Initial conditions and fuel-optimal control for formation flying of satellites

@+-act : .:<t. .;_ .;i -J This paper dealswith;&e formulation and solution of the initial condition,. dl$mination and fuel-optimal control problem in re@$$l: to formation flying of satellites. Unlike the rela$ve station-keeping problem for satellites in the same tiiane, formation -flying entails the creation of proper out-of-plane relative motion such that the satellites in the formation satisfy some mission requirements. Two methods for determining initial conditions of a satellite (Deputy), given the initial conditions of the chief satellite, for formation flying without thrust for a long period, are presented. The first method matches the mean J,-induced angular drift rates of the two satellites, and the second method is based on imposing periodic boundary conditions on the relative position and velocity in a rotating coordinate system. A fuel-optimal impulsive thrusting scheme is developed to establish a formation. A fuel-optimal, low-thrust, variable Isp propulsion scheme is presented for orbit maintenance.