Global optimization of fuel consumption in J2 rendezvous using interval analysis

Abstract

This paper addresses an open-time Lambert problem under first-order gravitational perturbations with unfixed parking time and transfer time. The perturbations are compensated by introducing its analytical solutions derived from Lagrange's planetary equations into Lambert problem. A drift vector of aim position correction is defined to reduce the aim position bias caused by the perturbations. The first purpose of optimization is to find sufficiently small intervals involving the global optimal parking time, transfer time, drift vector and velocity increment. The second is to determine the global solution or the solution close to it in these intervals. Interval analysis and a double-deck gradient-based method with GA estimating the initial range of drift vector are utilized to obtain the sufficiently small intervals including the global minimum velocity increment and the global minimum solution or one sufficiently close to it in these intervals.