Coupled translation and attitude tracking control for multi-satellite electromagnetic formation flight based on dual quaternion

Abstract

Electromagnetic formation flight technology utilizes electromagnetic force and torque between satellites to control satellites’ relative position and attitude without consuming propellant, thus having broad application prospects. However, the dynamics of electromagnetic formation flying are nonlinear and strongly coupled, posing challenges to the 6-DOF control of electromagnetic formation and the magnetic dipole allocation of satellites. The frequency division multiplexing method can approximate decoupling formation dynamics by loading multi-frequency AC carriers onto satellite magnetic dipoles and is likely to achieve more control functions. A design method for AC carriers based on frequency division multiplexing is proposed to decouple formation dynamics while controlling electromagnetic force and torque. This paper further provides an analytical solution for the magnetic dipoles of the electromagnetic force/torque equations. In addition, in response to external disturbances, model uncertainty, and the inability to obtain relative velocity and angular velocity information of the formation system, this paper establishes a 6-DOF coupling model based on dual quaternion and implements tracking control using the active disturbance rejection control method. Based on the internal force characteristics of the electromagnetic formation, an expression for the equilibrium distribution of reaction wheel torque is derived to avoid some reaction wheels’ rapid accumulation of angular momentum. Numerical simulation results show the effectiveness of the proposed control method.