Pseudospectral control for 6-DOF electromagnetic formation flying

Electromagnetic formation is a novel method of propellantless formation, which enables synchronous control of both relative translation and rotation in the array. To fully utilize the inherent electromagnetic coupling effects, an integrated relative dynamic model is established. Considering the reconfiguration of electromagnetic formation as an optimal control problem with regard to relative translation and angular momentum management, it is transformed into a constrained non-linear programming problem through the Legendre pseudospectral method. Facing the systems strong nonlinearity and coupling, a novel high-precision numerical computation method is developed. Feasible trajectories for a specific planar transformation and a more general case of reconfiguration are generated to verify the proposed dynamic model and optimization algorithm.