Time-varying group formation analysis and design for second-order multi-agent systems with directed topologies

Time-varying group formation control problems for second-order multi-agent systems with directed topologies are investigated. Firstly, a time-varying group formation control 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. In contrast to the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation discussed in the current paper, agents are classified into subgroups and each subgroup is required to form a specified time-varying sub-formation via inter-subgroup and intra-subgroup interactions.