Optimization of Spacecraft Trajectories: A Method Combining Invariant Manifold Techniques and Discrete Mechanics and Optimal Control

Abstract

A mission design technique that uses invariant manifold techniques together with the optimal control algorithm DMOC produces locally optimal, low ΔV trajectories. Previously, invariant manifolds of the planar circular restricted three body problem (PCR3BP) have been used to design trajectories with relatively small ΔV . Using local optimal control methods, specifically DMOC, it is possible to reduce the ΔV 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 ΔV applied in a distributed way along the trajectory. Additionally, DMOC allows for variable flight times, leading to smaller ΔV 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 ΔV of the DMOC results are, on average, 23%-25% better than the ΔV of trajectories produced using a Hohmann transfer.