Dynamics and Passive Control for Formation Keeping Between ShenZhou Spaceship and its Micro-satellite

BX-1, a micro-satellite made by the Chinese Academy of Sciences, was released successfully from the Sh enZhou VII spaceship (SZ-VII) on 27 September, 2008 and subsequently inserted into a relative elliptic orbit with respect to SZ-VII Orbital Module on 5 October 2008. Due to its 1-kg propellant limitation, BX-1 implemented one f ormation keeping maneuver only before it drifted away from S Z-VII. In order to employ BX-1 as a fly-around micr o-satellite for in-orbit service, we proposed a high-efficiency con troller with optimized fuel consumption for long-te rm stable formation keeping. After a brief review of dynamics for formation flying and the flight demonstration results of BX-1, a passive control method based on a new set of modifi ed Hill equations is developed. With respect to the SZ-VII-centered local vertical local horizontal frame, the relative drifting velocity and acceleration between two spa cecrafts in the along-track direction are derived analytically in t erms of the difference in the mean orbital elements of the two spacecrafts with the consideration of non-spherical Earth gravity and atmospheric drag perturbation. A limit-cycles controller is established to control a virtual center of formation flying and formation ke eping is realized by the attitude control of BX-1 to take full advantage of the diffe rent surface-mass ratio between two spacecrafts. Fu rthermore, a general form combined the passive control with the impulse control is given so that it is also availab le when the large delta-V maneuver or the time-constrained orbit tran sfer is required.