Rendezvous of Nonholonomic Robots via Output-Feedback Control under Time-varying Delays

Submitted to the IEEE Transactions on Control Systems Technolology in May 2021In this paper we address the rendezvous problem for nonholonomic vehicles with second-order dynamics, that is, to make them converge to a formation centered at a non-prespecified point on the plane. We assume that only output feedback is available; the output corresponding to the Cartesian position of the center of mass of each vehicle and its orientations. In addition, we suppose that the robots communicate over a wireless network, so the information travels with a time-varying delay. In contrast to more common practice in output-feedback control, we do not use an observer, but the controller is dynamic. In fact, it has a clear physical interpretation of a second-order oscillator that is hinged to the actual system. Furthermore, the controller is fully distributed; for each robot it depends on the coordinates of the actual agent, the controller's states and the information received from its neighbors. We show, both analytically and via realistic Gazebo-ROS simulations, that by exchanging the controller variables, as opposed to their own, the networked robots achieve full consensus, both in positions and orientations, in spite of the delays. To the best of our knowledge, output feedback consensus control of underactuated nonholonomic vehicles has been little studied, all the less in the presence of delays