Optimal Reconfiguration Control of Electromagnetic Satellite Formation

Electromagnetic formation flying uses the electromagnetic force between satellites to control the relative position of satellites without consuming propellant. Therefore, electromagnetic formation has broad application prospects. However, the electromagnetic formation system has strong nonlinear characteristics, bringing great challenges to the analysis of formation dynamics and the design of formation controllers. This paper establishes a novel electromagnetic coordinate system by introducing feasible engineering constraints of energy optimization. In this coordinate system, the magnetic dipole and electro-magnetic force are on the two-dimensional plane, which significantly simplifies the complex nonlinear relationship between the electromagnetic and dynamic models. We propose the cost function in electromagnetic formation reconfiguration by considering the multi-objective optimization problem of reconfiguration time and coil energy consumption. The optimal reconfiguration trajectory of the open-loop electromagnetic formation system is solved by the Gaussian pseudospectral method, and the open-loop continuous-time control law is obtained by numerical interpolation. We design a feedback controller to track the optimal open-loop trajectory and consider the control input saturation value of the real-time formation. The effectiveness of the optimal reconfiguration control method is verified by numerical simulation.