Further on Time-Varying Formation Control for Directed Networks with Switching Topologies

In this research, the time-varying formation (TVF) control problem is examined for general directed networks (DNs) subject to switching communication topologies, which widely arises in cooperative tasks of multiple mobile robots. In such practical scenarios, time-varying communication links induced by obstacles, agent mobility and bandwidth limitations bring nontrivial challenges for reliable formation maintenance. To address this issue, a distributed formation control protocol is developed by utilizing local formation error feedback, topology-dependent relative formation error coupling, a positive coupling strength, and a formation compensation signal. By virtue of the constructed control protocol combined with a nonsingular coordinate transformation, the anticipated TVF control task is recast as an exponential stability verification issue of a general switched system. Then, upon constructing an innovative topology-dependent time-varying Lyapunov function (TDTVLF) approach together with the dwell-time switching (DTS) strategy, the corresponding sufficient conditions are then derived to guarantee the exponential convergence of the formation error dynamics. Finally, the formation control of multiple mobile robots is carried out to validate the effectiveness and practical applicability of the proposed TVF control protocol.