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针对编队飞行中多个从星飞行任务设计问题,研究了用伪谱同伦算法对其进行优化的方法,以获得小推力时的最省燃料转移轨道。将无推力的转移轨道作为初始轨道,用伪谱法对其进行优化,使其转移轨道能量最优,所得轨道可作为初值,解决了同伦算法对初值敏感的问题。再用同伦算法进行优化,降低了间接法求解最优控制问题的难度,得到最省燃料轨道,解决了求解Bang-Bang控制产生的不光滑性。对运行于高度400km近地圆轨道上3颗完全相同的从星算例进行了求解,构建轨道跟飞/领飞构型的最省燃料轨道。结果表明:伪谱同伦算法能较大幅度节省燃料,对求解编队飞行从星转移轨道设计可行且有效。
Aiming at the design of multiple flight missions in formation flight, the method of using pseudo-spectral homotopy algorithm to optimize it is studied to obtain the most fuel-transfer trajectory at small thrust. The thrust trajectory is regarded as the initial orbit and optimized by pseudospectral method to optimize the transfer orbit energy. The obtained orbit can be used as the initial value to solve the problem that the homotopy algorithm is sensitive to the initial value. Then using the homotopy algorithm to optimize, it reduces the difficulty of the indirect method to solve the optimal control problem, obtains the most fuel-efficient trajectory and solves the unsmoothness of solving the Bang-Bang control. Three identical star cases running on a near-Earth orbit at a height of 400 km are solved to construct the most fuel-efficient orbit with the orbital / fly-by-fly configuration. The results show that the pseudospectral homotopy algorithm can greatly save fuel and is feasible and effective in solving the orbital flight design from the star transfer orbit.