Spacecraft formation-keeping using closed-form orbit propagator and optimization technique

In this paper, a simple method for modeling the relative orbital motion of and formation-keeping control strategy for multiple spacecraft flying is presented. Power series and trigonometry functions are used to express the relative orbital motion between the member spacecraft. Their coefficients are obtained using least square regression such that the difference between the exactly and numerically integrated position vector, and the approximate one obtained from the closed-form propagator, is minimized. Then, this closed-form orbit propagator and optimization technique is used to plan a series of impulsive maneuvers, which maintain the formation configuration within the specified limit. As an example, formation-keeping of four spacecraft is selected. The motion projected onto the local horizontal plane (along-and cross-track plane) is a circle where the leader satellite is located at the center and other follower satellites are positioned circumferentially. Not only the radial distance between the leader and the followers, but also the relative phase angles between the followers, are controlled. Results from nonlinear simulation are presented.