Time-varying formation control with attitude synchronization of multiple rigid body systems

In this article, we study the leader-following formation control problem for a group of rigid body systems whose followers' motions are described by dual quaternion equations. A few features are as follows. First, we introduce an exosystem to generate the leader's trajectory as well as the formation configuration, which can produce a large class of time-varying signals so that we can achieve a variety of time-varying formations. Second, to overcome the communication constraint described by a digraph, we extend the distributed observer to estimate not only the desired attitude and angular velocity but also the leader's position and linear velocity. Third, a novel distributed control law is synthesized to furnish a rigorous performance analysis of the closed-loop system. The effectiveness of our design is illustrated by a numerical example.