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This study proposes an analytical Delta-V approximation of short-time transfers based on the linear relative motion and a gradient-based nonlinear programming model of multi-target rendezvous and flyby trajectories. In previous studies, the Lambert's solution is commonly used to evaluate Delta-V of short-duration transfers. In this study, to avoid the iteration process for obtaining the Lambert's solution and its gradient, the linear relative motion equations are applied to form an analytical two-point boundary value model for the near-circular orbit rendezvous problems. Although the relative motion equations are usually applicable when the two orbits are close enough, and the position and velocity errors would become more significant as the orbital differences increase, the errors of the velocity increments were proved acceptable in our simulations. Moreover, the analytical formula facilitates the calculation of the gradients to the start epoch and flight time, which are used to establish a nonlinear programming model for sequence optimization that gradient-based algorithms can easily solve. Simulation results demonstrated that the analytical Delta-V approximation requires much less calculation than the Lambert's solution, and the proposed gradient-based nonlinear programming algorithms can obtain similar results in less time than previous methods.

A novel fast multi-impulse optimization method for long-duration perturbed orbit rendezvous is proposed. First, based on the analytically estimated impulses, the terminal rendezvous deviation with precise dynamics model can be predicted. Then, an analytical correction to the impulses using the deviations of orbit elements can be calculated based on the analytical J2 perturbed dynamics equation of a circular orbit. The iteration process repeating prediction and correction is then designed to quickly obtain a precise solution and trajectory. The simulation results proved that the iteration method adapts well to the analytical dynamics and high-precision dynamics. The deviation could always converge within five iterations.

The design of multitarget rendezvous missions requires a method to quickly and accurately approximate the optimal transfer between any two rendezvous targets. In this paper, a deep neural network (DNN)-based method is proposed for quickly approximating optimal perturbed long-duration impulsive transfers. This kind of transfer is divided into three types according to the variation trend of the right ascension of the ascending node (RAAN) difference between the departure body and the rendezvous target. An efficient database generation method combined with a reliable optimization approach is developed. Three regression DNNs are trained individually and applied to approximate the corresponding types of transfers. The simulation results show that the well-trained DNNs are capable of quickly estimating the optimal velocity increments with a relative error of less than 3% for all the three types of transfers. The tests on the debris chains with the total velocity increments of several thousand m/s show that the estimated results can be very close to the optimized ones with a final estimation error of less than 10 m/s., Comment: arXiv admin note: text overlap with arXiv:1902.03738

The design of low-thrust-based multitarget interplanetary missions requires a method to quickly and accurately evaluate the low-thrust transfer between any two visiting targets. Complete evaluation of the low-thrust transfer includes not only the estimation of the optimal fuel consumption but also the judgment of transfer feasibility. In this paper, a deep neural network (DNN)-based method is proposed for quickly evaluating low-thrust transfer. An efficient database generation method is developed for obtaining both the infeasible and optimal transfers. A classification DNN and a regression DNN are trained based on the infeasible and optimal transfers to judge the transfer feasibility and estimate the optimal fuel consumption, respectively. The simulation results show that the well-trained DNNs are capable of quickly determining the transfer feasibility with a correct rate of greater than 98% and approximating the optimal transfer fuel consumption with a relative estimation error of less than 0.4%. The tests on two asteroid chains further show the superiority of the DNN-based method for application to the design of low-thrust-based multitarget interplanetary missions