Time suboptimal formation flying manoeuvres through improved magnetic charged system search

The development of fast and reliable optimization algorithms is required in order to obtain real-time optimal trajectory on-board spacecraft. In addition, the wide spread of small satellites, due to their low costs, is leading to a greater number of satellite formations in space. This paper presents an Improved version of the Magnetic Charged System Search (IMCSS) metaheuristic algorithm to compute time-suboptimal manoeuvres for satellite formation flying. The proposed algorithm exploits some strategies aimed at improving the convergence to the optimum, such as the chaotic local search and the boundary handling technique, and it is able to self-tune its internal parameters and coefficients. Moreover, the inverse dynamics technique and the differential flatness approach, through the B-splines curves, are used to approximate the trajectory. The optimization procedure is applied to the circular J2 relative model developed by Schweighart and Sedwick and to the elliptical relative motion model developed by Yamanaka and Ankersen. The results of this paper show that the convergence is better achieved by using the proposed tools, thus proving the efficiency and reliability of the algorithm in solving some space engineering problems.