Periodic formation configuration design in multi-body systems based on semi-analytical gradient information

Periodic formation configurations are of great significance for space missions such as low-energy space interferometry and space situational awareness. However, in multi-body systems, the strongly nonlinear dynamics and the rapidly expanding solution space driven by increasing geometric complexity pose significant challenges to the convergence of periodic configuration optimization. To address this issue, this paper proposes a polynomial method for the design of periodic formation configurations. First, the objective function of the configuration optimization problem is formulated as an analytical polynomial of the design parameters, thereby enabling explicit gradient information. Second, based on the polynomial objective function, a gradient-enhanced differential evolution algorithm is developed, which performs a local gradient search in the neighborhood of the current best individual at each iteration, in order to enhance convergence and search efficiency. Finally, numerical simulations are conducted on several test cases in the Sun–Earth system to validate the proposed method. The results demonstrate that, compared with conventional heuristic algorithms, the proposed method offers significant advantages in both convergence and convergence speed, providing an effective new approach for periodic formation configuration design in multi-body systems.