一种无奇异的求解Lambert变轨的普适变量法

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.

Singularity free universal variables method to solve Lambert transfer

The conventional universal variables method has singularity in solving the velocities at transfer time of Lambert transfer orbit when angle between two position vectors is 180°, and may lose some important universal variables by using Newton method. The singularity free formulas for solving velocities were derived by using formula transformation to expurgate singular terms. And the range of universal variables was divided into several sections according to the loop number of transfer orbit, then artificial immune algorithm(AIA) was used to search universal variables solutions in each section, finally all Lambert transfer orbit were derived and the optimal one can be chosen. Simulation results show that, this modified universal variables method can availably avoid the singularity of conventional universal variables method, derive all Lambert transfer orbit and get the transfer orbit whose fuel penalty is optimal.