Repeat ground track equispaced formation design & control

This paper introduces the concept of equispaced spacecraft formations where formation members are equispaced within a common relative orbit. A method is introduced to design and maintain these equispaced spacecraft formations in Low Earth Orbit that simultaneously preserves formation geometry and satisfies global requirements such as repeating ground tracks and sun-synchronicity. Using the theory of averaging, nominal semi-major axis offsets are determined for formation members to equalize their perturbed mean motion under high order geopotential perturbations, ensuring long-term bounded motion. Secular drift arising from inclination differences is mitigated by introducing an additional small semi-major axis offset between participants. The analysis shows that lower order perturbation models are inadequate for predicting long-term inter-spacecraft drift. In contrast, higher order geopotential models provide the needed fidelity to compute the nominal semi-major axis offset for each formation member to mitigate this drift. Control strategies based on Gauss’s Variational Equations are developed to maintain relative trajectories while embedding global requirements, including repeating ground tracks, directly into the relative orbital elements. Global corrections are applied in a coordinated manner across the formation, ensuring collective compliance with global mission objectives while preserving relative separations and operational safety during all maneuvers.