Optimal Rendezvous Sequence for LEO Debris Capture

The primary purpose of this study is to exploit the effect of Earth＇s non-sphericity perturbation, particularly due to the J2 term, in order to optimize the capture sequence of potential orbital debris, that is the cumulative AV associated to the transfers between one object and the others. As results of several researches and model predictions, many international agencies agree that the growing population of objects and debris in LEO （low earth orbits）, will follow a diverging trend in the future. This, in turn, would constitute a serious threat to circum-terrestrial space safety and sustainability. In LEO, the ,J disturbance is prevailing over the others, and it acts by affecting the longitude of the ascending node （Ω）, the argument of perigee （ω） and, accordingly, the true anomaly （v）. Therefore, the goal of optimizing the AV is achieved by taking advantage of the rate of variation of Ω and ω, thereby compensating for the △Ω and △ω, present between the orbital transfer vehicle （chaser） and the debris to be captured （target）. Obviously, the perturbation will lead to favourable variations of the orbital parameters only for some combinations of Ω and ω. Yet the presence of a debris population with random distribution of Ω and ω, makes this application particularly suited to the problem. The single maneuver has been modelled with a 4-impulse time fixed rendezvous and the optimization problem has been addressed by implementing a hybrid evolutionary algorithm, which adopts, in parallel, three different strategies, namely, genetic algorithm, differential evolution and particle swarm optimization.

Hybrid planning for LEO long-duration multi-spacecraft rendezvous mission

For the low-earth-orbit （LEO） long-duration multi-spacecraft rendezvous mission, a mixed integer nonlinear programming （MINLP） model is built with consideration of the , perturbation and the time window constraints based on lighting condition. A two-level hybrid optimization approach is proposed. The up-level problem uses the visiting sequence, the orbital transfer duration and the service time after each rendezvous as design variables, and employs the mix-coded genetic algorithm to search the optimal solution; the low-level problem uses the maneuver time and impulses in each rendezvous as design vari- ables, and employs the downhill simplex method to search the optimal solution. To improve the solving efficiency of the low-level problem, a linear dynamic model with J~ perturbation is derived, and the approximate strategy of the low-level prob- lem is then proposed. The proposed method has been applied to several numerical problems. The results lead to three major conclusions： （1） The MINLP model for LEO long-duration multi-spacecraft rendezvous mission is effective, and the proposed hybrid optimization strategy can obtain good solutions that satisfy time window constraints; （2） The derived linear dynamic equations are good first-order approximation to the long-duration rendezvous trajectory under ,J2 perturbation; （3） Under J2 perturbation, the long-duration rendezvous problem has multiple local minimums either in the duration of multiple orbits or in a single orbit, and it agrees with the problem＇s characteristic to use the mix-coded genetic algorithm.

Planning for space station long-duration orbital mission under multi-constraints

An integrated nonlinear planning(NLP) model is built for space station long-duration orbital missions considering both the vehicle visiting schedules and the interaction effects between target phasing,vehicle return adjusting and Earth observation aiming.A two-level optimization approach is proposed to solve this complicated problem.The up-level problem employs the launch times of visiting vehicles as design variables,considers the constraints of crew rotations,resource resupplies and rendezvous launch windows,and is solved by a genetic algorithm.The low-level problems employ the maneuver impulses and burn times within each orbital mission as design variables,and a high-efficient shooting iteration method is proposed based on an analytical equation for the phase angle correction considering the J 2 perturbation.The results indicate that the integrated NLP model for space station long-duration orbital missions is effective,and the proposed optimization approach can obtain the optimal solutions that satisfy the multiple constraints and reduce the total propellant consumption.