Abstract: In order to maintain 1ong-term periodic relative motion trajectory with minimum fuel consumption,an optimal control method based onθ-D nonlinear control technique was investigated. A relative motion model,considering the J_2 perturbation and suitable for motion in general elliptic orbit,was used.Theθ-D nonlinear controI law was developed tO control the relative motion by dealing with the model of relative motion by the method of extending the state variables.The periodic relative orbit was designed based on the relative orbit elements and the mission requirements.Simulation results indicate that the proposed control method can carry out the suboptimal control of the periodic relative motion.

Key words: θ-D nonlinear control method, Relative motion model, Periodic relative motion, Orbital control, Spacecraft