5. Conclusion
This paper has presented a hybrid optimization approach for long-duration rendezvous phasing missions and then has demonstrated it for a typical two-week rendezvous phasing mission. The results show that the proposed approach can stably obtain the near optimal high-precision solution by integrating the perturbed trajectory only a few times.A long-duration rendezvous phasing plan is compatible with any initial phase angles that the in-plane velocity increment remains almost unchanged when the initial phase angle changes. However, under the same conditions, the out-of-plane velocity increment has considerable variations, which is caused by the coupling effect between in-plane and out-of-plane maneuvers. For a typical two-day rendezvous phasing plan, or plans with shorter mission duration, the total velocity increment has only one local minimum when the initial right ascension of ascending node (RAAN) of the chaser changes, and that local minimum corresponds to a quasi-coplanar launch opportunity of the chaser. However, for a long-duration rendezvous phasing plan, such as the plan with two-week mission duration, the total velocity increment has multiple local minimums as the initial RAAN of the chaser changes, and different local minimums correspond to different terminal revolution numbers. By aiming different terminal revolution numbers, a two-week plan could have more successive quasi-coplanar launch opportunities for the chaser (cargo spacecraft) than a two-day rendezvous phasing plan.
