广义多圈Lambert算法求解多脉冲最优交会问题

Generalized multiple-revolution Lambert algorithm for solving multiple-impulse rendezvous problem

基于一种高效高精度的Battin多圈Lambert算法提出一种考虑轨道摄动的广义多圈Lambert算法.与现有算法相比,本算法虽然原理复杂但计算流程非常简单,效率极高,分别通过几次内外循环就可满足精度要求.广义多圈Lambert算法结合一种可行解迭代交会模型构成了一个通用的多圈多脉冲交会规划框架,应用两步法求解此多变量的复杂工程优化问题,首先利用高效率的进化全局优化算法以及解析轨道模型作全局搜索,然后利用序列二次规划算法以及简化高精度轨道计算模型作局部搜索,此方法可以保证高效高精度的求解多圈多脉冲交会问题.算例表明此方法特别适用于满足实际工程约束的交会规划问题.

Techniques based on a high efficient high precision Battin multiple-revolution Lambert algorithm were extended to a generalized multiple-revolution Lambert algorithm which can consider orbital perturbations.The approach is difficult to understand but is high efficient with a simple calculation flow which needs only several inner and outer iterations.A unified multiple-revolution multiple-impulse rendezvous planning framework was proposed by combining the generalized multiple-revolution Lambert algorithm and a feasible iteration rendezvous approach.A two-step optimization method was used to solve this difficult multi-variable engineering optimization problem which first utilizing a high efficient evolutionary algorithm with an analytical orbit model for global search,then a sequential quadratic programming algorithm was used with a simplified high precision orbit model for local optimization.The proposed method can guarantee to solve multiple-revolution multiple-impulse rendezvous problem with high efficiency and precision.The demonstration validates that it is very suitable for rendezvous planning problem with practical engineering constraints.