Distributed attitude and position consensus for networked rigid bodies based on unit dual quaternion

This paper provides unified solutions for distributed attitude and position consensus problems for networked fully actuated rigid bodies under the fixed and undirected communication topology, based on unit dual quaternion. We investigate two kinds of consensus, i.e., leader-following consensus with a static leader and leaderless consensus. Firstly, the dynamics of rigid bodies are presented by unit dual quaternion. The control torques and the control forces of rigid bodies are also given from unit dual quaternion. Secondly, the consensus problem with a static leader is studied. And with the proposed control law, all rigid bodies converge to the constant desired attitude and the constant desired position. Thirdly, we propose a distributed control law to guarantee that the attitudes and positions of all rigid bodies converge to the same values respectively without a leader.