Time-varying Formation Control for Swarm Systems with Second-order Dynamics and Switching Directed Topologies

Formation control problems for second-order swarm systems with general directed topologies are addressed in this paper, where the desired formation can be time-varying and the directed topology can be switching. Firstly, a distributed time-varying formation control protocol using local neighboring state information is proposed. Then an algorithm to design the protocol with switching directed topologies is presented. Sufficient conditions for second-order swarm systems to achieve the predefined time-varying formation under the designed protocol are derived based on the piecewise Lyapunov function theory, where the formation feasibility constraint and the threshold for the dwell time are proposed, respectively. Moreover, an explicit expression of the formation reference function is obtained to describe the macroscopic trajectory of the whole time-varying formation under the influence of the switching directed topologies. Finally, a numerical simulation is provided to demonstrate the effectiveness of the obtained results.