On the Modulus Consensus of Multi-agent Systems with Double-Integrator Kinematics in Three-Dimensional Space under Linear Control

In this paper, we consider a group of double integrator systems in three dimensional space and study the modulus consensus problem problem with desired orientation. To solve this problem, we propose a distributed linear protocol with rotation matrices representing desired orientation. Then, the multi-agent system can be described as a linear system, whose system matrix contains the information of the interconnection topology and the orientation configuration. By exploring some special properties of the system matrix, we establish a necessary and sufficient condition under which the proposed linear protocol can achieve the modulus consensus. Specially, the modulus consensus under such linear protocol only depend on the initial velocity of each agent. Simulation results illustrate the effectiveness of our proposed approaches.