Consensus-based formation control of nonholonomic robots without velocity measurements

We present a novel smooth time-varying controller for the formation control of nonholonomic robots. The controller is of proportional-plus-derivative type, but it does not require velocity measurements; the latter are replaced by approximate differentiation. To overcome the difficulty imposed by the nonholonomy, the controller relies on a δ-persistently-exciting term which, roughly speaking, excites all the systems' modes while the position errors are away from zero. Assuming that the interconnection static graph is undirected and connected, it is showed that the nonholonomic robots converge to a given formation pattern around a rendezvous point and their orientations tend to a common angle. To the best of our knowledge, this is the first smooth controller for formation consensus control of nonholonomic systems, via a output feedback.