Spacecraft relative motion control using the state-dependent Riccati equation technique

In this paper, an overview of the state-dependent Riccati equation (SDRE) control technique is proposed, with focus on spacecraft relative motion control. The SDRE method offers a systematic and effective approach for designing nonlinear controllers and observers, with appealing properties of stability, optimality, and robustness. Such characteristics have made the method popular since the 1990s, and a wide number of applications can be found in literature. In this work, we focus our attention on its use for the development of guidance systems, aimed at controlling the relative motion between two or more spacecraft. In particular, the method is first used to design a guidance law for formation control around libration point. Then a set of modifications are proposed, aimed at increasing pointwise stability and at reducing computational cost. These are tested and compared on a debris mitigation mission in lower Earth orbit.