Nonlinear modeling and control of spacecraft relative motion in the configuration space

This paper presents a new methodology yielding high-order, nonlinear approximations to the relative orbital dynamics of spacecraft flying in formation. A nonlinear formationkeeping control law is then developed. Nonlinear models of relative spacecraft dynamics are parameterized as time-series. Instead of using the Cartesian initial conditions as constants of motion, classical orbital elements are utilized. Variation of these elements enables the incorporation of perturbations and control forces in a straightforward manner. The method presented in the paper does not require solution of the differential equations, thus offering a simple derivation of models for relative motion. The known inertial configuration space is utilized and projected onto a classical rotating Hill frame. Based on the nonlinear modeling, a globally asymptotically stabilizing low-thrust Lyapunov-based formationkeeping controller is developed. The merits of the proposed modeling and control are validated by a few illustrative examples.