基于正切推力的近地及火星探测轨道转移和轨道交会研究

Tangential thrust is the most efficient direction strategy since it changes the mechanical energy of the orbit at the maximum rate. Tangential thrust has many merits, e.g., simpler thrust direction, less energy consumption and significant improvement in transfer-trajectory safety. According to the magnitude of the thrust, tangential thrust can be divided into two categories: impulse tangential thrust and continuous tangential thrust. Classical Hohmann transfer is a two-impulse cotangent transfer between coplanar circular orbits, and it is the minimum-energy transfer among all the two-impulse orbital transfers. This project will study the Earth-Mars orbit design with the impulse tangential thrust and the two-body absolute motion and relative motion orbital transfer and orbital rendezvous with the continuous tangential thrust. For limited magnitude of the tangent impulse, we will use the patched conic method and the B-plane correction technique, to solve the minimum-energy transfer with two tangent impulses from the Earth parking orbit to the elliptic orbit around Mars. Considering the limited thrust acceleration and the bounded transfer-trajectory radius, we will utilize the shape-based inverse polynomial method to solve the constrained absolute orbit transfer and orbit rendezvous problems. When the relative range between two spacecraft is small, we will derive the nonlinear relative motion equation with the continuous tangential thrust in the chaser's frame, and use the generating function method to solve the optimal control for the relative-motion orbit rendezvous problem. The research of this project can provide theoretical basis for the orbit transfer and the orbit rendezvous missions in low Earth orbit and Mars exploration.

正切推力是改变瞬间轨道机械能最有效的方向策略，它具有简单的推力方向、更少的能量消耗、更安全的转移轨迹等优势。根据推力的大小，正切推力分为脉冲正切推力和连续正切推力。经典的霍曼转移是共面圆轨道之间的双脉冲双正切转移，在所有双脉冲转移中能量最小。本课题将研究脉冲正切推力在探火星三体轨道设计，以及连续正切推力在二体绝对运动和相对运动轨道转移和交会中的应用。考虑正切脉冲大小受限时，利用圆锥曲线拼接和B平面修正技术，研究两次正切脉冲实现从地球停泊轨道到环绕火星椭圆轨道的最小能量转移；考虑连续正切推力大小约束和转移轨迹半径约束，利用基于形状的逆多项式法求解约束条件下的绝对轨道转移和交会问题；考虑两飞行器距离较小时，研究追踪器坐标系下连续正切推力的非线性相对运动方程，利用生成函数法求解相对运动轨道交会的最优控制问题。本课题的研究可为正切推力下的近地、火星探测轨道转移和轨道交会任务提供理论依据。

正切推力是指推力方向沿着轨迹的切线方向，是改变瞬间轨道机械能最有效的方向策略。本项目针对正切推力轨道机动问题，主要研究了正切脉冲和正切连续小推力下的轨道转移、轨道交会和星下点轨迹调整问题。针对正切脉冲推力，研究了单次和多次脉冲的星下点轨迹调整轨道机动问题，考虑精确飞越和姿态摆动两种情况，得到了J2摄动下的脉冲近似解析解；针对脉冲轨道转移问题，提出了一种利用两次周向脉冲实现轨道转移的方法，适用于任何共面椭圆轨道情况。针对正切连续推力，研究了适用于轨迹半径、推力幅值等约束条件下的修正逆多项式形状函数法，可用于连续低推力下探火星和近地轨道初始轨道设计问题。针对共面椭圆低推力轨道转移和交会问题，提出了一种基于半长轴的形状函数法，严格证明了该形状函数对转移问题能够满足轨迹安全约束。针对异面椭圆低推力轨道转移和交会问题，基于初始轨道平面为参考平面，提出了一种新的仰角和轨迹半径函数，可适用于大范围轨道平面变化的异面轨迹优化问题。本课题的研究成果可为正切推力近地及深空探测轨道机动任务提供理论和技术支持。