一种月球表面飞跃转移轨迹设计方法

针对飞跃器在月球表面飞跃转移轨迹设计问题，提出了基于凸优化方法的整个飞跃过程燃料最优轨迹设计方法。与经典凸优化方法对轨迹分段求解后再拼接得到全轨迹设计的方法不同，在假设垂直上升、着陆时间固定条件下，根据实际工程需要对轨迹进行了分段设计约束，利用黄金分割法搜索上升着陆时间，通过将原问题转化为求解一个二阶锥问题得到了全飞行过程燃料最优轨迹，解决了经典方法中分段最优但全任务过程非最优的问题。仿真结果表明，在同样满足分段约束情况下，分段凸优化方法采用不同垂直起降速度约束时燃耗分别为25.7207kg和 25.3903kg，而全程凸优化方法的燃料消耗为24.9682kg，优于分段凸优化的结果。

An optimal trajectory design for lunar surface hop

For the lunar surface trajectory design problem of hoppers, the fuel optimal trajectory for the whole hop process based on convex optimization was presented. Different from the typical method that the trajectory was designed separately firstly and then connected to a whole trajectory, it was assumed that the vertical ascent and descent time was fixed, then the constraints of the whole trajectory were divided into phases so that the constraints at each phase were convex according to practical engineering requirements. And the golden section method was used to search for the fixed ascent and descent time. The original fuel optimization problem was transformed into a second-order cone problem (SOCP) and the fuel optimal trajectory was obtained by solving this problem. In this way, an optimal solution was found for the whole trajectory design instead of a connected piecewise optimal one given by the classical method. As is shown in simulation results, when the piecewise constraints are satisfied, the fuel consumption of the piecewise convex optimization which adopts different vertical ascent and descent speed constraints is 25.7207kg and 25.3903kg respectively. On the other hand, the fuel consumption of the whole convex optimization method is only 24.9682kg, which is better than that of the piecewise convex optimization solution.