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传统的普适变量法求解Lambert转移轨道的变轨点速度时,在两位置矢量夹角为180°处出现奇异,且用牛顿迭代法求解普适变量会丢失部分重要的解.通过公式变换消除奇异项而推导出一种无奇异的速度求解公式;且根据转移轨道的圈数对普适变量的取值范围进行分段,在每个区间用人工免疫算法AIA(Artificial Immune Algorithm)搜索普适变量正确解,解出所有Lambert转移轨道并从中选择最优转移轨道.仿真算例表明:这种改进的普适变量法能有效避免传统普适变量法的奇异性,而且能求得所有的Lambert转移轨道并得到燃料消耗最优的转移轨道.
When the conventional universal variable method is used to solve the velocity of the orbiting point of Lambert transfer orbit, singularity occurs at an angle of 180 ° between the two position vectors, and some important solutions are lost by solving Newton's iterative method with universal variables. Singular terms and derive a non-singular velocity formula; and according to the number of turns of the orbit transfer range of universal variables segment, in each interval with artificial immune algorithm AIA (Artificial Immune Algorithm) search for universal All the Lambert transfer orbitals are solved and the optimal transfer orbit is selected from the correct solutions of the variables.The simulation results show that the improved universal variable method can effectively avoid the singularity of the traditional universal variable method and can obtain all the Lambert Transfer orbit and get the best fuel consumption transfer orbit.