Unified approach to far-range space rendezvous

Far-range space rendezvous is a complex process, designed to achieve terminal conditions required for the subsequent close-range rendezvous phase. In far-range rendezvous, the relative dynamics between the chaser spacecraft and the target are nonlinear, thus challenging the simple orbit control methods used in close-range rendezvous. In this paper, a new nonlinear closed-loop low-thrust far-range rendezvous law applicable to both spacecraft rendezvous and minor celestial body rendezvous is developed by means of angular momentum and eccentricity vector matching, which steers the chaser into the target's orbital plane. This matching is realized by a nonlinear Lyapunov-based feedback control, in which the chaser and target angular momentum and eccentricity vectors are expressed in target-fixed local-vertical local-horizontal coordinates. In order to reduce the resulting along-track offset, the targeted semimajor axis is appended with an along-track-dependent bias, such that the along-track relative distance and speed are ultimately nullified. It is proven that the newly-developed rendezvous law remains invariant under the gravitational acceleration exerted by a minor celestial body, and is, therefore, applicable to minor celestial body rendezvous. Simulation results for both low Earth orbit spacecraft rendezvous and minor celestial body rendezvous indicate that the proposed far-range rendezvous algorithm is effective, steering the chaser spacecraft to close proximity of the target, thus enabling to initiate the close-range rendezvous phase.