An Approach for Time-Free Optimal Two-Impulse Trajectories Using Primer Vector Theory and Mathieu Transformation
In this paper, a semi-analytical approach combining primer vector theory and Mathieu transformation for a time-free optimal two-impulse transfer problem is proposed. The Mathieu transformation provides analytical expressions of the primer vector and its derivative for each coast arc. Using necessary optimality conditions of primer vector theory, continuous property of positions, and Pontryagin’s necessary conditions for optimality, twenty seven algebraical equations with twenty seven unknown constants are derived for the time-free two-impulse transfer problem. By solving such twenty seven unknown parameters using a nonlinear least square method and a genetic algorithm, the two-impulse transfer trajectory is determined. Two numerical examples are given to demonstrate the effectiveness of the proposed approach. The approach can be also extended to timefree N-impulse (N > 2) transfer problems by adding thirteen algebraical equations with thirteen unknown constants for each additional mid-coast arc.
optimal fuel impulse transfer primer vector theory Mathieu transformation
LI Maodeng WANG Dayi HUANG Xiangyu
National Laboratory of Space Intelligent Control, Beijing Institute of Control Engineering, Beijing 100190, P. R. China
国际会议
The 31st Chinese Control Conference(第三十一届中国控制会议)
合肥
英文
2246-2253
2012-07-01（万方平台首次上网日期，不代表论文的发表时间）