Synchronization of rigid body dynamics in SE(3) without velocity measurement

In this paper, we first propose a control law for synchronization of multi-agent systems in Special Euclidean group SE(3). Then, as an extension of the proposed synchronization algorithm, we propose another control algorithm for the same task without using velocity measurement. It will be shown that the synchronization can be enabled on the basis of an auxiliary dynamic system and double integrated consensus algorithm. Additionally, to overcome the disadvantage of the Euler angles, we use a quaternion. Using the Lyapunov stability analysis, we can verify that the proposed algorithms could ensure the synchronization in the attitude and position as well as in angular and linear velocities. Simulation results demonstrate the effectiveness of theoretical results.