摘要
针对星际探测任务中燃料最省小推力转移轨道问题,提出一种基于标称轨道的快速设计方法。首先以具有相同端点时刻的无摄动标称轨道为参考,对传统的非线性轨道优化模型进行合理变换,将复杂的优化问题简化为可解的两点边值问题;然后基于标称轨道3个独立积分推导出解析的状态转移矩阵,并以此为基础导出了两点边值问题的最优解析解。该方法无需数值迭代,有效地克服了数值优化方法收敛性差、计算效率低的缺点。最后,以探测火星的小推力转移轨道为例对该方法进行了验证,与精确的数值结果相比,该方法计算的燃料消耗误差小于1%。
A novel rapid method to design optimal-fuel interplanetary trajectory for low-thrust propulsion is presented based on normal trajectory approach. A simple two-point boundary value problem is formulated using a non-perturbation normal trajectory, which has the same endpoint time with low-thrust trajectory. The analytic state transition matrix is derived using three independent integrations of normal trajectory, and then the optimal solution of two-point boundary problem is obtained. The major advantage of this method is that it provides a more robust and efficient technique for solving interplanetary low-thrust transfer problem than traditional numerical optimization approaches. The rapid method introduced is demonstrated for an Earth-Mars low-thrust transfer application. The fuel cost computed using the proposed method exhibits a very close match （within 1%） with the corresponding fuel cost obtained with a precise numerical optimization approach.
出处
《航空学报》
EI
CAS
CSCD
北大核心
2007年第6期1281-1286,共6页
Acta Aeronautica et Astronautica Sinica
基金
国家自然科学基金(10672044)
关键词
小推力
最优解析解
标称轨道
燃料最省
两点边值
low-thrust
optimal analytic solution
normal trajectory
optimal-fuel
two-point boundary
