| A relative orbit control concept for collocated geostationary spacecraft is presented. One chief spacecraft, controlled from the ground, is responsible for the orbit determination and control of the remaining vehicles. Any orbit relative to the chief is described in terms of equinoctial orbit element differences and a linear mapping is employed for quick transformation from relative orbit measurements to orbit element differences. It is demonstrated that the concept is well-suited for spacecraft that are collocated using eccentricity-inclination vector separation and this formulation still allows for the continued use of well established and currently employed stationkeeping schemes, such as the Sun-pointing-perigee strategy. The relative approach allows to take determinisitc thruster cross-coupling effects in the computation of stationkeeping corrections into account. The control cost for the proposed concept is comparable to ground-based stationkeeping. A relative line-of-sight constraint between spacecraft separated in longitude is also considered and an algorithm is developed to provide enforcement options. The proposed on-board control approach maintains the deputy spacecraft relative orbit, is competitive in terms of propellant consumption, allows enforcement of a relative line-of-sight constraint and offers increased autonomy and flexibility for future missions. |
