Approximate time-optimal low-thrust rendezvous solutions between circular orbits

Abstract

Traditional planetocentric low-thrust solutions mainly focus on orbital rephasing or transfer maneuvers, while the rendezvous maneuver is more challenging to obtain and cannot be approximated by existing solutions in some mission scenarios. In this paper, approximate solutions to the time-optimal rendezvous problem between two close circular orbits are presented. First, the optimal control problem is established in terms of the true longitude by using the Sundman transformation, and a set of unified linearized equations of motion is derived to reduce the number of key parameters characterizing this problem. Then, we show that two key parameters can characterize the rendezvous problem, and that the rephasing (or transfer) corresponds to the case when one of the key parameters equals zero. Thus, a set of piecewise functions is developed to approximate the rephasing and transfer solutions. The rendezvous solutions are finally obtained by a traversal method and summarized in a set of contour maps. Numerical simulations demonstrate that the proposed solutions provide good initial guesses for solving the problem with nonlinear dynamics and accurately approximate the performance index for the preliminary mission design.