Parameterization Effects on Convergence when Optimizing a Low-Thrust Trajectory with Gravity Assists

Abstract

Low-thrust trajectories can be modeled by an evenly-spaced sequence of ¢V impulses connected by coasting arcs. Such a model transforms the trajectory optimization problem from an optimal control problem into a finite nonlinear programing problem. Analysis and experimental results are given to help decide which coordinate system to use for the ¢V vectors. In particular, we consider an Earth-Mars flyby mission, an Earth-Tempel 1 rendezvous mission, an Earth-Mars-Ceres rendezvous mission, an Earth-Mercury rendezvous mission, and an Earth-Jupiter flyby mission. If the initial guess is good (i.e. nearly optimal), we find that spherical coordinates lead to the fastest optimization convergence. If the initial guess is bad (i.e. not close to feasible), we find that a feasible solution will be found most quickly if Cartesian coordinates are used. While it would not be prudent to attempt any generalizations, we provide some conjectures for the observed behavior based on the nature of the coordinates we have investigated.