Jupiter exploration is one of the focuses of deep space exploration in the near future. Design and optimization of trajectories in the Jovian system are crucial technologies for Jupiter exploration missions due to the unique and challenging multi-body dynamical environment. Various methodologies have been proposed and developed. However, there is a lack of comprehensive review of these methodologies, which is unfavorable for further developing new design techniques and proposing new mission schemes. This review provides a systematic summarization of the past and state-of-art methodologies for 4 main exploration phases, including Jupiter capture, the tour of the Galilean moons, Jupiter global mapping, and orbiting around and landing on a target moon. For each exploration phase, the related methods are categorized according to the fundamental features. The advantages and capabilities of the methods are described or analyzed, revealing the research progress. Finally, a prospect of future development of the methods is presented, aiming at providing references for further studies on trajectory design and optimization in the Jovian system.

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For the mission requirement of collision-free asteroid landing with a given time of flight (TOF), a fast generation method of landing reachable domain based on section and expansion is proposed. First, to overcome the difficulties of trajectory optimization caused by anti-collision path constraints, a two-stage collision-free trajectory optimization model is used to improve the efficiency of trajectory optimization. Second, the velocity increment under a long TOF is analyzed to obtain the distribution law of the reachable domain affected by the TOF, and the generation problem of the reachable domain is transformed into the solution problem of the initial boundary and the continuous boundary. For the initial boundary, the section method is used to acquire a point on the boundary as the preliminary reachable domain boundary. The solution of continuous boundary is based on the initial boundary continuously expanding the section into the reachable domain until the boundary is continuous. Finally, the proposed method is applied to the asteroids 101955 Bennu and 2063 Bacchus. The simulation results show that this method can quickly and accurately obtain the reachable domain of collision-free asteroid landing in a given TOF and is applicable to different initial positions.

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