High-Fidelity Trajectory Optimization with Application to Saddle-Point Transfers

Abstract

A method to optimize space trajectories subject to impulsive controls is presented. The method employs a high-fidelity model and a multiple-shooting technique. The model accounts for an arbitrary number of gravitational attractions, their corrections due to celestial bodies oblateness, and solar radiation pressure. The peculiarity of this paradigm is that the equations of motion are written in a rotopulsating frame, where two primaries are at rest despite the fact that their motion and the one of the perturbers are given by a real ephemeris model. Direct transcription of the dynamics coupled with a multiple-shooting technique and an efficient computation of the Jacobian of the defects are used to optimize trajectories subject to a finite number of impulsive controls. The method has been applied to find a multitude of solutions to the problem of transferring a spacecraft from the sun–Earth collinear Lagrange points to the sun–Earth gravitational saddle point, where a theoretical zero background acceleration allows testing possible deviations from general relativity. The problem of targeting the sun–Earth saddle point with high accuracy represents a major flight dynamics challenge. The applicative scenario encompasses the possible mission extension option for LISA Pathfinder as special case.