Spatial Static Configuration Design and Formation Control of Multiple Electromagnetic Spacecrafts

This paper addresses the problem of static configuration design for a four-spacecraft electromagnetic formation. By analyzing the necessary conditions for the formation configuration, the degrees of freedom (DOFs) in configuration designation are reduced. Referring to the results of static configuration designation for a two-spacecraft formation, the upper and lower bounds are designed for the variable space in the reduced problem, resulting in a simplified static configuration solution. Since the relative dynamic system in the equilibrium point is unstable, a sliding mode controller based on an improved exponential reaching law is proposed for stabilizing the electromagnetic formation. Based on the output of the control law, the dipole arrangement problem is transformed into a multi-objective optimization problem. By utilizing the minimum electromagnetic torque objective in the optimization problem, a significant reduction in the coupling electromagnetic torque is achieved. The static configuration design and the control algorithm are validated through numerical simulation.