Shaping low-thrust trajectories with thrust-handling feature

Shape-based methods are becoming popular in low-thrust trajectory optimization due to their fast computation speeds. In existing shape-based methods constraints are treated at the acceleration level but not at the thrust level. These two constraint types are not equivalent since spacecraft mass decreases over time as fuel is expended. This paper develops a shape-based method based on a Fourier series approximation that is capable of representing trajectories defined in spherical coordinates and that enforces thrust constraints. An objective function can be incorporated to minimize overall mission cost, i.e., achieve minimum $\mathrm{\Delta }V$. A representative mission from Earth to Mars is studied. The proposed Fourier series technique is demonstrated capable of generating feasible and near-optimal trajectories. These attributes can facilitate future low-thrust mission designs where different trajectory alternatives must be rapidly constructed and evaluated.     

一种航天器空间机动轨道的改进形状设计方法

针对带推力约束的航天器三维空间机动轨道初始设计问题,提出了一种基于傅立叶级数展开的改进形状设计方法。首先,在柱坐标系下建立了航天器运动模型,并将基于傅立叶级数展开的形状方法推广到三维空间的机动轨道初始设计;然后,基于所得到的空间初始机动轨道,采用直接配点法进行了完整三维空间机动轨道的优化设计。仿真结果表明,提出的方法可以为带有任务约束的航天器三维空间机动轨道的优化设计提供更优的初始参数及其解析解,为空间机动轨道设计提供了新的方法。     

Optimal solar sail trajectory approximation with finite Fourier series

The heliocentric transfer of a solar sail-based spacecraft is usually studied from an optimal perspective, by looking for the control law that minimizes the total flight time. The optimal control problem can be solved either with an indirect approach, whose solution is difficult to obtain due to its sensitivity to an initial guess of the costates, or with a direct method, which requires a good estimate of a feasible (guess) trajectory. This work presents a procedure to generate an approximate optimal trajectory through a finite Fourier series. The minimum time problem is solved using a nonlinear programming solver, in which the optimization parameters are the coefficients of the Fourier series and the positions of the spacecraft along the initial and target orbits. Suitable constraints are enforced on the direction and magnitude of the sail propulsive acceleration vector in order to obtain feasible solutions. A comparison with the numerical results from an indirect approach shows that the proposed method provides a good approximation of the optimal trajectory with a small computational effort.     

基于轨迹成型法星际小推力转移轨道快速设计

给出了一种基于轨迹成型法星际小推力转移轨道的快速设计方法.首先介绍了基于轨迹成型法的有关内容,并通过与Hohmann变轨相对比验证了该方法描述小推力变轨的可用性.鉴于这种方法数学模型收敛性强,计算速度快的特点,以地火转移轨道为例,提出了不同推力条件下发射窗口的搜索方法.最后,利用基于轨迹成型法和真实数值仿真之间误差小、线性度好的特点,通过几次简单的线性迭代设计出小推力转移轨道.     

对数螺旋线非开普勒轨道的可行性分析

提出了基于形状的非开普勒轨道设计方法,并分析了对数螺旋线轨道的应用可行性。 首先在假定轨道形状的前提下,通过变量代换推导出了在极坐标系下一般曲线用于轨道设计 的基本方程;然后分析了对数螺旋线表达式中的关键参数与航迹角的关系,得到了相应轨道 的基本性质;最后对待定参数的对数螺旋线轨道应用的可行性进行了推导和分析,结果显示 采用对数螺旋线设计非开普勒轨道是可行的,但仅适用于从椭圆初始轨道实现转移的情况。