This paper investigates the potential control law that stabilizes relative trajectories about a Keplerian near-circular orbit with applications to the formation flight of spacecraft. A spacecraft is considered moving relative to a nominal Keplerian orbit, whose dynamics is usually described by the Tschauner-Hempel Equation (T-H Equation). Briefly reviewing the results from the T-H Equation, we analytically prove the applicability of the "local time approximation" to this problem, which has been shown to work well in controlling the formation about the halo orbits. With the guidance of this algorithm, we propose two methods of designing the control law, one in the time domain and the other in the true-anomaly domain, which enable us not only to stabilize the unstable relative trajectory, but to "re-construct" the "scaled" nominal orbit for our formation of spacecraft in the linearized scheme. Numerical simulations are also presented to demonstrate our work, in which the relative trajectory is stabilized in both linear and nonlinear level. Costs to perform formation are also provided to show the feasibility.
Journal of Aeronautics, Astronautics and Aviation, Series A 42(3), pp.171-178