Multiple-Shooting Analytical Adaptive Dynamic Programming Algorithm in the Circular Restricted Three-Body Problem

This paper presents a multi-shooting analytical adaptive dynamic programming (MS-AADP) method for optimal trajectory design in the circular restricted three-body problem (CR3BP). This method integrates a multiple-shooting structure into the AADP framework, effectively combining the analytical tractability of AADP with improved convergence robustness enabled by multi-shooting. Besides, a novel bi-level framework is proposed that separates local control synthesis from global trajectory coordination, enabling efficient construction of segment-wise solutions and consistent optimization of inter-segment connections. In the inner level, a segment-wise analytical control law is derived based on a proposed Riccati-based AADP formulation, enabling efficient construction of local value functions. In the outer level, a stitched cost formulation is developed to optimize the intermediate shooting variables analytically, ensuring smooth inter-segment connections and global trajectory coherence. Numerical simulations of transfers between periodic orbits demonstrate the effectiveness and applicability of the proposed method in astrodynamics.