Autonomous Robots

, 30:385 | Cite as

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

  • Lorenzo Sabattini
  • Cristian Secchi
  • Cesare Fantuzzi


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.


Formation control Artificial potential fields Arbitrarily shaped formations Coordinate transformation 


  1. Bachmayer, R., & Leonard, N. E. (2002). Vehicle networks for gradient descent in a sampled environment. In Proceedings of the IEEE international conference on decision and control (pp. 112–117). Google Scholar
  2. Balch, T., & Hybinette, M. (2000). Social potentials for scalable multi-robot formations. In Proceedings of the IEEE international conference on robotics and automation (pp. 73–80). Google Scholar
  3. Barnes, L., Fields, M. A., & Valavanis, K. (2007). Unmanned ground vehicle swarm formation control using potential fields. In Mediterranean conference on control and automation (pp. 1–8). CrossRefGoogle Scholar
  4. Borenstein, J., & Feng, L. (1996). Measurement and correction of systematic odometry errors in mobile robots. IEEE Transactions on Robotics and Automation, 12(6), 869–880. CrossRefGoogle Scholar
  5. Bullo, F., Cortes, J., & Martinez, S. (2008). Distributed Control of Robotic Networks.
  6. Chaimowicz, L., Michael, N. , & Kumar, V. (2005). Controlling swarms of robots using interpolated implicit functions. In Proceedings of the IEEE international conference on robotics and automation (pp. 2487–2492). CrossRefGoogle Scholar
  7. Ekanayake, S. W., & Pathirana, P. N. (2006). Artificial formation forces for stable aggregation of multi-agent system. In International conference on information and automation (pp. 129–134). CrossRefGoogle Scholar
  8. Han, F., Yamada, T., Watanabe, K., Kiguchi, K., & Izumi, K. (2000). Construction of an omnidirectional mobile robot platform based on active dual-wheel caster mechanisms and development of a control simulator. Journal of Intelligent & Robotic Systems, 29(3), 257–275. CrossRefzbMATHGoogle Scholar
  9. Hsieh, M. A., & Kumar, V. (2006). Pattern generation with multiple robots. In Proceedings of the IEEE international conference on robotics and automation (pp. 2442–2447). Google Scholar
  10. Leonard, N., & Fiorelli, E. (2001). Virtual leaders, artificial potentials and coordinated control of groups. In Proceedings of the IEEE conference on decision and control (pp. 2968–2973). Google Scholar
  11. Lindhé, M., Ögren, P., & Johansson, K. H. (2005). Flocking with obstacle avoidance: A new distributed coordination algorithm based on Voronoi partitions. In Proceedings of the IEEE international conference on robotics and automation (pp. 1785–1790). CrossRefGoogle Scholar
  12. Liu, Y., & Passino, K. M. (2004). Stable social foraging swarm in a noisy environment. IEEE Transactions on Automatic Control, 49(1), 30–44. CrossRefMathSciNetGoogle Scholar
  13. Marcolino, L. S., & Chaimowicz, L. (2008). No robot left behind: Coordination to overcome local minima in swarm navigation. In Proceedings of the IEEE international conference on robotics and automation (pp. 1904–1909). Google Scholar
  14. Matarić, M. J., Koenig, N., & Feil-Seifer, D. (2007). Materials for enabling hands-on robotics and STEM education. In AAAI spring symposium on robots and robot venues: resources for AI education. Google Scholar
  15. Meserve, B. E. (1983). Fundamental concepts of geometry. New York: Dover. Google Scholar
  16. Oriolo, G., Luca, A. D., & Vendittelli, M. (2002). WMR control via dynamic feedback linearization: Design, implementation, and experimental validation. IEEE Transactions on Control Systems Technology, 10, 835–852. CrossRefGoogle Scholar
  17. Rockafellar, R. T. (1997). Convex analysis. Princeton: Princeton University Press. zbMATHGoogle Scholar
  18. Sabattini, L., Secchi, C., & Fantuzzi, C. (2009). Potential based control strategy for arbitrary shape formations of mobile robots. In Proceedings of the 2009 IEEE/RSJ international conference on intelligent robots and systems (pp. 3762–3767). CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Lorenzo Sabattini
    • 1
  • Cristian Secchi
    • 2
  • Cesare Fantuzzi
    • 2
  1. 1.Department of Electronics, Computer Sciences and Systems (DEIS)University of BolognaBolognaItaly
  2. 2.Department of Sciences and Methods of Engineering (DISMI)University of Modena and Reggio EmiliaModena and Reggio EmiliaItaly

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