标题： 流形上的低推力机动准周期轨道 显示英文标题

标题： On-Manifold Low-Thrust Maneuvering of Quasi-Periodic Orbits

摘要： 一种双层最优控制框架被引入以解决在多体环境中准周期不变环面的低推力重新定位问题，其中在机动过程中远离环面的偏差被认为是不安全或不负责任的。 显示对于一大类机械系统，在非零控制输入期间符合环面流形是不可行的。 通过在环面空间中最小化虚构控制输入，使用通过环面函数映射的相空间控制变量生成环面表面上最可行的轨迹。 然后通过最小跟踪误差同伦和最小时间拼接解将这些参考轨迹过渡到相空间。 结果通过燃料消耗、累积环面误差以及机动期间在环面上的滑行时间等指标与无环面意识的低推力转移进行比较。 为了包含准周期性强迫动力系统，对框架进行了修改。 最后，具有自由最终环面条件的最小时间恢复轨迹揭示了所提出的框架与无环面意识方法之间的差异。 示例来自圆型和椭圆型限制三体问题。 显示英文摘要

摘要： A bi-level optimal control framework is introduced to solve the low-thrust re-phasing problem on quasi-periodic invariant tori in multi-body environments where deviations away from the torus during maneuver are considered unsafe or irresponsible. It is shown for a large class of mechanical systems that conformity to the torus manifold during periods of non-zero control input is infeasible. The most feasible trajectories on the torus surface are generated through the minimization of fictitious control input in the torus space using phase space control variables mapped via the torus function. These reference trajectories are then transitioned to the phase space both through a minimum tracking error homotopy and minimum time patched solutions. Results are compared to torus agnostic low-thrust transfers using measures of fuel consumption, cumulative torus error, and coast time spent on the torus during maneuver. Modifications to the framework are made for the inclusion of quasi-periodically forced dynamical systems. Lastly, minimum time recovery trajectories with free final torus conditions expose the disparity between the proposed framework and torus agnostic approaches. Examples are drawn from the circular and elliptical restricted three-body problems.