Relative E/I vector-based optimal and suboptimal control for continuous low thrust formation reconfiguration in circular orbits

Abstract

This paper addresses the fuel-optimal satellite formation reconfiguration problem with continuous low-thrust control. Based on the relative eccentricity and inclination (E/I) theory, a comprehensive approach to optimal continuous low-thrust reconfiguration in circular or near-circular orbits is proposed. By analyzing the feasible fuel cost lower bound, the reconfiguration scenarios are categorized into four types, and the corresponding optimal or suboptimal control schemes are derived. More specifically, for suboptimal continuous control schemes, the relation between user-defined variables with fuel-cost is derived, providing a clear direction for better fuel cost. Compared with previous work that gives only feasible analytical solutions or obtains optimal solutions with numerical methods, the proposed method provides an efficient approach to optimal continuous low thrust reconfiguration for feasible scenarios and adjustable sub-optimal schemes for unfeasible scenarios. The proposed framework contributes to the practical application in engineering, enabling the design and analysis of more cost-effective space missions. The analysis of fuel cost reveals that the optimal continuous low thrust reconfiguration is limited with scenarios. The overall solutions are simulated and validated in four reconfiguration scenarios.