Direct Method for Trajectory Planning of Electromagnetic Formation Reconfiguration

Formation flying with inter-satellite electromagnetic force offers an attractive alternative to tradition propellant-based technology for space missions due to its prominent advantages. Trajectory planning for the formation reconfiguration is considered as an optimal control problem, and addressed using a direct method that bases on inverse dynamics in the virtual domain. By mapping the physical trajectory from time to virtual domain, the optimization of spatial trajectory and speed profile is decoupled. The reconfiguration trajectory is parameterized using a polynomial in the virtual domain, while some of the coefficients are firsthand determined according to the given boundary conditions. Thus the trajectory planning problem is converted into the optimization of few varied parameters. Numerical results are discussed to illustrate the effectiveness of the proposed planning method.