利用凸优化方法的多航天器编队重构轨迹规划  

Trajectory Planning of Multi-spacecraft Formation Reconfiguration Using Convex Optimization Method

作　　者：刘幸川 陈丹鹤 徐根 廖文和[1] LIU Xingchuan;CHEN Danhe;XU Gen;LIAO Wenhe(School of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学机械工程学院,南京210094

出　　处：《宇航学报》2023年第6期934-945,共12页Journal of Astronautics

基　　金：国家自然科学基金(51905272);The Innovation and Talent Recruitment Base of Theory and Key Technology for Intelligent Ammunition System资助课题。

摘　　要：针对近地圆轨道多航天器编队重构问题,提出一种使用凸优化方法的编队重构最优轨迹规划方法。基于相对轨道根数(ROE)推导了航天器在非球形引力摄动与差异大气阻力摄动影响下的相对运动模型,考虑微小型航天器推力限制与重构过程中的安全距离等约束,建立了多航天器重构机动的凸优化数学模型,设计了利用CVX软件的最优重构轨迹求解方法,最后通过数值仿真验证了提出的轨迹优化方法。结果表明,该方法解决了在地球引力摄动与差异大气阻力摄动影响及推力缺失、幅值限制与安全距离等工程约束下的多航天器编队协同重构轨迹优化问题,并且计算速度更快、求解精度更高。可为多航天器协同编队重构提供理论基础。Aiming at the problem of multi-spacecraft formation reconfiguration in low-Earth orbit,an optimal trajectory planning method is proposed based on the convex optimization method.Firstly,the relative motion model of spacecraft is derived under the influence of non-spherical gravitational perturbation and differential atmospheric drag perturbation based on the relative orbital elements(ROE).Secondly,the convex optimization mathematical model of multi-spacecraft reconfiguration maneuvering is established considering some constraints of thrust limitation and safe distance during the process of reconfiguration,and an optimal reconfiguration trajectory solution method using CvX software is designed.Finally,the proposed trajectory optimization method is verified by numerical simulation.The results show that this method can solve the trajectory optimization problem of multi-spacecraft formation reconfiguration effectively with fast computational speed and high accuracy,in condition of the influence of non-spherical gravitational perturbation and differential aerodynamic drag,as well as engineering constraints of loss of thrust,amplitude constraint and safe distance.It provides a theoretical basis for cooperative reconfiguration of multi-spacecraft formation.

关 键 词：编队重构 相对运动模型 多约束问题 轨迹优化 凸优化 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]