Hybrid Cartesian and Orbit Element Feedback Law for Formation Flying Spacecraft

A spacecraft formation e ying control strategy is discussed where the desired orbit is prescribed in terms of specie c orbit element differences and the relative orbit is measured in terms of Cartesian coordinates of the rotating reference frame centered on the chief satellite. A direct method to map orbit element differences to their corresponding local Cartesian coordinates is presented. A numerical study illustrates theaccuracy with which this linearized transformation performs this coordinate transformation. A hybrid continuous feedback control law is thendevelopedthathasthedesired relativeorbitgeometryexplicitlygivenin termsoforbitelementdifferencesand the actual orbit given in terms of local Cartesian coordinates. A numerical simulation illustrates the performance and limitations of such feedback control laws. Using the linearized mapping between the relative orbit coordinates causes only a small performance penalty. However, it is advantageous to work in mean element space when determining the relative orbit tracking error.