Bell-shaped potential functions for multi-agent formation control in cluttered environment

In this paper we analyze stability properties of multi-agent control system in a cluttered environment with an artificial potential based on bell-shaped functions. In our approach attractive and repulsive forces created by potential gradient have the same form which allows definition of target formation that is parameter invariant. Due to the fact that agents are identical, the proposed structure of formation potential is invariant to the interchange of agents configurations, hence, target in which particular agent would eventually end up, depends only on formation initial condition and environment structure (obstacles). We show that position of unwanted stable equilibria can be controlled by parameters that define elementary potential functions. This fact has been used for synthesis of an adaptation algorithm, such that arrival of agents at required formation is guarantied. Simulation results, presented at the end of the paper, confirm correctness of the proposed control scheme.