J Intell Robot Syst (2010) 58:165–189 DOI 10.1007/s10846-009-9361-7 Multi-Agent Formation Control Based on Bell-Shaped Potential Functions Kristian Hengster-Movri´ c · Stjepan Bogdan · Ivica Draganjac Received: 17 July 2009 / Accepted: 17 August 2009 / Published online: 29 August 2009 © Springer Science + Business Media B.V. 2009 Abstract In this paper we analyze stability properties of multi-agent control system with an artificial potential based on bell-shaped functions. In our approach attractive and repulsive forces created by potential gradient have the same form. This particular property 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 particu- lar agent would eventually end up, depends only on formation initial condition. It has been demonstrated that stability analysis, given for stationary targets, applies to moving targets formation as well. We show that position of unwanted stable equi- libria can be controlled by a single parameter that defines an elementary potential function. 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. Keywords Multi-agent systems · Formation control · Potential navigation function 1 Introduction In the last decade multi-agent systems have attracted a lot of attention among researchers. As unmanned vehicles are becoming more capable and more afford- able, their potential for employment in a wide range of applications is increasing. Effective deployment of autonomous mobile teams made up from numerous units calls for sophisticated communication, cooperation and control mechanisms. Use of cooperative formation of agents enables achieving goals that would not be possible K. Hengster-Movri´ c · S. Bogdan (B ) · I. Draganjac LARICS—Laboratory for Robotics and Intelligent Control Systems, Department of Control and Computer Engineering, Faculty of EE&C, University of Zagreb, Unska 3, 10000 Zagreb, Croatia e-mail: stjepan.bogdan@fer.hr