Nonlinear orbit control with longitude tracking

The growing level of autonomy of unmanned space missions has attracted a significant amount of research in the aerospace field towards feedback orbit control. Existing Lyapunov-based controllers can be used to to transfer a spacecraft between two elliptic orbits of given size and orientation, but do not consider the stabilization of the spacecraft phase angle along the orbit, which is a key requirement for application to formation flying missions. This paper presents a control law based on the orbital element parametrization, which is able to track a given true longitude (i.e. a reference phase angle), in addition to the parameters describing the reference orbit shape and orientation. A numerical simulation of an orbital rendezvous demonstrates the effectiveness of the proposed approach.