We consider a team of autonomous kinematically controlled non-holonomic planar Dubins car-like vehicles. The team objective is to encircle a given target so that all vehicles achieve a common and pre-specified distance from it and are uniformly distributed over the respective circle, and the entire formation rotates around the target with a prescribed angular velocity. The robots do not communicate with each other and any central decision-maker. The sensing capacity of any vehicle is heavily restricted: It has access only to the distance to the target and to the distances to the companion vehicles that are in a given disc sector centered at the vehicle at hand; no robot can distinguish between its companions, and does not know their parameters. A distributed control law is proposed, and mathematically rigorous proofs of its non-local convergence as well as collision avoidance property are presented. The performance of the control law is illustrated by computer simulations and experiments with real robots.