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.