Arbitrary 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 ob- tain a formation with the shape of a regular polygon. We provide a formal proof of the asymptotic stability of the sys- tem, 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 forma- tion, thus obtaining a completely arbitrarily shaped forma- tion. Simulations and experimental tests are provided to val- idate the control strategy.