Arbitrarily shaped formations of mobile robots: artificial potential fields and coordinate transformation

In this paper we describe a novel decentralized control strategy to realize formations of mobile robots. We first describe how to design artificial potential fields to obtain a formation with the shape of a regular polygon. We provide a formal proof of the asymptotic stability of the system, based on the definition of a proper Lyapunov function. We also prove that our control strategy is not affected by the problem of local minima. Then, we exploit a bijective coordinate transformation to deform the polygonal formation, thus obtaining a completely arbitrarily shaped formation. Simulations and experimental tests are provided to validate the control strategy.