摘要
针对现有求解模型复杂、收敛速度慢等问题,在将经典Lambert转移问题转化为超越方程的基础上,提出一种基于解析梯度的Lambert问题迭代求解算法。选择转移轨道的真近点角为迭代变量,导出转移时间关于真近点角的解析梯度,构造一种基于解析梯度的牛顿迭代算法,降低了算法计算复杂度。理论分析表明该算法具有二阶以上的收敛速度。依据偏心率向量与转移轨道形状的关系,通过几何方法分析得到转移轨道在初始位置处的速度约束条件,推导转移轨道真近点角的最大值和最小值的解析表达式,并采用线性插值方法确定迭代初值,进一步提高了迭代算法的收敛速度。数学仿真结果表明在各种转移条件下算法均能快速收敛,采用所给出的初值选取方法初值确定精度高,进而能够加快收敛速度,而与较割线法相比较收敛速度快、计算量小,验证了所提出算法的有效性。
A method based on analytical gradients for solving classical Lambert orbit transfer problem is presented for existing complex solution model and slow convergence rate. The Lambert problem is transformed into transcendental equation for solving the constrained problem with transfer time. The true anomaly is selected as the iterative variable. The analytical gradient of the transfer time with respect to the true anomaly is to update the true anamaly at each iteration step.Theoretical analysis show that the algorithm has above second-order velocity constraints deduced from the relationship between eccentricity vector and transfer orbit shape by use of the geometric method,and the iteration interval is derived from transfer orbit shape by use of the geometric method,and the iteration initial value of true anomaly is determined by using the linear interpolation algorithm to improve initial guess accuracy. Several simulations have been conducted to demonstrate the validity of the algorithm. The results indicate that the proposed method with high initial guess accuracy improves the convergence rate and converges fast under different transfer conditions. The method can not only converges faster but also has smaller computational complexity compared with the secant iteration algotithm.
出处
《宇航学报》
EI
CAS
CSCD
北大核心
2016年第3期316-324,共9页
Journal of Astronautics
基金
国家自然科学基金重大计划项目(91438202)
哈工大青年拔尖人才选聘计划
