Neighboring optimal guidance and attitude control of low-thrust earth orbit transfers

Recently, low-thrust propulsion is gaining strong interest from the research community and has already found application in some mission scenarios. This paper proposes an integrated guidance and control methodology, termed variable-time-domain neighboring optimal guidance and proportional derivative-rotation matrix (VTD-NOG and PD-RM), and applies it to orbit transfers from a low Earth orbit (LEO) to a geostationary orbit (GEO), using low thrust. The VTD-NOG is a closed-loop guidance approach based on minimization of the second differential of the objective functional along the perturbed path, and it avoids the singularities that occur using alternate neighboring optimal guidance algorithms. VTD-NOG finds the trajectory corrections considering the thrust direction as the control input. A proportional-derivative scheme based on rotation matrices (PD-RM) is used in order to drive the actual thrust direction toward the desired one determined by VTD-NOG. Reaction wheels are tailored to actuate attitude control. In the numerical simulations, thrust magnitude oscillations, displaced initial conditions, and gravitational perturbations are modeled. Extensive Monte Carlo campaigns show that orbit insertion at GEO occurs with excellent accuracy, thus proving that VTD-NOG and PD-RM represents an effective architecture for guidance and control of low-thrust Earth orbit transfers.