Combined Leaderless Control of Translational, Shape-Preserving, and Affine Multirobot Formations

This letter considers existing leaderless distributed controllers that achieve three types of planar multirobot formation. Concretely, these formations are equal to a reference configuration up to translation (type F1), shape-preserving transformation (type F2), and affine transformation (type F3). As contribution, we show that a linear combination of these controllers maintains their convergence properties, while also allowing specific control of the formation during the trajectory. This latter control is not possible when using the individual controllers separately, and is interesting in practical cases. As an example scenario, we study rotation-and-resizing formation maneuvers, where the goal is to achieve an F1 formation while remaining close to an F2 formation in the transient period. We show that, in this scenario, our combined controller produces trajectories approximating shortest-path shape-preserving maneuvers, which are desirable for efficiency and safety. We validate the controller in this and other scenarios using simulations and experiments with physical mobile robots.