Dynamics and control of low-altitude formations

Formation flying missions require high performance orbital control strategies, which are based on accurate study and modelling of the spacecraft relative dynamics. To this aim, different techniques have been proposed, based either upon drastically simplified dynamics (Hill's equations) or upon non linear dynamics (approaches leading to the Lyapunov method). Recent work suggested that the inclusion of main perturbing effects, even if in a simplified linearized form, could improve the expected performances. This paper, focusing on the low altitude orbits, recalls the models adopted for the most significant effects, i.e. the air drag and the J 2 perturbations, and shows how these models could be introduced in a classical Linear Quadratic Regulator approach. A realistic evaluation of the control performances will depend on the accuracy of the knowledge of the spacecraft kinematic state. The determination of the state adds the deficiencies of the navigation system to the errors generated by the approximation of the dynamics involved. A navigation filter is therefore included in the process. Uncertainties of a GPS(GNSS) receiver, assumed as the most fitting navigator currently available for autonomous on-board applications, are injected into the model in a statistical way, leading to a Linear Quadratic Gaussian approach, in order to better represent the overall system performances. The final aim of the paper is to provide a global frame to evaluate and select formation flying control strategies at low orbit altitudes.