基于分段常值推力的水滴悬停构型控制策略

针对航天器编队飞行任务对相对运动控制的要求，研究了在分段常值推力控制下航天器受迫绕飞构型的设计与控制问题。首先，基于脉冲控制下的水滴悬停构型，提出了多段常值推力控制实现水滴悬停构型的打靶方程；将打靶方程转化为求解极值问题，采用最小二乘法来求解；分析了一段常值推力可行性。然后，以连续常值小推力控制方程为基础，推导了小邻域定理，分析了近距离相对运动条件下两段常值推力控制的可行性；针对可能出现求解精度差的问题，提出了小推力增量方程来修正精度，并证明在靠近理想解的情况下多次迭代可以趋近于理想解。最后，通过数值仿真实现常值小推力控制下的水滴悬停相对运动。数值仿真结果表明常值小推力控制策略可行，研究成果完善了航天器受迫绕飞构型设计与控制的相关理论，为工程应用提供参考。 

Teardrop hovering configuration control strategy based on piecewise constant thrust

In order to meet the requirements of relative motion control for spacecraft formation flying missions, design and control of spacecraft's forced fly-around formation under the control of piecewise constant thrust are investigated. For teardrop hovering configuration under pulse control, a multi-level constant thrust control strategy is proposed. The shooting equation is transformed into the solution of the extreme value problem, and the least square method is used to solve it. In this paper, constant thrust feasibility is also analyzed. Based on continuous constant small-thrust control equations, the small neighborhood theorem is deduced, and the feasibility of two-segment constant thrust control is analyzed in near-distance relative motion. In addition, a small-thrust increment equation is proposed to improve the solution accuracy, and it is proved that multiple iterations can precisely approximate the ideal solution. Finally, numerical simulations show that a constant small-thrust control strategy is feasible for the teardrop hovering relative motion. The theory of spacecraft forced fly-around design and control is enriched, and the results provide a reference for engineering applications.