Pareto-optimal control of relative motion in the orbital maneuvering problem of spacecraft with finite thrust

帕累托-有限推力航天器轨道机动问题中相对运动的最优控制

¹ Samara University, Samara 443086, Russia
² Northwestern Polytechnical University, Xi'an 710072, China

Received: 18 July 2022

Abstract

To solve the time-free rendezvous problem of two spacecraft, the multi-criteria optimization of the relative motion trajectory of the linear motion model in an orbiting cylindrical reference frame is studied. The equations for describing the secular and periodic parameters of the relative motion are obtained. The structure of the nominal control program for the longitudinal motion control variant with finite transversal thrust is investigated in some detail, and its analytical solutions are obtained. An algorithm for solving the Pareto-optimal control program for arbitrary boundary conditions and thrust control acceleration values in the standard time including maneuver time and total time is developed. The algorithm uses the Pareto optimal method to achieve two kinds of multi-objective optimization (total time optimization and fuel optimization). The numerical calculation results on the geostationary planar orbit parameter correction variants are given.

摘要

针对时间自由的两航天器交会问题, 考虑了在轨道圆柱参考系中线性运动模型的相对运动轨迹的多准则优化。得到了描述相对运动的长期参数和周期参数方程。详细研究了具有有限横向推力的纵向运动控制变体的标称控制程序结构, 并获得了解析解。开发了一种求解任意边界条件和推力控制加速度值的帕累托最优控制程序在标准空间(机动时间、总时间)中的算法。该算法中, 使用帕累托最优方法, 实现了多目标的优化(总时间最优, 燃料最优), 给出了地球静止轨道平面上参数校正变体的数值计算结果。