Dynamics and control of spacecraft formation flying in three-body trajectories

This paper addresses the problem of relative position control of spacecraft formation flying (SFFj utilizing the framework of the circular restricted three body problem (CR3BP) with the Sun and Earth as the primary gravitational bodies. The use of CR3BP trajectories necessitate the development of specialized tools. Particularly, the general, non-restrictive equations of motion are used. To generate a model of the relative spacecraft dynamics, a linearization is performed relative to an arbitrary non-Keplerian reference trajectory, so that linear time-varying differential equations result. It is rigorously proved that the open-loop linearized SFF dynamics is unstable but controllable. It is further proposed to use continuous plasma electric propulsion to control the formation. A time-varying continuous linear-quadratic control law, which inherently offers both stationkeeping and formationkeeping capabilities is then developed. A complete internal disturbance model is used, rendering a robust disturbance rejection performance.