Spacecraft formation flying: relative orbit control based on Euler orbital elements

This work addresses a nonlinear Lyapunov-like feedback control to establish and maintain a given relative orbit. Traditional feed-back of cartesian position and velocity tracking error vectors results in an accurate, but expensive, control action. Working with orbit elements eventually allows to reduce such cost by accomplishing corrective manoeuvres on particularly convenient conditions. Moreover it allows to define convenient target relative motions. Hence, by pursuing this approach, here errors in Euler orbit elements are fed-back, thus joining to the previously mentioned benefits the intrinsic more exhaustive exploitation of the dynamics that the Euler set carries with him. These elements, in fact, arise from the solution of the Generalized Problem of Two Fixed Centres, hence already take into account the contributions of $J_2$, $J_3$ and partially $J_4$ zonal harmonics. A critical analysis of the design process of the controller is carried out.