Semianalytical Bounded Formation Configuration Screening Method Based on Poincaré Contraction Mapping

This paper proposes a semi-analytical method combining Poincaré Contraction Mapping (PCM) with Conditional Variational Autoencoder (CVAE) for efficient screening of bounded relative orbit across perturbed environments. The PCM projects high-dimensional system parameters to a two-dimensional (2D) feature parameter pair of crossing period and separation angle, which is surjective but non-injective. To address the one-to-many inverse mapping challenge, a CVAE-based deep learning model is developed to raise the dimensionality from the 2D feature parameters back to the state space, enabling rapid and diverse generation of long-duration relative orbits with bounded amplitude. And the PCM-CVAE method is validated in both Earth-centered displaced orbits (DO) and Earth-Moon libration point orbits (LPO), demonstrating consistent generality. Moreover, the accuracy and dispersion of CVAE method are evaluated and compared with ANN and KNN-GMM algorithms. Results of the scenario of DO demonstrate that the time-angle accuracy of PCM-CVAE method realizes an average value (0.53%, 2.48%) and an optimal value (1.92×10-4, 5.94×-4). Meanwhile, compared to the previous traversal search method by finding intersection of contour maps, PCM-CVAE reduces the search time from 6.44 hours to 7.83 minutes, achieving 98% reduction in computational cost with high accuracy.