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Multi-asteroid tour missions require consideration of the visiting sequences and trajectory optimization for each leg, which is a typical global optimization problem. In this paper, the problem is divided into a multi-level optimization problem. Determination of the visiting sequence plays a key part for a tour mission. In this paper, the energy differences between different orbits and phase differences are used to estimate the energy required for a tour mission. First, this paper discusses the relation between fuel cost for transfer and classical orbit elements difference based on the energy relation of Keplerian orbits and the characteristics of low-thrust spacecraft. Second, the phase difference is combined with the energy difference to achieve the rendezvous energy. In addition, the lower and upper bounds of rendezvous time can be estimated by analyzing the phase difference. Very-low-thrust trajectory optimization problems have always been considered difficult problems due to the large time scales. In this paper, a hybrid algorithm of PSO (particle swarm optimization) and DE (differential evolution) is used to achieve a solution to the energy-optimal tour mission. Based on GTOC-3 (Global Trajectory Optimization Competition), this paper determines the exploration sequence and provides the optimal solution.

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Based on the trajectory design of a mission to Saturn, this paper discusses four different trajectories in various swingby cases. We assume a single impulse to be applied in each case when the spacecraft approaches a celestial body. Some optimal trajectories of EJS, EMS, EVEJS and EVVEJS flying sequences are obtained using five global optimization algorithms: DE, PSO, DP, the hybrid algorithm PSODE and another hybrid algorithm, DPDE. DE is proved to be superior to other non-hybrid algorithms in the trajectory optimization problem. The hybrid algorithm of PSO and DE can improve the optimization performance of DE, which is validated by the mission to Saturn with given swingby sequences. Finally, the optimization results of four different swingby sequences are compared with those of the ACT of ESA.

At present, optical autonomous navigation has become a key technology in deep space exploration programs. Recent studies focus on the problem of orbit determination using autonomous navigation, and the choice of filter is one of the main issues. To prepare for a possible exploration mission to Mars, the primary emphasis of this paper is to evaluate the capability of three filters, the extended Kalman filter (EKF), unscented Kalman filter (UKF) and weighted least-squares (WLS) algorithm, which have different initial states during the cruise phase. One initial state is assumed to have high accuracy with the support of ground tracking when autonomous navigation is operating; for the other state, errors are set to be large without this support. In addition, the method of selecting asteroids that can be used for navigation from known lists of asteroids to form a sequence is also presented in this study. The simulation results show that WLS and UKF should be the first choice for optical autonomous navigation during the cruise phase to Mars.