Relative motion coupled control for formation flying spacecraft via convex optimization

Formation initialization control is of paramount importance for building a drift-free relative orbit, and is a challenging problem due to the coupled translational and rotational dynamics, e.g. the orientation of the thrust vector is constrained by the attitude and its angular velocity. We establish a nonlinear coupled dynamic model for formation flying spacecraft, and develop a relative orbit and attitude controller. The attitude angular velocity induced thrust vector constraint is then converted into thrust vector maneuverability constraint, which is nonconvex and cannot be implemented in the optimization framework directly. Thus the orbit and attitude controller can be designed separately. When designing the relative orbit controller, we use a relaxation method to convexify the nonconvex constraint and tailor the optimization problem to a semidefinite program, because of its low complexity and the existence of deterministic convergence properties. Then a variable structure attitude controller is used to track the optimized thrust direction. The validity of the proposed approach is demonstrated in a typical application of a dual-spacecraft formation initialization.