Suppression of Formation Flying Deviation in Near-Circular Orbits under the J₂ Perturbation

Abstract

Station-keeping maneuvers are necessary for the precise formation flying of spacecraft, because various disturbing forces deviate their relative motion. The objective of this study is to derive a two-impulsive control law for the formation flying of two spacecraft in an orbit with a small eccentricity under the J₂ perturbation, especially one that suppresses the relative position deviation during the control period. Because of the J₂ perturbation, the relative position and velocity have secular terms. However, it is possible to compensate for the secular terms of the relative motion and create an artificial periodic motion by conducting the impulsive control. In this study, a state transition matrix of the relative motion based on the osculating orbital elements with the first order of J₂ is utilized, in order to calculate the secular and periodic terms of the relative motion, to derive an impulsive control law, and to determine the appropriate initial conditions for suppressing the deviation of formation flying. The numerical results of the proposed control law are compared with those of another method, which is based on the relative mean orbital elements, and it is shown that the proposed control law successfully suppresses the formation deviation.