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Distance-based Formation Control Using Angular Information Between Robots

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Abstract

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.

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References

  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)

  2. Arai, T., Pagello, E., Parker, L.E.: Guest editorial advances in multirobot systems. IEEE Trans. Robot. Autom. 18(5), 655–661 (2002)

    Article  Google Scholar 

  3. Arkin, R.: Behavior-Based Robotics. MIT Press, Cambridge (1998)

    Google Scholar 

  4. Balch, T., Arkin, R.: Behavior-based formation control for multirobot teams. IEEE Trans. Robot. Autom. 14(6), 926–939 (1998)

    Article  Google Scholar 

  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)

  6. Cao, Y., Fukunaga, A., Kahng, A.: Cooperative mobile robotics: Antecedents and directions. Auton. Robots 4(1), 7–27 (1997)

    Article  Google Scholar 

  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. 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

    Article  MathSciNet  MATH  Google Scholar 

  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)

  10. Desai, J.: A graph theoretic approach for modeling mobile robot team formations. J. Robot. Syst. 19(11), 511–525 (2002)

    Article  MATH  Google Scholar 

  11. Desai, J., Ostrowski, J., Kumar, V.: Modelling and control of formations of nonholonomic mobile robots. IEEE Trans. Robotics Autom. 6, 905–908 (2001)

    Article  Google Scholar 

  12. Dimarogonas, D.: Sufficient conditions for decentralized potential functions based controllers using canonical vector fields. IEEE Trans. Automat. Contr. 57(10), 2621–2626 (2012)

    Article  MathSciNet  Google Scholar 

  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)

  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)

  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)

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

  21. Ge, S., Fua, C.: Queues and artificial potential trenches for multirobot formations. IEEE Trans. Robot. 21(4), 646–656 (2005)

    Article  Google Scholar 

  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)

  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)

  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)

  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)

    Article  Google Scholar 

  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. 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. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5 (1), 90–98 (1986)

    Article  MathSciNet  Google Scholar 

  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)

  30. Krick, L., Broucke, M., Francis, B.: Stabilisation of infinitesimally rigid formations of multi-robot networks. Int. J. Control 82(3), 423–439 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

  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)

    Article  Google Scholar 

  34. Marshall, J., Broucke, M., Francis, B.: Formations of vehicles in cyclic pursuit. IEEE Trans. Autom. Control 49(11), 1963–1974 (2004)

    Article  MathSciNet  Google Scholar 

  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. 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)

  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)

    Article  MathSciNet  Google Scholar 

  38. Oh, K., Ahn, H.: Distance-based formation control using euclidean distance dynamics matrix: General cases. Amer. Control Conf., 4816–4821 (2011)

  39. Oh, K., Ahn, H.: Distance-based formation control using euclidean distance dynamics matrix: Three-agent case. Amer. Control Conf., 4810–4815 (2011)

  40. Oh, K.K., Park, M.C., Ahn, H.S.: A survey of multi-agent formation control. Automatica 53(0), 424–440 (2015)

    Article  MathSciNet  Google Scholar 

  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)

  42. Ren, W., Beard, R.: Distributed consensus in multi-vehicle cooperative control: Theory and applications. Communications and Control Engineering Series. Springer-Verlag, London (2008)

    Book  MATH  Google Scholar 

  43. Tanner, H., Pappas, G., Kumar, V.: Leader-to-formation stability. IEEE Trans. Robot. Autom. 20(3), 443–455 (2004)

    Article  Google Scholar 

  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)

  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)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Electrical Engineering Department, Universidad Católica del Uruguay, 11600, Montevideo, Uruguay

    E. D. Ferreira-Vazquez

  2. Engineering Department, Universidad Iberoamericana, 01219, Mexico City, Mexico

    E. G. Hernandez-Martinez & P. Paniagua-Contro

  3. Mathematics Department, Universidad Católica del Uruguay, 11600, Montevideo, Uruguay

    J. J. Flores-Godoy

  4. Physics and Mathematics Department, Universidad Iberoamericana, 01219, Mexico City, Mexico

    G. Fernandez-Anaya

Authors
  1. E. D. Ferreira-Vazquez
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  2. E. G. Hernandez-Martinez
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  3. J. J. Flores-Godoy
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  4. G. Fernandez-Anaya
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  5. P. Paniagua-Contro
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Correspondence to E. D. Ferreira-Vazquez.

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Ferreira-Vazquez, E.D., Hernandez-Martinez, E.G., Flores-Godoy, J.J. et al. Distance-based Formation Control Using Angular Information Between Robots. J Intell Robot Syst 83, 543–560 (2016). https://doi.org/10.1007/s10846-015-0312-1

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  • DOI: https://doi.org/10.1007/s10846-015-0312-1

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