Decentralized Connectivity Preserving Formation Control with Collision Avoidance for Nonholonomic Wheeled Mobile Robots

The preservation of connectivity in mobile robot networks is critical to the success of most existing algorithms designed to achieve various goals. The most basic method to achieve this involves each agent preserving its edges for all time. More advanced methods preserve a (minimum) spanning tree in the network. Other methods are based on increasing the algebraic graph connectivity, which is given by the second smallest eigenvalue λ2(L) of the graph Laplacian L that represents the network. These methods result in a monotonic increase in connectivity until the network is completely connected. A continuous feedback control method was proposed which allows the connectivity to decrease, that is, edges in the network may be broken. This method requires global knowledge of the network. In this paper we modify the controller to use only local information. The connectivity controller is based on maximization of λ2(L) and artificial potential functions and can be used in conjunction with artificial potential based formation controllers. The controllers are extended for implementation on non-holonomic wheeled mobile robots, and the performance is demonstrated in experiment on a team of wheeled mobile robots.