Analytical solution of two-point boundary value problem for spacecraft relative motion

The two-point boundary value problem (TPBVP) of a leader-follower spacecraft formation flying was studied. Aiming at unperturbed elliptical reference orbits, the state transfer matrix representing actual relative position and velocity was derived, and the first-order analytical solution of TPBVP is obtained, which can deal with the problems of the specified rendezvous time, fuel optimization and compromise between fuel and time, and is applicable to the periodic and non-periodic relative motion. The simulation results show that the normalized accuracy of this solution achieves 10 ^-6 level. Furthermore, the fuel cost of relative transfer increases with eccentricity increasing, and decreases with semi-major axis increasing, and appears periodic change with initial true anomaly increasing, and decreases as the transfer time increasing.