Rendezvous via differential drag with uncertainties in the drag model

At Low Earth Orbits a differential in the drag acceleration between coplanar spacecraft can be used for controlling their relative motion in the orbital plane. Current methods for determining the drag acceleration may result in errors due to the inaccuracy of density models and misrepresentation of the drag coefficient. In this work a novel methodology for relative maneuvering of spacecraft under bounded uncertainties in the drag acceleration is developed. In order to vary the relative drag acceleration, the satellites modify their pitch angle. Two approaches are proposed. First, a dynamical model composed of the mean semi-major axis and argument of latitude is utilized for describing long range maneuvers. For this model, a Linear Quadratic Regulator (LQR) is implemented, accounting for the uncertainties in the drag force. This controller guarantees asymptotic stability of the system up to a certain magnitude of the state vector, which is determined by the uncertainties. Furthermore, based on a cartesian relative motion formulation, a min-max control law is designed for short range maneuvers. This provides asymptotic stability under bounded uncertainties. The two approaches are tested in numerical simulations illustrating a long range re-phasing, performed using the LQR controller, followed by a short range rendezvous maneuver, accomplished using the min-max controller.