基于T-H方程的多脉冲最优交会方法

针对椭圆参考轨道交会问题，采用T-H方程描述相对运动，提出了一种时间固定燃料最省的多脉冲最优交会方法，优化参数为交会脉冲及其施加时刻.当考虑到J2摄动或航天器初始相对距离较大时，用T-H方程进行状态预测其线性化误差一般不容忽略，而若用轨道积分预测则耗时较多，进而导致优化时间过长.针对此问题，提出一种采用前一优化脉冲节点的状态导出的轨道根数预测当前节点状态的预测方法.该方法简单实用，有效地加快了优化收敛速度.最后基于多脉冲优化解进行了数值轨道积分以验证交会精度.仿真结果表明，即使加上J2摄动，在初始相对距离为1 000 km时，该方法的终端位置精度仍能达到75 m.

Optimal multi-impulse rendezvous based on T-H equations

For rendezvous near an elliptic reference orbit, relative motion was described by T-H equations. One time-fixed fuel-optimum multi-impulse rendezvous method was proposed to determine the optimal impulse and its time. If J2 perturbation or the far initial relative distance was considered, the T-H equations linearization error couldn't be ignored, while the trajectory integration was more time-consuming and the optimal convergence rate decreased. For this problem, a new method was put forward that the current node state could be predicted with the orbit element computed by the previous one. It was very simple and valid for making optimal convergence faster. Based on the optimal impulse time, the trajectory numerical integration was carried out to verify the rendezvous precision. The results indicate that the terminal position has higher accuracy up to 75 m even under J2 perturbation and the initial relative distance of 1 000 km.