Stabilisation of directed cycle formations and application to two-wheeled mobile robots

In this study, the authors deal with a formation of autonomous mobile agents in the distance-based formation control setup, where the formation is represented by a directed cycle. They use gradient control law to stabilise the mobile agents and provide analysis of the behaviour of the agents under the given control law. Although a particular formation shape cannot be achieved by controlling only the inter-agent distances with more than three agents in the plane, at least they can make the inter-agent distances converge to the desired distances and stabilise the agents so that they converge. They found that there are invariant subsets where the agents may not achieve desired distances. However, they show that those invariant sets are not attractive. Simulation results and experimental results verifying their analysis are provided.