Distributed control for bi-connectivity of multi-robot network

This paper approaches a bi-connectivity preservation problem for networked multi-robot systems in a distributed control fashion. Since a bi-connected network topology is robust against single node removal, networked multi-robot systems are required to preserve bi-connectedness in cases robots may fail. By employing a perturbed graph Laplacian to find if the network is disconnected after a node is removed, we analyse a sufficient condition that the network is bi-connected. Then we design a distributed control law to preserve the bi-connectedness from the sufficient condition. Moreover, considering cases a robot fails, we propose a control law to let a uni-connected network be bi-connected forcibly. A condition to restore the bi-connectedness by the proposed control is theoretically proved. The effectiveness of the proposed control laws is demonstrated by numerical simulations.