Time-Varying Formation Control for Second-Order Discrete-Time Multi-Agent Systems With Directed Topology and Communication Delay

Time-varying formation control protocol design and analysis problems for the second-order discrete-time multi-agent systems with directed interaction topology and communication delay are investigated. A local information-based distributed protocol is designed by utilizing the delayed state information of neighbors. Through system decomposition and stability analysis, an explicit description of the feasible time-varying formation set is given. Necessary and sufficient conditions for the systems with the directed topology and communication delay to achieve time-varying formation are obtained, which are related to the topology of the interaction graph and the feasibility of the predefined formation. Necessary constraints on the gain parameters and the sampling period are proposed, so as to guide the design of parameters in the protocol. The numerical simulation results indicate that the protocol can steer the agents to accomplish the desired time-varying formation and effectively tolerate the relatively large bounded communication delay. Outdoor experiment with quadrotors is presented to demonstrate the effectiveness of the obtained theoretical results with one sampling period delay.