Shape Control of Maneuvering Planar Formations Based on Distributed Deformation Minimization

This paper presents a novel scheme for controlling planar multirobot formations. We assume the multirobot team’s overall motion is guided by a subset of independently moving leader robots. We propose a strategy to control the other robots, called followers, based on minimizing a distributed deformation cost. This cost is based on a team organization in triads, i.e., three-robot subsets. Our strategy allows the team to maintain a prescribed formation shape while maneuvering under the leaders’ guidance during, e.g., collaborative object transport or navigation tasks. We also study how to restrict the leaders’ dynamics to facilitate formation tracking by the followers under motion constraints. The control laws we propose are distributed, can be designed locally, and rely on relative position measurements only. We illustrate our scheme with simulations considering single-integrator and unicycle robot dynamics.