Distributed translation and attitude synchronization for multiple rigid bodies using dual quaternions

In this paper, we investigate the distributed synchronization problem for multiple fully actuated rigid bodies without a leader. A new mathematical tool-dual quaternion is employed to design the distributed control law. The definition and some properties about dual quaternion are introduced. A distributed control law is proposed to control the attitude and translation of these rigid bodies simultaneously with notion concision and non-singularity. And the analysis based on dual quaternion is a unified solution for the attitude and translation. Finally, the proposed control algorithm is simulated to illustrate the theoretical results.