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Purpose The purpose of this paper is to develop a theoretical design for the attitude control of electromagnetic formation flying (EMFF) satellites, present a nonlinear controller for the relative translational control of EMFF satellites and propose a novel method for the allocation of electromagnetic dipoles. Design/methodology/approach The feedback attitude control law, magnetic unloading algorithm and large angle manoeuvre algorithm are presented. Then, a terminal sliding mode controller for the relative translation control is put forward and the convergence is proved. Finally, the control allocation problem of electromagnetic dipoles is formulated as an optimization issue, and a hybrid particle swarm optimization (PSO) – sequential quadratic programming (SQP) algorithm to optimize the free dipoles. Three numerical simulations are carried out and results are compared. Findings The proposed attitude controller is effective for the sun-tracking process of EMFF satellites, and the magnetic unloading algorithm is valid. The formation-keeping scenario simulation demonstrates the effectiveness of the terminal sliding model controller and electromagnetic dipole calculation method. Practical implications The proposed method can be applied to solve the attitude and relative translation control problem of EMFF satellites in low earth orbits. Originality/value The paper analyses the attitude control problem of EMFF satellites systematically and proposes an innovative way for relative translational control and electromagnetic dipole allocation.

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