Time-varying formation control for double-integrator multi-agent systems with jointly connected topologies

Time-varying formation analysis and design problems for double-integrator multi-agent systems with jointly connected topologies are investigated. Different from the previous work on formation control, in this paper, the formation is specified by time-varying piecewise continuously differentiable vectors and the topology can be disconnected at any time instant. First, a distributed formation control protocol is constructed using local neighbour-to-neighbour information. In the case where the switching topology is jointly connected, necessary and sufficient conditions for double-integrator multi-agent systems to achieve time-varying formations are proposed, where the formation feasibility constraint is also derived. To describe the macroscopic movement of the whole formation, explicit expressions of the formation reference are presented, the motion modes of which can be partially assigned. Moreover, an approach to design the formation control protocol is given, which is fully distributed and requires no global information about the topology. Finally, the obtained theoretical results are applied to deal with the time-varying formation control problems of multi-vehicle systems.