Journal of Intelligent & Robotic Systems

, Volume 83, Issue 3–4, pp 543–560 | Cite as

Distance-based Formation Control Using Angular Information Between Robots

  • E. D. Ferreira-VazquezEmail author
  • E. G. Hernandez-Martinez
  • J. J. Flores-Godoy
  • G. Fernandez-Anaya
  • P. Paniagua-Contro


Distance-based formation of groups of mobile robots provides an alternative focus for motion coordination strategies respect to the standard consensus-based formation strategies. However, the setup formulation introduces non rigidity problems, multiple formation patterns that verify the distance constraints or local minima appeared when collision avoidance strategies are added to the control laws. This paper proposes a novel combined distance-based potential functions with attractive-repulsive behavior in order to simplify the navigation problem as well as the use of angular information between robots to reduce the likelihood of unwanted formation patterns. Moreover, this approach eliminates the local minima generated by the control laws to reach the desired formation configuration in the case of three robots. The analysis addresses the case of omnidirectional robots and is extended to the case of unicycle-type robots with numerical simulations and real-time experiments.


Mobile robots Formation control Unicycles Artificial potential functions Collision avoidance 


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  1. 1.
    Anderson, B., Lin, Z., Deghat, M.: Combining distance-based formation shape control with formation translation. In: Qiu, L., Chen, J., Iwasaki, T., Fujioka, H. (eds.) New Trends in Control and Networked Dynamical Systems. 1, vol. 1, pp 121–130. IET (2012)Google Scholar
  2. 2.
    Arai, T., Pagello, E., Parker, L.E.: Guest editorial advances in multirobot systems. IEEE Trans. Robot. Autom. 18(5), 655–661 (2002)CrossRefGoogle Scholar
  3. 3.
    Arkin, R.: Behavior-Based Robotics. MIT Press, Cambridge (1998)Google Scholar
  4. 4.
    Balch, T., Arkin, R.: Behavior-based formation control for multirobot teams. IEEE Trans. Robot. Autom. 14(6), 926–939 (1998)CrossRefGoogle Scholar
  5. 5.
    Brockett, R.: Asymptotic stability and feedback stabilization. In: Brockett, R.W., Millman, R.S., Sussmann, H.J. (eds.) Differential Geometric Control Theory, pp 181–191. Birkhauser, Boston (1983)Google Scholar
  6. 6.
    Cao, Y., Fukunaga, A., Kahng, A.: Cooperative mobile robotics: Antecedents and directions. Auton. Robots 4(1), 7–27 (1997)CrossRefGoogle Scholar
  7. 7.
    Chen, H., Ding, S., Chen, X., Wang, L., Zhu, C., Chen, W.: Global finite-time stabilization for nonholonomic mobile robots based on visual servoing. Int. J. Adv. Robot Syst. 11, 1–13 (2014). doi: 10.5772/59307 Google Scholar
  8. 8.
    Chen, H., Wang, C., Liang, Z., Zhang, D., Zhang, H.: Robust practical stabilization of nonholonomic mobile robots based on visual servoing feedback with inputs saturation. Asian J. Control 16(3), 692–702 (2014). doi: 10.1002/asjc.829 MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chen, Y., Wang, Z.: Formation control: A review and a new consideration. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), pp. 3181–3186 (2005)Google Scholar
  10. 10.
    Desai, J.: A graph theoretic approach for modeling mobile robot team formations. J. Robot. Syst. 19(11), 511–525 (2002)CrossRefzbMATHGoogle Scholar
  11. 11.
    Desai, J., Ostrowski, J., Kumar, V.: Modelling and control of formations of nonholonomic mobile robots. IEEE Trans. Robotics Autom. 6, 905–908 (2001)CrossRefGoogle Scholar
  12. 12.
    Dimarogonas, D.: Sufficient conditions for decentralized potential functions based controllers using canonical vector fields. IEEE Trans. Automat. Contr. 57(10), 2621–2626 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Dimarogonas, D., Johansson, K.: On the stability of distance-based formation control. In: 47th Conference on Decision and Control, pp. 1200–1205. IEEE (2008)Google Scholar
  14. 14.
    Dimarogonas, D., Johansson, K.: Further results on the stability of distance-based multi-robot formations. In: American Control Conference, pp. 2972–2977. IEEE (2009)Google Scholar
  15. 15.
    Dimarogonas, D., Kyriakopoulos, K.: Formation control and collision avoidance for multi-agent systems and a connection between formation infeasibility and flocking behavior. In: IEEE Conference on Decision and Control, pp. 84–89. IEEE (2005)Google Scholar
  16. 16.
    Dimarogonas, D., Kyriakopoulos, K.: Distributed cooperative control and collision avoidance for multiple kinematic agents. In: 45th IEEE/CDC Conference on Decision and Control, pp. 721–726 (2006)Google Scholar
  17. 17.
    Dimarogonas, D.V., Johansson, K.H.: Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control. Automatica 46(4), 695–700 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Ferreira, E., Hernandez-Martinez, E., Flores-Godoy, J.: Formation control of multiple robots avoiding local minima. In: XVI Latin american Congress of Automated Control (in spanish), pp. 1–6. IFAC (2014)Google Scholar
  19. 19.
    Fidan, B., Gazi, V., Zhai, S., Cen, N.: Single-view distance-estimation-based formation control of robotic swarms. IEEE Trans. Indus. Electron. 60(12), 5781–5791 (2013)CrossRefGoogle Scholar
  20. 20.
    Flores-Resendiz, J., Aranda-Bricaire, E.: Cyclic pursuit formation control without collisions in multi-agent systems using discontinuous vector fields. In: XVI Latin american Congress of Automated Control (in spanish), pp. 941–946. IFAC (2014)Google Scholar
  21. 21.
    Ge, S., Fua, C.: Queues and artificial potential trenches for multirobot formations. IEEE Trans. Robot. 21(4), 646–656 (2005)CrossRefGoogle Scholar
  22. 22.
    Glavaški, S., Williams, A., Samad, T.: Connectivity and convergence of formations. In: Shamma, J. (ed.) Cooperative Control of Distributed Multi-Agent Systems, Chap. Connectivity and Convergence of Formations, pp 43–62. Wiley, England (2008)Google Scholar
  23. 23.
    Hernandez-Martinez, E., Aranda-Bricaire, E.: Multi-agent formation control with collision avoidance based on discontinuous vector fields. In: 35th Annual Conference of the IEEE Industrial Electronics Society, pp. 2283–2288. IEEE (2009)Google Scholar
  24. 24.
    Hernandez-Martinez, E., Aranda-Bricaire, E.: Convergence and collision avoidance in formation control: A survey of the artificial potential functions approach. In: Alkhateeb, F., Maghayreh, E.A., Doush, I.A. (eds.) Multi-Agent Systems—Modeling, Control, Programming, Simulations and Applications, pp 103–126. INTECH, Austria (2011)Google Scholar
  25. 25.
    Hernandez-Martinez, E., Aranda-Bricaire, E.: Non-collision conditions in multi-agent virtual leader-based formation control. Int. J. Adv. Robot. Syst. 9(1), 1–10 (2012)CrossRefGoogle Scholar
  26. 26.
    Hernandez-Martinez, E.G., Aranda-Bricaire, E.: Decentralized formation control of multi-agent robots systems based on formation graphs. Stud. Inf. Control 21(1), 7–16 (2012)Google Scholar
  27. 27.
    Kang, S., Park, M., Lee, B., Ahn, H.: Distance-based formation control with a single moving leader. Amer. Control Conf. 1, 305–310 (2014)Google Scholar
  28. 28.
    Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5 (1), 90–98 (1986)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Krick, L., Broucke, M., Francis, B.: Stabilization of infinitesimally rigid formations of multi-robot networks. In: IEEE Conference on Decision and Control, pp. 477–482. IEEE (2008)Google Scholar
  30. 30.
    Krick, L., Broucke, M., Francis, B.: Stabilisation of infinitesimally rigid formations of multi-robot networks. Int. J. Control 82(3), 423–439 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Li, Y., Chen, X.: Extending the potential fields approach to avoid trapping situations. In: International Conference on Intelligent Robots and Systems, pp. 1386–1391. IEEE/RSJ (2005)Google Scholar
  32. 32.
    Liu, T., Jiang, Z.: A nonlinear small-gain approach to distributed formation control of nonholonomic mobile robots. In: American Control Conference (ACC), 2013, pp. 3051–3056 (2013)Google Scholar
  33. 33.
    de Marina, H.G., Cao, M., Jayawardhana, B.: Controlling rigid formations of mobile agents under inconsistent measurements. IEEE Trans. Robot. 31(1), 31–39 (2015)CrossRefGoogle Scholar
  34. 34.
    Marshall, J., Broucke, M., Francis, B.: Formations of vehicles in cyclic pursuit. IEEE Trans. Autom. Control 49(11), 1963–1974 (2004)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Mou, S., Morse, A., Anderson, B.: Toward robust control of minimally rigid undirected formations. In: 2014 IEEE 53rd Annual Conference on Decision and Control (CDC), pp. 643–647. doi: 10.1109/CDC.2014.7039454 (2014)
  36. 36.
    Muhammad, A., Egerstedt, M.: Connectivity graphs as models of local interactions. In: 43rd IEEE Conference on Decision and Control, vol. 1, pp. 124–129 (2004)Google Scholar
  37. 37.
    Ogren, P., Fiorelli, E., Leonard, N.: Cooperative control of mobile sensor networks:adaptive gradient climbing in a distributed environment. IEEE Trans. Autom. Control 49(8), 1292–1302 (2004)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Oh, K., Ahn, H.: Distance-based formation control using euclidean distance dynamics matrix: General cases. Amer. Control Conf., 4816–4821 (2011)Google Scholar
  39. 39.
    Oh, K., Ahn, H.: Distance-based formation control using euclidean distance dynamics matrix: Three-agent case. Amer. Control Conf., 4810–4815 (2011)Google Scholar
  40. 40.
    Oh, K.K., Park, M.C., Ahn, H.S.: A survey of multi-agent formation control. Automatica 53(0), 424–440 (2015)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Pereira, G., Das, A., Kumar, V., Campos, M.: Formation control with configuration space constraints. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), vol. 3, pp. 2755–2760 (2003)Google Scholar
  42. 42.
    Ren, W., Beard, R.: Distributed consensus in multi-vehicle cooperative control: Theory and applications. Communications and Control Engineering Series. Springer-Verlag, London (2008)CrossRefzbMATHGoogle Scholar
  43. 43.
    Tanner, H., Pappas, G., Kumar, V.: Leader-to-formation stability. IEEE Trans. Robot. Autom. 20(3), 443–455 (2004)CrossRefGoogle Scholar
  44. 44.
    Xiaoyu, C., De-Queiroz, M.: Adaptive rigidity-based formation control of uncertain multi-robotic vehicles. In: American Control Conference (ACC), pp. 293–298 (2014)Google Scholar
  45. 45.
    Zhiyun, L., Broucke, M., Francis, B.: Local control strategies for groups of mobile autonomous agents. IEEE Trans. Autom. Control 49(4), 622–629 (2004)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • E. D. Ferreira-Vazquez
    • 1
    Email author
  • E. G. Hernandez-Martinez
    • 2
  • J. J. Flores-Godoy
    • 3
  • G. Fernandez-Anaya
    • 4
  • P. Paniagua-Contro
    • 2
  1. 1.Electrical Engineering DepartmentUniversidad Católica del UruguayMontevideoUruguay
  2. 2.Engineering DepartmentUniversidad IberoamericanaMexico CityMexico
  3. 3.Mathematics DepartmentUniversidad Católica del UruguayMontevideoUruguay
  4. 4.Physics and Mathematics DepartmentUniversidad IberoamericanaMexico CityMexico

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