Bipartite consensus-based formation control of high-order multi-robot systems with time-varying delays

This paper considers a multi-robot formation control scheme for high-order bipartite consensus under time-varying delays. First, a third-order bipartite consensus protocol under time-varying delays is presented, and then a high-order bipartite consensus protocol is extended from it. Then, necessary and sufficient conditions for third-order and high-order multi-agent systems without time-delays are given to attain bipartite consensus following the protocols. Communication time-delays are added to the protocols, and the theory of Lyapunov asymptotic stability is used to obtain sufficient conditions for the multi-agent systems with communication delays to ultimately attain a bipartite consensus. Furthermore, the given protocol is employed for the formation control of multi-robot systems, and a formation control scheme for multi-robot systems with time-varying delays is proposed. Finally, a few simulations are implemented to demonstrate the rationality and availability of the method.