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

This paper provides unified solutions for distributed attitude and translation consensus problems for networked fully actuated rigid bodies under the fixed and undirected communication topology with the tool of unit dual quaternion. We investigate two kinds of consensus, that is, leaderless consensus and leader-following consensus with a static leader. Firstly, the dynamics of rigid bodies are presented by unit dual quaternion. The control inputs of rigid bodies are also obtained from unit dual quaternion. Secondly, we propose a distributed consensus law in the form of dual quaternion to guarantee that the attitudes and translations of all rigid bodies reach consensus, respectively, without a leader. Thirdly, the leader-following consensus problem with a static leader is studied. With the proposed leader-following consensus law, the states of all rigid bodies converge to the corresponding states of the static leader, including the attitude and the translation. Finally, numerical examples are provided to validate the effectiveness of the theoretical results.