Since most spacecraft multiple-impulse trajectory optimization problems are complex multimodal problems with boundary constraint, finding the global optimal solution based on the traditional differential evolution (DE) algorithms becomes so difficult due to the deception of many local optima and the probable existence of a bias towards suboptimal solution. In order to overcome this issue and enhance the global searching ability, an improved DE algorithm with combined mutation strategies and boundary-handling schemes is proposed. In the first stage, multiple mutation strategies are utilized, and each strategy creates a mutant vector. In the second stage, multiple boundary-handling schemes are used to simultaneously address the same infeasible trial vector. Two typical spacecraft multiple-impulse trajectory optimization problems are studied and optimized using the proposed DE method. The experimental results demonstrate that the proposed DE method efficiently overcomes the problem created by the convergence to a local optimum and obtains the global optimum with a higher reliability and convergence rate compared with some other popular evolutionary methods.

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.

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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.

To prevent the proliferation of space debris and stabilize the space environment, active debris removal (ADR) has increasingly gained public concern. Considering the complexity of space operations and the viability of ADR missions, it would be necessary to schedule the ADR process in order to remove as much debris as possible. This paper presents an active debris removal mission planning problem, devoted to generate an optimal debris removal plan to guide the mission process. According to the problem characteristics, a two-layer time-dependent traveling salesman problem(TSP) mathematical model is established, involving the debris removal sequence planning and the transfer trajectory planning. Subsequently, two main novel methods based on machine learning are proposed for the ADR mission planning problem, including a deep neural networks(DNN)-based estimation method for approximating the optimal velocity increments of perturbed multiple-impulse rendezvous and an reinforcement learning(RL)-based method for optimizing the sequence of debris removal and rendezvous time. Experimental results of different simulation scenarios have verified the effectiveness and superiority of the proposed method, indicating the good performance for solving the active debris removal mission planning problem.