Spacecraft rendezvous by differential drag under uncertainties

At low Earth orbits, differentials in the drag forces between spacecraft can be used for controlling their relative motion in the orbital plane. Current methods for determining the drag force may result in errors due to inaccuracies in the density models and drag coefficients. In this work, a methodology for relative maneuvering of spacecraft based on differential drag, accounting for uncertainties in the drag model, is proposed. A dynamical model composed of the mean semimajor axis and the argument of latitude is used for describing long-range maneuvers. For this model, a linear quadratic regulator is implemented, accounting for the uncertainties in the drag force. The actuation is the pitch angle of the satellites, considering saturation. The control scheme guarantees asymptotic stability of the system up to a certain magnitude of the state vector, which is determined by the uncertainties. Numerical simulations show that the method exhibits consistent robustness to accomplish the maneuvers, even in the presence of realistic modeling of density fields, drag coefficients, the corotation of the atmosphere, and zonal harmonics up to J(8).