Control of spacecraft formation about a near-circular orbit

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", which has been shown to work well in controlling the formation about the halo orbits, to this problem. 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 given to demonstrate our works, though the nonlinear trajectories is not as good as expected and should be investigated more.