Improved Solution of Optimal Impulsive Fixed-Time Rendezvous

A linear approach to the minimum-fuel problem of fixed-time multi-impulse rendezvous between vehicles on close circular orbits has proven to be simple and convenient. It deals with the linearized motion of the active vehicle relative to a reference point moving on a circular reference orbit. This paper shows that the normalized characteristic velocity is invariant with respect to each choice of reference orbit in the domain of normalized initial angular difference-normalized rendezvous time. Numerical examples are used to demonstrate the adaptability of linear solutions to the nonlinear case by means of a hybrid method. It is shown that the proposed mean velocity reference orbit more accurately describes the impulse locations and magnitudes than does the mean radius reference orbit.