A Semi-analytical Stable Formation Configuration Screening Method Based on Poincaré Contraction Map

This paper proposes a semi-analytical method integrating Poincaré Compressed Mapping (PCM) with Conditional Variational Autoencoder (CVAE) for efficient screening of bounded relative orbit. PCM is applied to reduce the four-dimensional state parameters to a two-dimensional feature parameter pair of crossing period and separation angle, which is surjective but non-injective. In the feature parameter plane, contour maps of the state parameters are constructed, whose intersections correspond to long-duration formation with limited amplitude. However, this ergodic search method suffers from high computational cost and low flexibility, which can be simplified into an inverse mapping from the chief’s feature parameters to the deputy’s state parameters for rapid configuration screening. Therefore, a semi-analytical PCM-CVAE method is developed for dimensional raising from the two-dimensional feature parameters of the chief to the four-dimensional state parameters of the deputy, enabling diverse screening of feasible bounded relative orbits. Results under the displaced orbit scenario demonstrate that PCM-CVAE method achieves an optimal accuracy of (1.92×10^-4, 5.94×10^-4), while reducing the search time from the hour level to 7.83 minutes.