基于特征模型的Halo轨道维持控制

平动点，尤其是共线平动点轨道在未来深空探测活动中具有重要的应用价值，但由于共线平动点轨道不稳定，运行在其上的航天器在无控情况下将很快偏离标称轨道，因此在实际任务中，轨道维持必不可少。针对地月系L₂点附近的Halo轨道维持问题，首先在圆型限制性三体模型下，利用Richardson三阶近似解析解、微分修正以及打靶法获得了用于维持控制的标称轨道；然后设计了基于特征模型理论的黄金分割控制器用于速度跟踪以及PD控制器用于位置跟踪；最后分别在圆型限制性三体模型和双圆限制性四体模型下进行了仿真分析。结果表明：在两种模型下，位置和速度的跟踪精度分别优于100 m和0.003 m/s，但双圆限制性四体模型下所需总的速度增量比圆型限制性三体模型下所需总的速度增量高一个数量级。

Characteristic model-based station-keeping control for Halo orbit

Orbits around libration points have a key value in future deep space explorations. However, due to the instability of libration points, explorers that are running on the orbits around them will, if without control, deviate at a high speed. As a result, station-keeping is essential in practical missions. To solve the station-keeping problem of the periodical Halo orbits around Earth-Moon L₂ point, a baseline orbit was obtained through Richardson three-order analytical solution, differential correction, and target shooting strategy. Then, a characteristic model-based golden-section controller was designed for velocity tracking and a PD controller was designed for position tracking. Finally, simulations were conducted under restricted three-body model and bicircular restricted four-body model. Results show that, under both circumstances, the tracking accuracy was better than 100 m in position and 0.003 m/s in velocity, while the controller consumption of bicircular restricted four-body model was an order of magnitude higher than that of the restricted three-body model.