利用环面坐标下的准周期对称性设计晕轨道附近编队飞行的线性二次调节器
LQR Design For Formation Flying Near Halo Orbits Exploiting Quasi-Periodic Symmetry In Toroidal Coordinates
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中文总结 AI 辅助
针对圆型限制性三体问题的晕轨道相对运动控制，利用环面坐标准周期对称性设计LQR控制器，控制量较基准方案降低约40%且跟踪精度相当，可完成不变环面的重构机动。
中文摘要 AI 辅助
本工作针对圆型限制性三体问题（CR3BP）中周期轨道附近的相对运动控制，设计了线性二次调节器（LQR），该调节器基于非奇异环面坐标构建。核心结果利用了环面坐标变换的旋转准周期性，通过对相关差分黎卡提方程镇定解的唯一性论证，证明最优控制增益仅需计算一个轨道周期即可。该控制器在地月系统的L1北晕轨道上针对完整非线性CR3BP动力学进行了验证，还针对高保真星历模型开展了验证，结果表明其能在不变环面上以低控制量完成成功的重构机动。与脉冲式瞄准和保持基准方案相比，所提控制器达到了相当的跟踪精度，同时将总控制量降低了约40%。
英文摘要
This work presents the design of a Linear Quadratic Regulator for relative motion control near periodic orbits in the Circular Restricted Three-Body Problem (CR3BP), formulated in non-singular toroidal coordinates. The key result exploits the rotational quasi-periodicity of the toroidal coordinate transformation. A uniqueness argument on the stabilizing solution of the associated difference Riccati equation proves the optimal control gains need only be computed for a single orbital period. The controller is validated against the full non-linear CR3BP dynamics on an L1 Northern halo orbit in the Earth-Moon system, and further against a high-fidelity ephemeris model, demonstrating successful reconfiguration maneuvers on the invariant torus with low control effort. Compared with an impulsive targeting and station-keeping baseline, the proposed controller attains a comparable tracking accuracy while reducing the total control effort by approximately 40%.
