Time-varying group formation control for multi-agent systems with second-order dynamics and directed topologies

Time-varying group formation control problems for second-order multi-agent systems with directed topologies are investigated, where the agents in the multi-agent system are classified into subgroups and each subgroup is required to form a specified time-varying sub-formation. In contrast to the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation, there could be multiple sub-formations. Firstly, a time-varying group formation protocol is constructed using local relative positions and velocities of each agent and its neighbors. Then based on graph theory, nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for second-order multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. Moreover, by solving an algebraic Riccati equation, an approach to design the time-varying group formation protocol is proposed. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained results.