Focusing on the long-distance rapid cooperative rendezvous of two spacecraft under finite continuous thrust, this paper proposes a practical strategy for space operation using multiple specific-direction thrusts. Based on the orbital dynamic theory and Pontryagin’s maximum principle, the dynamic equations and optimal control equations for radial, circumferential, and normal thrust are determined. The optimization method is a hybrid algorithm. The initial costate variables for the fuel-optimal rapid cooperative rendezvous problem are obtained using quantum particle swarm optimization and subsequently set as the initial values in the sequence quadratic programming to search for the exact convergent solution. The elliptical and near-circular mission orbital rendezvous for spacecraft with multiple specific-direction thrusts are simulated and optimized. Numerical examples verifying the proposed method are provided. The results facilitate easier realization of rapid spacecraft maneuvering under continuous thrust conditions.

中文翻译：

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多方向推力快速协同航天器交会优化控制

针对有限连续推力作用下两艘航天器的长距离快速协同交会，提出了一种多方向特定推力空间运行的实用策略。基于轨道动力学理论和庞特里亚金极大值原理，确定了径向、周向和法向推力的动力学方程和最优控制方程。优化方法是一种混合算法。燃料最优快速协作交会问题的初始协变量是使用量子粒子群优化获得的，随后设置为序列二次规划中的初始值以搜索精确收敛解。对具有多个特定方向推力的航天器的椭圆和近圆形任务轨道交会进行了仿真和优化。提供了验证所提出方法的数值例子。结果有助于在连续推力条件下更容易地实现航天器的快速机动。