Multiplicative potential energy function for swarm control

This paper presents a novel method for shape control of a swarm of robots based on region control concept. Multiplicative potential energy function is used to form the overall desired shape of the entire swarm. The shape formed using this method is a union of all the regions defined by corresponding inequality functions. This proposed method is a complement to our previous method where the additive potential energy is used to form the desired shape. By combining the multiplicative and additive potential energies, a variety of complicated shapes can be formed. Lyapunov-like function is presented for convergence analysis of the multi-robot systems. Simulation results are presented to illustrate the performance of the proposed method.