Translation and attitude synchronization for multiple rigid bodies using dual quaternions

In this paper, we investigate two attitude and translation synchronization problems for multiple fully actuated rigid bodies. A receiving little attention mathematical tool-dual quaternion is employed to design synchronization control laws. And the analysis based on dual quaternion is a unified solution for attitude and translation simultaneously. The definition and some properties about dual quaternion are introduced firstly. Then, a leaderless distributed control law is proposed for the attitude and translation synchronization of these rigid bodies with notion concision and non-singularity. Moreover, the final angular velocities and linear velocities are nonzero under the proposed control law if the synchronization is achieved. Next, we address the tracking synchronization for a group of rigid bodies with a time-varying leader. In addition, not only the synchronization performances under the acyclic communication topology are investigated, but the performances under the communication topology containing cycles are also analyzed. Finally, two examples are given to validate the effectiveness of the theoretical results.