Orbital formation control of multiple spacecraft

Spacecraft dynamics derived from the solutions of Hill's equations have an amazing simple geometric shape. In this paper, the desired formation geometry in 2D is based on the solution of the linear, unperturbed relative motion equations. Distinctly, by a linear transformation on along-track axis, the coplanar spacecraft cluster will be seen as an equiangular formation. The control law is performed via the artificial potential approach. Furthermore, stability analysis using LaSalle's invariant set theorem guarantees that the formation keeping will be maintained successfully.