Relative orbit initialization control for formation flying spacecraft with thrust direction maneuverability constraints

Spacecraft formation offers more powerful and robust architectures than single traditional large spacecraft and is an enabling technology for a number of space missions. The formation initialization control is of paramount importance for building a drift-free relative orbit for the succeed formation missions, and is challenging for the thrust direction maneuverability constraints imposed by the limited maximum attitude angular velocity. Hence, we present a relative orbit initialization control algorithm of a cluster of spacecraft with non-convex thrust direction maneuverability constraints. And we use a relaxation method to convexify the non-convex constraints that cannot be implemented in the optimization framework directly. The optimization problems are then tailored to a semidefinite program (SDP), because of the low complexity and the existence of deterministic convergence properties of SDP problems. The validity of the proposed controller is demonstrated in a typical application of the formation initialization of a fleet of spacecraft.