Distributed algorithm for controlling scaled-free polygonal formations

This paper presents a distributed algorithm for controlling the deployment of a team of agents in order to form a broad class of polygons, including regular ones, where each agent occupies a corner of the polygon. The algorithm shares the properties from the popular distance- based rigid formation control but with the advantage of requiring fewer pairs of neighboring agents. Furthermore, the scale of the polygon can be controlled by only one pair of neighboring agents. We also exploit the exponential stability of the system in order to steer the prescribed formation with translations and rotations in a controlled way. We provide both theoretical analysis and illustrative simulations