Graph-Theoretic Connectivity Control of Mobile Robot Networks This paper develops an analysis for groups of vehicles connected by a communication network; control laws are formulated to accomplish tasks requiring rendezvous, and swarm in group formations.
Michael M. Zavlanos, Magnus Egerstedt, George J. Pappas · 2011
In this paper, we provide a theoretical framework for controlling graph connectivity in mobile robot networks. We discuss proximity-based communication models composed of disk-based or uniformly-fading-signal-strength communica- tion links. A graph-theoretic definition of connectivity is pro- vided, as well as an equivalent definition based on algebraic graph theory, which employs the adjacency and Laplacian matrices of the graph and their spectral properties. Based on these results, we discuss centralized and distributed algorithms to maintain, increase, and control connectivity in mobile robot networks. The various approaches discussed in this paper range from convex optimization and subgradient-descent algo- rithms, for the maximization of the algebraic connectivity of the network, to potential fields and hybrid systems that main- tain communication links or control the network topology in a least restrictive manner. Common to these approaches is the use of mobility to control the topology of the underlying com- munication network. We discuss applications of connectivity control to multirobot rendezvous, flocking and formation con- trol, where so far, network connectivity has been considered an assumption.