Indirect optimization of interplanetary trajectories including spiral dynamics.

摘要

In the future small, robotic probes and large, human-crewed spacecraft will utilize long-duration, finite-burning engines. These types of engines have already been proven in several missions and research is on-going for the design of newer engines of this class. The trajectories they generate are significantly different than those that use conventional high-thrust chemical propulsion. The indirect method was chosen for the optimization of the missions presented due to its mathematical elegance and other problem specific issues. The goal was to choose a difficult optimization problem for an engine of this class and determine techniques, trends, and formulations that help overcome the indirect method's traditional shortcoming: the numerical difficulty of generating an accurate first guess for complex missions. The problem chosen was the optimization of interplanetary trajectories, with particular results presented for the problem of transferring from Low Earth Orbit (LEO) to Low Mars Orbit (LMO). Most previous attempts at this problem use an array of simplifications to the engine system and/or problem dynamics to make the optimization feasible. These simplifications are systematically removed here.; The complete trajectory was broken down into its component phases and careful study was paid to each. Analysis of the escape and capture spirals provided useful insight into the appropriate coordinate frames for spirals. This study yielded a technique that quickly and accurately estimates the unknown Lagrange multipliers. These results were applied to the full LEO to LMO mission as part of a sequential process for a two-dimensional solar system model and the equivalent three-dimensional model. This process includes many new derivations that facilitate the generation of an accurate first guess for these LEO to LMO missions. One new derivation in particular is vital where the co-states for a Mars capture spiral referenced to a Martian coordinate frame are transformed into their Earth based equivalents. This sets up a multiple shooting problem integrated in a single coordinate frame which is different than the single shooting method used in published benchmarks. The new approach generates more fuel efficient trajectories and significantly more complex numerically achievable capture sequence compared with such benchmarks.