质量不确定下椭圆轨道交会的依赖视界Tube MPC
Horizon-Dependent Tube MPC for Elliptical-Orbit Rendezvous Under Mass Uncertainty
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中文总结 AI 辅助
本文推导椭圆轨道交会中Tube MPC保证失效的距离作为设计准则，在火星样本返回任务中可优化推进剂消耗，圆形轨道省29%、偏心轨道省40%，但未声明递归可行性与渐近稳定性。
中文摘要 AI 辅助
航天器从300公里处接近目标直至对接，在五个数量级的距离范围内采用单一制导律；在近距离下经证明安全的控制器，在远距离下虽仍正常运行但可能完全丧失该安全保证。本文推导了保证失效的距离并将其用作设计准则。该界限将预测模型自身的线性化误差与控制器需抑制的扰动集进行比较，仅需采样周期、轨道及该扰动界即可，无需任何仿真即可评估。在火星样本返回的接近任务中，该准则排除了消耗大部分推进剂的寻的阶段，而认可另外两个阶段。将被排除的阶段重新表述为相对轨道元素可恢复保证；将准则已认可的阶段在精度高两个数量级的坐标系中重新表述，推进剂变化不到0.1%，正是这一二次预测使该准则可证伪而非仅为描述性的。约束收紧还将预测视界与可行性关联，使视界搜索限成为任务参数而非求解器设置。针对已发表基准的重新实现（推进剂复现误差在1%以内），在匹配种子下每个案例进行500次分散蒙特卡洛转移，该控制器在圆形目标轨道上节省29%推进剂，在偏心轨道上节省40%，几乎所有试验的对接均满足0.20米捕获要求，中位脱靶量接近5厘米。存在两个相反结果：节省推进剂以飞行时间和计算量为代价，且节省来自保证对终端条件的要求而非更好的扰动抑制；未声明递归可行性和渐近稳定性。
英文摘要
A spacecraft closing on a target from three hundred kilometres to contact flies one guidance law across five orders of magnitude of range, and a controller that is provably safe at close range can lose that guarantee completely at long range while continuing to fly as though nothing were wrong. This paper derives the range at which the guarantee lapses and uses it as a design rule. The bound compares the prediction model's own linearisation error against the disturbance set the controller was built to reject, and needs only the sampling period, the orbit and that disturbance bound, so it can be evaluated before any simulation. On a Mars Sample Return approach it disqualifies the homing phase, where most of the propellant is spent, and clears the other two. Re-posing the disqualified phase in relative orbital elements restores the guarantee; re-posing a phase the rule already clears, in a frame two orders of magnitude more accurate, changes propellant by under a tenth of one per cent, and it is that second prediction that makes the rule falsifiable rather than descriptive. The constraint tightening also ties the prediction horizon to feasibility, so the horizon search limit becomes a mission parameter rather than a solver setting. Against a reimplementation of a published benchmark that reproduces its propellant to within one per cent, over five hundred dispersed Monte Carlo transfers per case on matched seeds, the controller saves 29% of the propellant on a circular target orbit and 40% on an eccentric one, docking inside the 0.20 m capture requirement on essentially every draw at a median miss near 5 cm. Two results run the other way: the saving is bought with time of flight and computation, and it comes from what the guarantee demanded of the terminal condition rather than from better disturbance rejection. Recursive feasibility and asymptotic stability are not claimed.
