Stationkeeping Strategies for Non-Natural Cislunar Constellations Represented by Approximate Series

Future cislunar missions require autonomous navigation and stationkeeping capabilities that remain robust under nonlinear dynamics and limited deep space communication capabilities. This work investigates continuous stationkeeping strategies for Multi-Revolution Elliptic Halo (ME-Halo) orbits represented by a compact trigonometric series formulation, suitable for ephemeris broadcast. These non-natural orbits, derived from the Elliptic Restricted Three-Body Problem (ER3BP) and refined through segmented fitting, preserve the geometric characteristics of Libration point orbits (LPOs). Within a high-fidelity ephemeris environment, residual accelerations along the trig-fitted nominal path indicate an idealized stationkeeping requirement. Building on this benchmark, two continuous controllers are developed and evaluated: an improved Linear Quadratic Regulator (LQR) and a Sliding Mode Control (SMC) scheme capable of compensating for modeling errors. The simulation results show that both controllers maintain the spacecraft within the required position accuracy and obtain a total delta-v neighboring the benchmark, with SMC demonstrating increased robustness to model mismatch and fitting errors. These findings support the feasibility of integrating ME-Halo orbits and trigonometric series representations into future cislunar Position, Navigation, and Timing (PNT) constellations.