基于A*算法的摄动Lambert同伦迭代方法  

Homotopic perturbed lambert algorithm based on A*algorithm

作　　者：谢聪 杨震[1,2] 梁彦刚[1,2] XIE Cong;YANG Zhen;LIANG Yangang(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China;Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学空天科学学院,长沙410073 [2]国防科技大学空天任务智能规划与仿真湖南省重点实验室,长沙410073

出　　处：《航空学报》2025年第4期188-199,共12页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(12372052);湖南省自然科学基金(2023JJ20047);载人航天工程科技创新团队项目(2021-JCJQ-QT-047)。

摘　　要：摄动Lambert问题是航天器交会对接、在轨维修等任务的基础问题。由于摄动Lambert问题没有解析解,仅能通过迭代计算得出数值解,因此现有方法主要针对迭代收敛性与计算效率进行改进。在现有同伦迭代的基础上,引入通用图搜索A*算法思想,提出了剪枝同伦迭代方法。首先,将当前末位置偏差到初速度增益的状态转移矩阵梯度方向与目标方向结合得到迭代方向,设计了基于A*算法的同伦映射;其次,基于泰勒展开设计了线性摄动矩阵,实现了对末位置发散路径的剪枝,解决了牛顿打靶法、拟线性化等传统方法无法排除初速度发散的无效迭代问题。仿真结果表明,本方法在保证获得最优解的同时较现有同伦法提升25%以上的计算效率,具有更大的收敛范围;同时本方法具有良好的初值收敛特性,地月三体系统轨道转移案例较拟线性化方法提升30%以上计算效率。Perturbed Lambert Problem forms the fundamental basis for tasks such as spacecraft rendezvous and onorbit servicing.Due to the lack of an analytical solution for the perturbed Lambert problem,numerical solutions can only be obtained through iterative computations.Consequently,existing methods primarily focus on improving iteration convergence and computational efficiency.Building upon current homotopic iteration methods,this paper introduces the general concept of the A*algorithm for graph search and proposes a pruned homotopic iteration approach.Firstly,by combining the gradient direction of the state transition matrix from the terminal position error to the initial velocity in⁃crement with the target direction,an iteration direction is derived,and a homotopic mapping based on the A*algorithm is designed.Secondly,utilizing Taylor expansion,a linear perturbation matrix is devised,enabling pruning of diver⁃gent end-position paths.This addresses the issue of ineffective iterations due to initial velocity divergence that conven⁃tional methods such as Newton’s shooting method and quasi-linearization fail to exclude.Simulation results demon⁃strate that while ensuring the attainment of optimal solutions,our proposed method improves computational efficiency by over 25%,compared to existing homotopic methods,featuring a broader convergence range.Moreover,the method exhibits favorable characteristics regarding initial value convergence.In the case of orbit transfer in the EarthMoon three-body system,it achieves more than a 30%increase in computational efficiency compared to quasilinearization techniques.

关 键 词：摄动Lambert问题 同伦迭代法 轨道转移 A*算法 三体问题 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]