Consensus control of network connected mobile robots with input delay

This study investigates the consensus control problem of linear multi-agent systems with input time delay. By exploring the certain features of Laplacian matrix, we transform the consensus problem into an asymptotic stability problem. The key element in our work is introducing the semi-discretization method to identify the optimal consensus control conditions and develops a mapping of the system response in a finite dimensional state space. Consensus region and consensus boundary can be obtained by comparing the maximum absolute value of the mapping´s eigenvalues with 1. By minimizing the maximum absolute value of the eigenvalues, the optimal convergence speed can be obtained. Simulations and experiments with Amigobots experimental environment validate the proposed method with convergence and formation control test. The results show the performance with our optimal method.