Attitude synchronization of multiple rigid bodies in SE(3) over proximity networks

This paper investigates the attitude synchronization of a group of moving rigid bodies whose states including positions and rotation matrices evolve in the Lie group SE(3). The commonly used circular neighborhood is adopted, and the neighbor graphs are described by proximity networks. In order to avoid introducing discussions on the abrupt changes of neighbor graphs, a dwell time is introduced. The distributed sampled-data control law for the angular velocity is designed. Under the assumptions on the initial states, we provide sufficient conditions for the attitude synchronization of multiple rigid body system. Compared with the existing results, our condition depends only on the neighborhood radius, the moving velocity and the dwell time.