Connectivity preserving state agreement for multiple unicycles

This paper presents a decentralized feedback control strategy that drives a system of multiple nonholonomic kinematic unicycles to agreement, maintaining at the same time the connectivity properties of the initially formed communication graph. The communication graph is created based on the initial relative distances between the team members. The proposed control law guarantees that if the communication graph is initially connected, then it remains connected throughout the closed loop system evolution. This is achieved via a control design that renders the set of edges of the initially formed communication graph positively invariant for the trajectories of the closed loop system. The proposed nonholonomic control law is discontinuous and time-invariant and tools from nonsmooth stability theory and matrix theory are used to check the stability of the overall system. The convergence properties are verified through computer simulations.