Optimal control of two-craft electromagnetic formation in circular orbit

Optimal reconfigurations of two-craft electromagnetic formation in low earth circular orbit are discussed. Equations of motion for two-spacecraft electromagnetic formation are derived according to the motion of tethered satellite. Three optimality criteria considered are minimum time, minimum acceleration, and minimum control acceleration. Two examples are presented to demonstrate the feasibility with different DOFs. The two-point-boundary-value problem is numerically solved via Gauss pseudo-spectral methods. A general framework of calculating control currents in electromagnetic coils according to the required control forces is presented. Analytical solutions of control currents for the case of two-craft are derived considering energy consumption equilibrium.