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

In this paper, a simple method for modeling the relative orbital motion of multiple spacecraft and their formation-keeping control strategy is presented. Power series and trigonometric 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 exact numerically integrated position vector and the approximate vector 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 a specified limit. As an example, formation-keeping of four spacecraft is investigated. The motion projected onto the local horizontal plane (along- and cross-track plane) is a circle with the leader satellite located at its center and follower satellites positioned circumferentially. The radial distance between the leader and the followers, and the relative phase angles between the followers are controlled. Results from the nonlinear simulation are presented.