基于多项式设计法的小推力轨迹设计

Low-thrust trajectory design of rendezvous based on polynomial function

形状逼近法是小推力轨迹设计中的一种有效方法,然而现有的方法大都假定运动轨迹为某一特定的形状,而且没有考虑推力加速度的约束限制。针对小推力轨道交会问题,提出一种基于多项式的轨迹设计方法。结合极坐标系,建立基于多项式的三自由度轨迹运动模型,将轨迹设计问题转化为求解多项式的系数问题;根据运动模型推导轨迹的动力学特性,建立约束方程,并以消耗燃料最少作为性能指标,采用序列二次规划的方法对多项式的系数进行寻优计算。该方法不仅能求解多个形状设计参数不确定性问题,而且还能满足推力加速度的约束限制。仿真验证了该方法的正确性和可用性,该方法可为任务设计初步阶段的轨迹设计和燃料消耗预估提供一定的技术参考。

Shape-based approximation is an effective method for the low-thrust trajectory design. However, the vast majority of methods assume that the motion trajectory is a specific shape, and there is no constraint on the thrust acceleration. In this representation, according to the issue of low-thrust spacecraft rendezvous, a new method for transfering trajectory design was proposed. Based on the polar coordinates, the trajectory design was successfully turned into solving polynomial coefficients problem through three degrees of freedom motion model built by introduced polynomial function. Meanwhile, the dynamic characteristics of the trajectory as well as the constraint equations were deduced. Subsequently, the optimal polynomial coefficients were solved by the approach of sequential quadratic programming. This method can not only solve problems with a greater number of free parameters, but also meet the thrust acceleration constraints. The simulation has confirmed that this method is accuracy and availability. It can provide a certain technical reference for the trajectory design and fuel consumption estimation during the preliminary stage.