Distributed consensus-formation of force-controlled nonholonomic robots with time-varying delays

We solve the leaderless consensus-formation control problem for nonholonomic robots under the influence of time-varying communication delays and via smooth feedback. The control objective is to ensure that both the Cartesian positions of the vehicles and their orientations on the plane converge to a given position in a formation pattern, relatively to an a priori unknown barycenter and a common orientation, respectively. Our controller, being of proportional-plus-damping type and smooth time-varying, is easy to implement. Furthermore, it relies on δ-persistency of excitation to overcome the well-known obstacle that for nonholonomic systems a set-point is not stabilizable by smooth time-invariant feedback. We establish asymptotic convergence of the tracking errors and we provide some simulation results that support our theoretical findings.