Group Consensus Analysis for Second Order Collective Model with Spatial Coordinates Coupling

Abstract

This paper focuses on the group consensus issue of multi-agent systems, where the agents in a network can reach more than one consistent values asymptotically. A rotation matrix is introduced to an existing consensus algorithm for double-integrator dynamics. Based on algebraic matrix theories, graph theories and the properties of Kronecker product, some necessary and sufficient criteria for the group consensus are derived. where we show that both the eigenvalue distribution of the Laplacian matrix and the Euler angle of the rotation matrix play an important role in achieving group consensus. Furthermore, we show that the agents will eventually keep moving on a linear pattern, cylindrical spiral pattern, and logarithmic spiral pattern when the damping gain is above a certain bound, the Euler angle is below, equal and above a critical value. simulated results are presented to demonstrate the theoretical results.