航天器相对运动的两点边界值问题解析解

Analytical Solution of Two-Point Boundary Value Problem for Spacecraft Relative Motion

针对无摄椭圆轨道,推导了表示真实相对位置速度的状态转移矩阵,进而推导出了相对运动两点边界值问题的一阶解析解。所得结果不仅可指定转移时间、还可在时间范围内进行全局的燃料优化或在时间和燃料两者间折中;对于周期和非周期的相对运动均适用。仿真结果表明此解的归一化精度达到10-6。进一步的仿真发现相对转移过程的燃料消耗会随目标轨道偏心率的增加而增加;随长半轴的增加而减少;随初始真近点角的增加呈现周期性变化;随着转移时间增加,燃料消耗的总趋势是减少的。

The two-point boundary value problem（TPBVP） of a leader-follower spacecraft formation flying was studied.Aiming at unperturbed elliptical reference orbits,the state transfer matrix representing actual relative position and velocity was derived,and the first-order analytical solution of TPBVP is obtained,which can deal with the problems of the specified rendezvous time,fuel optimization and compromise between fuel and time,and is applicable to the periodic and non-periodic relative motion.The simulation results show that the normalized accuracy of this solution achieves 10-6 level.Furthermore,the fuel cost of relative transfer increases with eccentricity increasing,and decreases with semi-major axis increasing,and appears periodic change with initial true anomaly increasing,and decreases as the transfer time increasing.