Dual-Quaternion-Based Translation-Rotation-Vibration Integrated Dynamics Modeling for Flexible Spacecraft

In this paper, we investigate a leader-follower spacecraft formation flying (SFF) mission, which is comprised of two identical spacecraft carrying large-scale antenna arrays. The mission requires spaced antenna arrays and an ultraclose separation distance from the edge of the spaced antenna arrays in order to have an accuracy within millimeters. During maneuvers, the vibration of the antenna is excited by the translational and rotational motion of the spacecraft; in return, the coupling effect influences the accuracy of the spaced antenna arrays and leads to the risk of collision. For this reason, we present a coupled dynamics model of a flexible spacecraft utilizing dual quaternion parameterization. A novel feature of this model is that the translational motion, rotational motion, and vibration of the flex-rigid system can all be described under the same mathematical framework by representing the vibration utilizing dual quaternion parameterization in the modal coordinates. Numerical results are presented to quantify the kinematic coupling effect and to show that the effect is a key consideration for ultraclose formations.