Optimal cooperative time-fixed impulsive rendezvous

Abstract

A method has been developed for determining optimal, i.e. minimum fuel, trajectories for the fixed-time cooperative rendezvous of two spacecraft. The method assumes that the vehicles perform a minimum of three impulsive maneuvers with each vehicle being active, that is, making at least one maneuver. The cost of a reference rendezvous solution is improved by an optimizer which uses an analytical gradient developed using primer vector theory and a new solution for the optimal terminal (rendezvous) maneuver. Results are presented for a large number of cases in which the allotted time for rendezvous and other problem parameters including initial relative position, engine efficiencies, initial masses, and fuel mass fractions of the two vehicles are varied. Further improvement in cost may be realized when an additional, i.e. mid-course, impulse is allowed as part of one of the vehicles' trajectory. The criteria for addition of a mid-course impulse to a neighboring solution trajectory has been developed. The cooperative rendezvous proves advantageous particularly in missions with relatively short durations and when fuel constraints are present.