Hybrid Cartesian and orbit element feedback law for formation flying spacecraft
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A spacecraft formation flying control strategy is discussed where the desired orbit is prescribed in terms of specific 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 the accuracy with which this linearized transformation performs this coordinate transformation. A hybrid continuous feedback control law is then developed that has the desired relative orbit geometry explicitly given in terms of orbit element differences and 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.
