Measurement and Adjustment of the Membrane Reflector Antenna Surface Considering the Influence of Gravity

Accurately characterizing the structural state of membrane reflector antennas (MRA) remains challenging due to the difficulty in determining stress distribution through geometric measurement alone. Although photogrammetry provides high-precision geometric data, it falls short of capturing mechanical pre-tension and is notably influenced by gravity, which limits its utility in guiding surface accuracy adjustments. This paper proposed an integrated approach combining photogrammetry with a nonlinear finite element method (NFEM) to achieve high-fidelity imaging and effective shape adjustment of electrostatically formed MRA, explicitly accounting for gravity effects during ground-based measurement and shape control. The proposed method establishes a mechanical model that incorporates real-world geometric data under gravity and performs force–shape matching to reconcile discrepancies between physical and simulation models. Experimental validation demonstrates that the gravity-corrected NFEM model closely aligns with the physical antenna, with a deviation in surface accuracy within 9.9%. Using this refined model, we successfully optimized electrode voltages and cable tensions, improving the surface accuracy of the physical model from an initial 0.7033 mm to 0.5723 mm. This work provides a reliable and efficient strategy for the shape control and adjustment of membrane space structures under gravity, with potential applications in large deployable antennas, solar sails, and other tension-controlled flexible systems.