Model predictive control for velocity tracking in synchronous fly-around based on dual quaternion error dynamics

6DOF coupled synchronous fly-around control is critical for observer spacecraft's on-orbit inspection. To meet precision and trajectory requirements in proximity operations, an accurate modeling-based control scheme is proposed to resolve translation-rotation coupling. In this paper, a dual quaternion framework is adopted to establish unified kinematics and dynamics models for relative pose (attitude-position) description. A linearized error state-space equation is adopted to replace PWA at the equilibrium point, simplifying control design with guaranteed modeling accuracy. A Model Predictive Control (MPC) scheme is designed based on the linearized models, with the cost function modified to solve velocity tracking. Lyapunov stability analysis proves the asymptotic convergence of relative state errors, ensuring control reliability. Practical engineering constraints are considered for realism. Numerical simulations verify the scheme, especially for velocity tracking missions poorly addressed by similar methods. Results demonstrate the MPC scheme's effectiveness in 6DOF coupled fly-around control.