Neighboring optimal guidance and proportional-derivative attitude control applied to low-thrust orbit transfers

This work presents a unified guidance and control architecture, termed VTD-NOG & PD-RM, and describes its application to low-thrust orbit transfer from a low Earth orbit to a geostationary orbit. The variable time-domain neighboring optimal guidance (VTD-NOG) is a feedback guidance technique based upon minimizing the second differential of the objective function along the perturbed trajectory, and was proven to avoid the numerical difficulties encountered with alternative neighboring optimal algorithms. VTD-NOG identifies the trajectory corrections assuming the thrust direction as the control input. A proportional-derivative attitude control based on rotation matrices (PD-RM) is used to drive the actual thrust direction toward the desired one, determined by VTD-NOG. Reaction wheels are employed to perform the attitude control action. In the dynamical simulations, thrust oscillations, errors on the initial conditions, and gravitational perturbations are considered. Extensive Monte Carlo simulations point out that orbit injection occurs with very satisfactory accuracy, even in the presence of nonnominal flight conditions.