Controllability properties for aircraft formations

This paper studies the controllability of formations of n identical aircraft maintaining constant distances. Aircraft are modeled as a planar kinematic system with constant velocity and curvature bounds. The challenges of achieving controllability of such system are that it is an affine system with drift and its admissible controls are determined by its configuration variables. We begin with the study of a pair of aircraft maintaining a constant distance. As a result, we show that if the specified distance is sufficiently large, a pair of aircraft is completely controllable, i.e. can be steered between any two arbitrary configurations. In case of small distances, a description of the reachable sets is provided. Finally, we provide the controllability results for three basic formations of n aircraft.