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提出一种基于同伦方法限制性三体问题小推力推进转移轨道设计方法。首先根据最优控制原理分析了航天器在轨道转移中不同性能指标时的最优控制律,然后引入同伦参数构造新的性能指标,在基于遗传算法和打靶法得到能量最优的解基础上,采用伪弧长法跟踪同伦轨迹,进而得到燃料最优的转移轨道。最后对地月系下从GEO轨道到L1点Lyapunov轨道的转移轨道进行优化。仿真结果表明:利用遗传算法能优化得到较为合适的流形拼接点和协态变量初始值,利用打靶法能有效地优化得到小推力燃料最优转移轨道。
A small thrust propulsion transfer trajectory design method based on the homotopy method is proposed. Firstly, according to the principle of optimal control, the optimal control law of the spacecraft during orbit transfer with different performance indexes is analyzed. Based on the homotopy parameters, a new performance index is constructed. On the basis of the optimal energy solution based on genetic algorithm and shooting method , Using pseudo-arc length method to track the homotopy trajectory, and then get the optimal fuel transfer orbit. Finally, the orbital system from GEO orbit L1 L1 Lyapunov orbit transfer orbit optimization. The simulation results show that the genetic algorithm can be used to optimize the initial values of the manifolds and the covariates, and the optimal transfer trajectory of the small thrust fuel can be effectively optimized by using the shooting method.