Comparison between analytical and optimal control techniques in the differential drag based rendez-vous

The focus of this study is on differential drag for propellantless satellite rendez-vous. This technique is particularly attractive for low-Earth-orbit small satellites for which stringent weight constraints apply. Most existing contributions are based on bang-bang strategies, which may be difficult to implement in practice. This is why the present paper proposes a novel strategy integrating pseudospectral optimal control for maneuver planning and model predictive control for dealing with uncertainties and unmodeled dynamics. One important advantage of this methodology is that it can naturally account for attitude dynamics and constraints, which, in turn, paves the way for the practical realization of differential drag-based rendez-vous. A realistic scenario involving two nanosatellites of the QB50 constellation is considered to illustrate and validate the proposed developments. In addition, a comparison of this numerical technique with an existing analytic solution is carried out, and their respective pros and cons are discussed.