A comparison of control algorithms for spacecraft formation flying in the J2-perturbed two-body dynamics

In the last decades a lot of attention has been dedicated to spacecraft formation flying, i.e., the proximity flight of multiple satellites. As a matter of fact, many possible application of this technology can be found in literature, such as interferometry or ground-track observations. For these reasons, a large amount of research has been dedicated to both theoretical and practical aspects of spacecraft formation flying. The main challenge for formation flying is the control of the configuration maintaining a specific relative distance between the satellites. In order to work as a collective, the individuals must be kept in close proximity by reducing their relative drift, while minimizing the fuel expenditure. In this thesis, we aim at conducting a survey of guidance and control algorithms for spacecraft formation keeping. For this purpose, we study the equations of motion governing the relative dynamics of a chaser with respect to a target for both the Kepler two-body model, as well as for the J2-perturbed scenario. Then, the definition of bounded motion is introduced, and the initial conditions allowing a chaser to orbit on a closed trajectory near the target are shown. Finally, through a set of simulations, we compare different guidance and control algorithms, by evaluating their propellant expenditure in the J2-perturbed model.