Rendezvous of multiple mobile agents with preserved network connectivity

In coordinative control of a network of multi-agent systems, to guarantee the stability of the coordinated motion, a basic assumption typically is that the underlying topology of the network can maintain its connectivity frequently enough during the motion evolution. However, for a given set of initial conditions, this assumption is very difficult to satisfy and verify. In particular, the connectivity of the initial network generally cannot guarantee the connectivity of the network throughout the evolution. In this paper, we propose a rendezvous protocol with double-integrator dynamics, which combines the functions of motion control and connectivity preservation. This protocol can enable the group of mobile agents to converge to the same position and move with the same velocity while preserving the connectivity of the whole network during the evolution if the initial network is connected. We find that there is a trade-off between the maximum overshoot and the settling time of the velocity convergence. Furthermore, we investigate the rendezvous protocol with a virtual leader and show that all agents can asymptotically attain a desired velocity even if only one agent in the team has information about the virtual leader. We finally show some numerical simulations to verify and illustrate the theoretical results.