Ga-based optimization for formation flying initialization

On condition of J2 and atmosphere drag perturbation are both present, an optimization algorithm for formation design is proposed, by which the designed formation subjects to destroyment influence from perturbation to the least extent. First, the concept of relative eccentricity and relative inclination vector are introduced and the corresponding relative motion dynamics is established. Then, based on relationship between relative eccentricity, relative inclination and initial relative position, relative velocity, a performance index function describing the extent of formation deviation from its desired state under the action of perturbation is established, which takes formation deviation problem into account from viewpoint of harmonic vibration error, constant error and secular drift. After that, based on theory of mean orbital elements, Genetic Algorithm is used to optimize the given function to get its minimum value, from which the objective of formation design is achieved. In the end, comparing simulation results between the formation designed by J2 invariant formation theory and that from proposed method shows effectiveness and superiority of the given algorithm.