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arXiv · 2608.10726

LQR Design For Formation Flying Near Halo Orbits Exploiting Quasi-Periodic Symmetry In Toroidal Coordinates

Joaquin G. Lopez-Cepero·Rafael Vazquez·Julio C. Sanchez
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Abstract

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%.

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Joaquin G. Lopez-Cepero, Rafael Vazquez, Julio C. Sanchez. 2026-08-11. LQR Design For Formation Flying Near Halo Orbits Exploiting Quasi-Periodic Symmetry In Toroidal Coordinates. https://arxiv.org/abs/2608.10726

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