Semianalytical Bounded Formation Configuration Screening Method Based on Poincaré Contraction Mapping

This article proposes a semianalytical 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 noninjective. 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. The PCM-CVAE method is validated in both Earth-centered displaced orbits (DO) and Earth–Moon libration point orbits, demonstrating consistent generality. Moreover, the accuracy and dispersion of the 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 × 10⁻⁴). Meanwhile, compared to the previous traversal search method by finding intersection of contour maps, PCM-CVAE reduces the search time from 6.44 h to 7.83 min, achieving 98% reduction in computational cost with high accuracy.