Thrust vector control of upper stage with a gimbaled thruster during orbit transfer

In launching Multi-Satellite with One-Vehicle, the main thruster provided by the upper stage is mounted on a two-axis gimbal. During orbit transfer, the thrust vector of this gimbaled thruster (GT) should theoretically pass through the mass center of the upper stage and align with the command direction to provide orbit transfer impetus. However, it is hard to be implemented from the viewpoint of the engineering mission. The deviations of the thrust vector from the command direction would result in large velocity errors. Moreover, the deviations of the thrust vector from the upper stage mass center would produce large disturbance torques. This paper discusses the thrust vector control (TVC) of the upper stage during its orbit transfer. Firstly, the accurate nonlinear coupled kinematic and dynamic equations of the upper stage body, the two-axis gimbal and the GT are derived by taking the upper stage as a multi-body system. Then, a thrust vector control system consisting of the special attitude control of the upper stage and the gimbal rotation of the gimbaled thruster is proposed. The special attitude control defined by the desired attitude that draws the thrust vector to align with the command direction when the gimbal control makes the thrust vector passes through the upper stage mass center. Finally, the validity of the proposed method is verified through numerical simulations.