Graph Laplacian Based Formation Control with Historic Control Command from Neighbors

Abstract

This paper concentrates on the problem of distributed formation control of multi-agent systems over directed networks. Two directed graphs, which are sensing graph and communication graph, are applied to characterize the local interaction among agents. Associated with these two graphs, complex Laplacian and real Laplacian are introduced to actualize formation control and velocity synchronization, respectively. For both single integrator kinematics and double integrator dynamics, graph Laplacian based formation control laws are provided by involving historic control command from neighbors. Under the proposed strategies, the equilibrium state of the system forms the desired moving formation. Moreover, it is also shown that proposed strategies guarantee global stability of the entire system and delay-independence for any nonnegative delay. Simulation results are provided to validate the effectiveness of the proposed algorithms.