Pseudospectral methods are used to efficiently solve complex, non-linear optimal control problems and can be used to develop rapid and robust control solutions in astrodynamics applications. With the renewed efforts in resuming future manned missions to the moon or near-earth asteroids, fuel optimal flight trajectories are desired in order to alleviate the need for overestimates in fuel carried onboard, which has a negative impact on the overall spacecraft design. This thesis uses a pseudospectral optimal control solver, DIDO, to solve for a fuel optimal moon-to-earth trajectory using only the auxiliary engines of the Orion Crew Exploration Vehicle (CEV) for the entire mission. Additionally, higher-order necessary conditions are examined to test the extremality of the computed solution. Singular arcs that appear in a main engine variable thrust, fuel optimal trajectory are examined by applying the Bellman Pseudospectral method. The feasibility of using the CEV auxiliary engines in place of the main engines for the singular arc maneuver is also investigated.
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