Controllability for pairs of vehicles maintaining constant distance

This paper studies the controllability of pairs of identical nonholonomic vehicles maintaining a constant distance. The study provides controllability results for the five most common types of robot vehicles: Dubins, Reeds-Shepp, differential drive, car-like and convexified Reeds-Shepp. The challenge of achieving controllability of such systems is that their admissible control domains depend on configuration variables. A theorem of controllability specifical for such systems has been obtained based on known controllability theorems. As a result, we show that pairs of the latter three types are completely controllable, i.e. can be steered between any two arbitrary configurations. The same does not hold for pairs of Dubins or Reeds-Shepp vehicles, and a description of the reachable sets in these cases is provided. Finally, as direct extension of controllability results of pairs of identical vehicles, the controllability results for two kinds of formation of n identical vehicles are presented.