Optimization of Many-Burn Orbital Transfers

Abstract

Optimization of medium and low-thrust orbital transfers is important for future upper stages. Previous research has generally either considered a fairly small number of burns with medium thrust or has assumed continuous thrusting for low-thrust transfers. The acceleration level considered in this paper is too high to use orbit averaging and too low (in most cases) to use only a few burns. The optimization scheme used is an optimal control solution for each burn, and a parameter optimization for the ensemble of burns. The solution for each burn is available in open-loop and closed-loop form, so that the method also provides a guidance scheme for flying the transfers. The optimization includes oblateness terms, complicating many-burn transfers with plane change. Results compare favorably to several published cases. This paper also includes additional transfer cases and parametric results. These results are easy to obtain in comparison with many-burn (non-averaged) multi-point boundary value problem solutions, which require the determination of a number of sensitive parameters. Cases examined include transfer to high-Earth orbit, transfer to geostationary orbit, transfer to the Global Positioning System (GPS) orbit, escape from orbit, and transfer to the lunar sphere of influence.