Evolved spacecraft trajectories for low earth orbit

Abstract

In this paper we use Differential Evolution (DE), with best evolved results refined using a Nelder-Mead optimization, to solve complex problems in orbital mechanics relevant to low Earth orbits (LEO). A class of so-called 'Lambert Problems' is examined. We evolve impulsive initial velocity vectors giving rise to intercept trajectories that take a spacecraft from given initial positions to specified target positions. We seek to minimize final positional error subject to time-of-flight and/or energy (fuel) constraints. We first validate that the method can recover known analytical solutions obtainable with the assumption of Keplerian motion. We then apply the method to more complex and realistic non-Keplerian problems incorporating trajectory perturbations arising in LEO due to the Earth's oblateness and rarefied atmospheric drag. The viable trajectories obtained for these difficult problems suggest the robustness of our computational approach for real-world orbital trajectory design in LEO situations where no analytical solution exists.