Optimal control of Lorentz spacecraft rendezvous on circular equatorial orbit

Electrostatically charged spacecraft accelerates when orbiting a central body with magnetic field due to the Lorentz perturbations. This Lorentz perturbation could make compensate for the acceleration needed for spacecraft rendezvous. This paper builds the linearized relative dynamics model between the Lorentz spacecraft and the target spacecraft on circular equatorial orbit and gives approximate analytical expressions of the dynamics model. Based on this model, both open-loop and close-loop control law for rendezvous are designed, proposing an optimal control method. Classic numerical simulations prove the validity of both proposed dynamics model and control law.