Optimization of an orbital long-duration rendezvous mission

The phasing segment of the rendezvous mission between a cargo spacecraft and a space station usually lasts for several weeks, and actually presents an orbital long-duration problem. In this study, this orbital long-duration problem is formulated as a mixed integer nonlinear programming (MINLP) problem in which the maneuver revolution numbers (integers), maneuver arguments of latitude and impulse magnitude are used as design variables at the same time. A hybrid approach is then proposed to solve this MINLP problem. First, a linear dynamics model considering the J2 term of the Earth non-spherical gravity is employed to formulate an approximate phasing problem, which is optimized using a genetic algorithm. Second, a shooting iteration process considering the coupling effect between the in-plane and out-of-plane maneuvers is proposed to improve the approximate solution to satisfy the terminal conditions of the high-precision problem. The proposed approach is demonstrated 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. Furthermore, 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. Compared with a two-day rendezvous phasing plan, a two-week plan could have several successive coplanar launch opportunities for the chaser by aiming different terminal revolution numbers.