Satellite formation keeping control in the presence of gravity perturbations

The performance of linear control laws for satellite formation keeping in the presence of gravity perturbations is considered. Control using a linear quadratic regulator to minimize the error between the actual and desired relative satellite motion is assessed for its ability to maintain a particular formation geometry in the presence of the Earth oblateness gravity perturbation. The desired formation geometry is based on the solution to the linear, unperturbed relative motion equations. Specifically, a formation of satellites is chosen whose projected motion onto the Earth´s tangential plane is a one kilometer circle. It is shown that the linear control laws maintain the formation within error bounds in the presence of gravity perturbations. Furthermore, simulations provide estimates of the maneuvering propellant required to maintain such a formation, providing a baseline for future studies involving formations based on less taxing desired trajectories and more carefully chosen control strategies