Rapid cooperative optimization of continuous trajectory for electric sails in multiple formation reconstruction scenarios

Abstract

In satellite formation missions, conventional low-thrust spacecraft need to continuously consume fuel to maintain a stable formation configuration, which limits the mission period. The electric sail is more conducive to long-term scenarios and multiple formation reconstruction due to its propellant-free characteristic. However, electric sails rely on the solar wind to adjust attitude, which results in a slower control. Therefore, the propulsive acceleration of the electric sail is required to be continuous. Besides, a fast and reasonable initial guess is necessary for accurate design methods such as direct and indirect methods in complex formation missions. Accordingly, the rapid optimization of continuous cooperative trajectory of electric sails in multiple formation reconstruction scenarios with the integrative Bezier shaping approach (IBSA) was implemented in this study. Multiple deputy electric sails arrived at multiple determined positions relative to the chief electric sail at the same time and avoided collisions through distance constraints during multiple formation reconstructions. During multiple reconstructions of the formation, the velocity and acceleration of deputy electric sails are constrained to be continuous. In the proposed method, the relative motion is described without simplified steps, which is more suitable for general elliptic orbits. For electric sail formation, the analytical state and analytical acceleration based on the IBSA are derived. Additionally, in the IBSA, the relationship between Bezier coefficients and relative states replaces the boundary constraints and intermediate constraints of the proposed NLP problem, which can greatly improve the solution efficiency. However, in this paper, IBSA not only represents the multi-segment trajectory optimization problem as an overall optimization problem, but also considers multiple electric sails at the same time. To verify the rapidity and accuracy of the proposed method, numerous numerical simulations were carried out on the electric sail formation. Compared with traditional BSA, the IBSA can get better overall index in a shorter computing time. Taking the result of IBSA as the initial value, the Gauss pseudospectral method (GPM) can further optimize the cooperative trajectories and converge to a better result. Through the comparison of the results, it is found that the overall index of the IBSA is only 16.81% different from the GPM but the calculation time is only 0.28% of the GPM, which is of great significance for the design of multiple formation reconstruction missions with long period.