Relative Motion Dynamics and Control in the Two-Body and in the Restricted Three-Body Problems

The objective of the present Thesis is a detailed study of relative motion dynamics and control in a two-body and a three-body gravity fields. For the former scenario, a general set of equations for the inclusion of arbitrary orbital perturbations is derived. The equations are then used for the design of a nonlinear H-infinity controller based on the state-dependent Riccati equation technique. A closed-form solution for the H-infinity control problem for the relative motion control on elliptic orbits is also presented, based on a linearized time-varying set of equations. Relative motion in the three-body scenario is also studied. In particular, a nonlinear set of equations for relative motion description in the local-vertical local-horizon frame is derived. Starting from this set, simplified equations are proposed and their performance compared. The computation of rendezvous maneuvers adopting both impulses or continuous thrust is then presented, in order to establish potential feasible trajectories.