Evolutionary approach to lambert's problem for non-Keplerian spacecraft trajectories

Abstract

In this paper, we use differential evolution (DE), with best-evolved results refined using a Nelder-Mead optimization, to solve boundary-value complex problems in orbital mechanics relevant to low Earth orbits (LEO). A class of Lambert-type problems is examined to evaluate the performance of this evolutionary method in its application to solving nonlinear boundary value problems (BVP) arising in mission planning. In this method, we evolve impulsive initial velocity vectors giving rise to intercept trajectories that take a spacecraft from given initial position in space to specified target position. The positional error of the final position is minimized subject to time-of-flight and/or energy (fuel) constraints. The method is first validated by demonstrating its ability to recover known analytical solutions obtainable with the assumption of Keplerian motion; the method is then applied to more complex non-Keplerian problems incorporating trajectory perturbations arising in low Earth orbit (LEO) due to the Earth's oblateness and rarefied atmospheric drag. The viable trajectories obtained for these challenging problems demonstrate the ability of this computational approach to handle Lambert-type problems with arbitrary perturbations, such as those occurring in realistic mission trajectory design.