Aas 09-257 Optimization of Spacecraft Trajectories: a Method Combining Invariant Manifold Techniques and Discrete Mechanics and Optimal Control

A mission design technique that uses invariant manifold techniques together with the optimal control algorithm DMOC produces locally optimal, low ∆V trajectories. Previously, invariant manifolds of the planar circular restricted three body problem (PCR3BP) have been used to design trajectories with relatively small ∆V . Using local optimal control methods, specifically DMOC, it is possible to reduce the ∆V even further. This method is tested on a trajectory which begins in Earth orbit and ends in ballistic capture at the Moon. DMOC produces locally optimal trajectories with much smaller total ∆V applied in a distributed way along the trajectory. Additionally, DMOC allows for variable flight times, leading to smaller ∆V necessary for lunar orbit insertion. Results from different Earth to Moon missions are presented in table form to show how the DMOC results fit in with actual missions and different trajectory types. The ∆V of the DMOC results are, on average, 23%-25% better than the ∆V of trajectories produced using a Hohmann transfer.