Distance-based control of formations with hybrid communication topology: Three-agent case

Abstract

In this paper, we focus on the control of triangular multi-agent formations with hybrid communication topology though distance-based approach. By saying hybrid topology, we mean that the communication topology contains both undirected and directed links, or in other words, the underlying graph of the formation contains both undirected and directed edges. A new type of graph, namely hybrid graph, is introduced. We discuss the persistence of a hybrid graph and present the persistence verification strategy for hybrid graphs. It is proved that all the persistent hybrid graphs can be obtained from persistent directed graphs by the operation of edge transformation. As the main result, it is shown that triangular multi-agent formations modelled by hybrid graphs can be stabilized locally under distance-based controllers.