodicsolutionobtainedwasthenusedasthereferenceorbitofaPDcontrollawforformationkeepingbasedontheLyapunovstabilitytheory.Simulationresultsshowthattheperiodicsolutionbasedonthenonlinearrelativemotionmodelofellipticalorbitismoreaccuratethanthatbasedonlinearrelativemotionmodelofellipticalorbit.Andtheformationmaintaincontrollawwithperiodicreferenceorbitbasedonnonlinearmodelcansavemuchmorefuelcomparedwiththatbasedonthelinearmodel.

Key words: Perturbationapproach, Periodicsolution, Nonlinearrelativemotionmodel, Ellipticalorbit, Formationflying, Maintaincontrol, Spacecraft