Generalized spacecraft formation design through exploitation of quasi-periodic tori families

This work establishes a general-purpose method for designing passive spacecraft formations by characterizing the vehicles’ motion on quasi-periodic tori. First, a torus centric formulation of relative motion is presented. Then, relative distance between spacecraft is examined for two spacecraft on the same torus separated by small angle displacements. This examination motivates the creation of a new design tool known as an ellipse map. This new tool is then applied to several systems. The systems of interest were the averaged J₂ problem and the circular restricted three body problem (CR3BP). In the CR3BP, both Lissajous and Quasi-halo formations were considered. The ellipse map proved to be a valuable tool for designing formations in all cases. The creation of this generalized approach towards understanding and exploiting bounded relative motion is a critical next step for formation flight research. Whereas most modern studies solve relative motion problems in particular environments, the techniques discussed in this paper can be applied to a wide variety of systems.