Robust decentralized control of consensus-based formations of leader-follower networks with uncertain directed topologies on bounded velocity trajectories undefined for followers via backstepping method

In this paper, decentralized control of formation of a special category of leader-follower networks on bounded velocity trajectories is addressed. The network of the agents in this study is supposed to have a directed graph with a spanning tree rooted at the leader agent. Moreover, follower agents do not receive online or have offline velocity of the desired trajectory, such as in tracking problem of trajectories which are not predefined or when the total bandwidth is narrow. Furthermore, the leader does not receive any information from any agent and its control is fully centralized. In the present study, formation problem is considered a consensus problem. The controller is designed for integrator and double-integrator agents via backstepping. Furthermore, suitable condition of the robustness of the controller against the changes of the communication topology of the network is derived. Simulations verify the capability and robustness of the designed control law. In a simulation, formation keeping error reduction by tuning a gain of the controller, as claimed in the design procedure, is demonstrated.