Low computational sequential optimization for large-scale satellite formation reconfiguration

Large-scale satellite formations enhance mission flexibility and redundancy but also increase challenges in coordination, computational load and collision risks. This paper develops a low computational sequential optimization method for fuel-efficient and passively-safe reconfiguration. We propose using an optimal three-impulse analytical solution to identify passively unsafe satellites, thereby reducing the number of satellites that require further optimization. This analytical solution also serves as an initial guess, shrinking the search space for the optimization. The problem is then decomposed into multiple single-satellite reconfiguration subproblems, which are optimized in parallel to improve computational efficiency. Two optimization strategies for subproblems are proposed: fuel-optimal and fuel-suboptimal optimization. When passive safety requirements are not met in certain iterations, the optimization relaxes fuel constraints to prioritize safety. The sequential constraint management process dynamically adjusts the trade-off between fuel costs and passive safety based on the current scenarios. This flexibility allows the method to adapt the varying reconfiguration scenarios, since not all scenarios can meet the passive safety requirements under fuel-optimal conditions. This method provides a more scalable and flexible solution to large-scale satellite formation reconfiguration optimization over traditional centralized methods. It is particularly beneficial for medium to large satellite formations (≥100 satellites). Finally, a numerical simulation is given to verify the computational efficiency and passive safety improvements of the proposed method. The algorithm is tested on a 100-satellite formation. The passive safety parameter improved from 0.0189 to 21.1165 m, and runtime was reduced by 67% compared to centralized optimization result.