One of the challenges of autonomous guidance and control of formation flying is related to the on-board prediction of the relative motion between both spacecraft, which has to remain accurate over long propagation periods and be valid for large separation distances on highly elliptical orbits. In this context, this paper addresses the problem of nonlinear analytical guidance for spacecraft formation flying reconfiguration maneuvers. Specifically, a nonlinear analytical solution for predicting the radial, along-track, and cross-track relative motion on J2-perturbed elliptical orbits is first obtained and then used in a back-propagation scheme for closed-loop guidance purposes. Finally, the relative orbital element-based guidance solution is combined with an impulsive controller to demonstrate its efficiency in terms of propellant savings to execute a reconfiguration maneuver over a period of ten orbits.

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Conference AAS/AIAA Astrodynamics Specialist Conference, 2017
Kuiack, B. (Bradley), & Ulrich, S. (2018). Orbital element-based relative motion guidance on J2-perturbed eccentric orbits. In Advances in the Astronautical Sciences (pp. 2619–2633).