Analytical Perturbation Analysis And Mixed-integer Multiobjective Planning Approaches For Space Rendezvous Missions

Space rendezvous and docking(RVD) is a n enable technology for complicated space missions, such as building a space station and servicing a satellite in space. Mission planning is a key content of RVD. A rendezvous mission is affected by orbital perturbations and the relations between two spacecraft, between the spacecraft and the Earth, and between the spacecraft and the sun. The planning of rendezvous missions usually needs to search discrete and continuous variables at the same time, has a complicated model and is hard to solve. This dissertation proposes an analysis method based on analytical perturbations, a mixed- integer multiobjective modeling framework and three solving frameworks for the planning of rendezvous missions, and then studies three complicated rendezvous mission planning problems, including the planning of long-duration and perturbed rendezvous trajectories, the arranging of multi- spacecraft perturbed rendezvous missions, and the arranging of multiphase rendezvous missions. The main results achieved in this dissertation are summarized as follows.An analysis method based on analytical pe rturbations is proposed for long-duration rendezvous missions.(1) A relative dynamics model using the orbital element differences is derived, which considers the J2 perturbation and the coupling effects between in-plane and out-of-plane relative movements. Based on that model, the relations between the time of flight and the velocity increment for long-duration two- impulse rendezvous problems are analyzed.(2) By deriving analytical approximate expressions accounting for the J2 perturbation, the effects of an orbital maneuver on the spacecraft-Earth and spacecraft-Sun relations are revealed.Based on domain knowledge, mixed-integer multiobjective modeling and solving frame works for the planning of rendezvous missions are proposed.(1) The domain knowledge for complicated rendezvous mission planning problems is analyzed from three aspects: the selection of design variables, the designing of objective functions, and the handling of constraints, and then the rules for design variable selection, the rules for objective designing, the methods for constraint handling, and the modeling procedure are proposed.(2) The solving difficulties of rendezvous mission planning problems are analyzed, based on which three solving frameworks are proposed, including the two- level solving framework, the hybrid solving framework, and the two- level hybrid solving framework. Three genetic algorithm(GA) improving models are designed according to the three solving frameworks.The hybrid approach for fast optimizing long-duration perturbed rendezvous trajectories is proposed. For a target spacecraft phasing mission and a long-duration rendezvous phasing mission, two mixed integer no nlinear programming(MINLP) models are established respectively, and then their approximating simplified planning models considering the J2 perturbation are both developed. A hybrid approach integrating sequential quadratic programming and branch-and-bound is designed to optimize the approximating target spacecraft phasing problem, and a n integer coded GA is used to optimize the approximating long-duration rendezvous phasing problem. Furthermore, using shooting iterations, the approximating solutions are both improved to the high-precision solutions which satisfy the terminal condition of the numerical integration trajectory with orbital perturbations. The results show that the near-optimal high-precision solutions can be obtained successfully and rapidly by the proposed approaches. Relative to common rendezvous missions, long-duration rendezvous missions can save maneuver propulsion by adjusting the maneuver numbers of revolution and the terminal number of revolution. The final time of the target phasing mission changes with the change of maneuver data, while the long-duration rendezvous phasing mission has multiple launch windows in the neighborhood of one coplanar chance.The hybrid multiobjective approach for arranging multi-spacecraft long-duration perturbed rendezvous missions is proposed. The two- level hybrid arranging models accounting for the J2 perturbation and the time window constraints are built respectively for a multi-spacecraft long-duration rendezvous and service mission(MSLDRSM) and the long-duration refueling and reconfiguration mission of a constellation(LDRRMC). A two- level hybrid solving approach based on the hybrid-encoding GA(HEGA) and down-hill simplex algorithm is proposed to optimize the MSLDRSM, and a two- level hybrid solving approach based on the multiobjective HEGA is proposed to optimize the LDRRMC. The results show that the proposed approaches can successfully obtain the near-optimal solutions. The window constraints cause the increase of propellant consumption and several breaks in the Pareto front. In addition, under the effects of the J2 perturbation and window constraints, the optimal rendezvous order is quite different from that of the two-body unconstrained missions. The property that the optimal rendezvous order can be determined simply according to the orbital plane difference and argument of latitude, was identified by previous studies, and cannot apply to the rendezvous problems considering orbital perturbations.The hybrid multiobjective approaches for arranging multiphase rendezvous missions are proposed to improve the mission ove rall performance.(1) The hybrid multiobjective arranging model for a nominal multiphase rendezvous mission is developed, in which the phase-connecting parameters and the parameters in each individual phase are used as design variables at the same time. A multiobjective HEGA is designed and used to find the Pareto-optimal solutions.(2) A multiobjective optimization model is developed for arranging the multiphase re-rendezvous process to recover the mission from a failure situation, and a multiobjective genetic algorithm is used to identify the Pareto-optimal solutions. The results show that the proposed approaches can obtain the near-optimal solutions effectively and can help compare the performance of the rendezvous missions with different phase numbers. Moreover, the obtained Pareto fronts effectively reveal the tradeoff relationships between the velocity increment, the time of flight, the solar energy available and the trajectory robustness for multiphase rendezvous missions.Among the approaches presented above, the long-duration perturbed rendezvous trajectory optimization approach and the multiphase rendezvous mission arranging approach have been validated by engineering application, and have been successfully applied to the rendezvous missions between the Shenzhou-8, Shenzhou-9 and Shenzhou-10 spacecraft and the Tiangong-1 space lab. The proposed multi- spacecraft rendezvous mission arranging approach corresponds to on-orbit service, which is an important direction of development for the aerospace industry. Contributing to the successful treatment of engineering factors, the proposed multi- spacecraft rendezvous mission arranging approach is much closer to engineering application than previous studies. Therefore, the studies in this dissertation have important values of engineering application. This dissertation extends the rendezvous trajectory planning theory and rendezvous mission arranging studies, proposes the analysis method based on analytical perturbations and the mixed- integer multiobjective modeling and solving framework, and has successfully revealed new characteristics of rendezvous mission planning problems in different levels. Consequently, the studies in this dissertation have some theoretical significance.