Spacecraft Formation Flying Control Using Mean Orbit Elements

Two nonlinear feedback control laws are presented for reestablishing a desired J2 invariant relative orbit. Since it is convenient to describe the relative orbit of a deputy with respect to a chief satellite in terms of mean orbit element differences, and because the conditions for a relative orbit being J2 invariant are expressed in terms of mean orbit elements, the first control law feeds back errors in terms of mean orbit elements. Dealing with mean orbit elements has the advantage that short period oscillations are not perceived as tracking errors; rather, only the long term tracking errors are compensated for. The second control law feeds back traditional Cartesian position and velocity tracking errors. For both of the control laws, the desired orbit is computed using mean orbit elements. A numerical study compares and contrasts the two feedback laws.