论文标题
封闭形式的最佳冲动控制航天器相对运动，使用可及的集合理论
Closed-Form Optimal Impulsive Control of Spacecraft Relative Motion Using Reachable Set Theory
论文作者
论文摘要
本文解决了航天器相对轨道重新配置问题，即在固定时间内达到所需的状态，以最大程度地降低冲动控制动作的增量成本。该问题在相对轨道元素（ROE）空间中提出，该空间可深入了解相对运动几何形状，并可以直接包含线性时变形式的扰动。到达集合理论用于将成本最小化问题转化为几何路径规划问题，并制定可触及的Delta-V最小值，这是一种新的指标，以评估操纵方案的最佳性和量化可达性。接下来，本文提出了一种计算符合这一新最优标准并实现规定重新配置的机动计划的方法。尽管该方法适用于任何线性的时间变化系统，但本文利用了ROE中的状态表示，以在任意偏心率的轨道中得出新的全球最佳操纵方案。当最佳解决方案无法达到时，该方法还用于生成量化的亚最佳解决方案。此外，本文确定了不确定性对实现所需终端状态的数学影响，并提供了这些对可及集合的影响的几何可视化。在现实的重新配置方案中测试了所提出的算法，并在高保真模拟环境中进行了验证。
This paper addresses the spacecraft relative orbit reconfiguration problem of minimizing the delta-v cost of impulsive control actions while achieving a desired state in fixed time. The problem is posed in relative orbit element (ROE) space, which yields insight into relative motion geometry and allows for the straightforward inclusion of perturbations in linear time-variant form. Reachable set theory is used to translate the cost-minimization problem into a geometric path-planning problem and formulate the reachable delta-v minimum, a new metric to assess optimality and quantify reachability of a maneuver scheme. Next, this paper presents a methodology to compute maneuver schemes that meet this new optimality criteria and achieve a prescribed reconfiguration. Though the methodology is applicable to any linear time-variant system, this paper leverages a state representation in ROE to derive new globally optimal maneuver schemes in orbits of arbitrary eccentricity. The methodology is also used to generate quantifiably sub-optimal solutions when the optimal solutions are unreachable. Further, this paper determines the mathematical impact of uncertainties on achieving the desired end state and provides a geometric visualization of those effects on the reachable set. The proposed algorithms are tested in realistic reconfiguration scenarios and validated in a high-fidelity simulation environment.
