Intelligent Service Robotics

, Volume 11, Issue 2, pp 207–224 | Cite as

A switched-system approach to formation control and heading consensus for multi-robot systems

  • Jingfu Jin
  • Juan-Pablo Ramirez
  • SungGil Wee
  • DongHa Lee
  • YoonGu KimEmail author
  • Nicholas GansEmail author
Original Research Paper


This paper proposes a novel, hybrid and decentralized, switched-system approach for formation and heading consensus control of mobile robots under switching communication topology, including collision avoidance capability. The set of robots consists of nonholonomic wheeled mobile robots and can include a teleoperated UAV. The key feature of this approach is a virtual graph, which is derived by adding a set of relative translation vectors to the real graph of the multiple robots. Our approach results in the robots in the real graph moving to the desired formation and achieving heading consensus while the virtual robots on the virtual graph reach pose consensus. If any robot detects a nearby obstacle or other robot, the robot will temporarily move along an avoidance vector, which is perpendicular and positively projected onto the attractive vector, such that collision is avoided while minimally deviating from its formation control path. Experimental results are provided by two different research groups to demonstrate the effectiveness of our approach. These experiments extend the theoretical development by introducing a teleoperated quadrotor as a leader robot of the multi-robot systems. The same control law works for the extended system, with no modifications.


Multi-robot systems Formation control Obstacle avoidance Switched-system control Nonholonomic systems 


  1. 1.
    Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ren W (2006) Consensus based formation control strategies for multi-vehicle systems. In: American control conference, p 6Google Scholar
  3. 3.
    Ji M, Egerstedt M (2007) Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Robot 23:693–703CrossRefGoogle Scholar
  4. 4.
    Listmann KD, Masalawala MV, Adamy J (2009) Consensus for formation control of nonholonomic mobile robots. In: IEEE international conference on robotics and automation, pp 3886–3891Google Scholar
  5. 5.
    Casbeer DW, Kingston DB, Beard RW, McLain TW (2006) Cooperative forest fire surveillance using a team of small unmanned air vehicles. Int J Syst Sci 37(6):351–360CrossRefzbMATHGoogle Scholar
  6. 6.
    Acevedo JJ, Arrue BC, Maza I, Ollero A (2014) A decentralized algorithm for area surveillance missions using a team of aerial robots with different sensing capabilities. In: IEEE international conference on robotics and automation, pp 4735–4740Google Scholar
  7. 7.
    Michael N, Fink J, Kumar V (2011) Cooperative manipulation and transportation with aerial robots. Auton Robots 30:73–86CrossRefzbMATHGoogle Scholar
  8. 8.
    Mellinger D, Shomin M, Michael N, Kumar V (2013) Cooperative grasping and transport using multiple quadrotors. In: Distributed autonomous robotic systems. Springer, New York, pp 545–558Google Scholar
  9. 9.
    Noguchi N, Will J, Reid J, Zhang Q (2004) Development of a master-slave robot system for farm operations. Comput Electron Agric 44(1):1–19CrossRefGoogle Scholar
  10. 10.
    Guillet A, Lenain R, Thuilot B, Martinet P (2014) Adaptable robot formation control: adaptive and predictive formation control of autonomous vehicles. Robot Autom Mag IEEE 21:28–39CrossRefGoogle Scholar
  11. 11.
    Desai JP, Ostrowski J, Kumar V (1998) Controlling formations of multiple mobile robots. In Robotics and automation, 1998. Proceedings. 1998 International conference on IEEE, vol 4, pp 2864–2869Google Scholar
  12. 12.
    Shao J, Xie G, Yu J, Wang L (2005) Leader-following formation control of multiple mobile robots. In: Intelligent control, 2005. Proceedings of the 2005 IEEE international symposium on, mediterrean conference on control and automation. IEEE, pp 808–813Google Scholar
  13. 13.
    Poonawala HA, Satici AC, Spong MW (2013) Leader-follower formation control of nonholonomic wheeled mobile robots using only position measurements. In: The 9th IEEE Asian control conference, pp 1–6Google Scholar
  14. 14.
    Nguyen Ad, Ngo Vt et al. (2006) Collision-free formations with reactively-controlled virtual head robot tracking. In: IEEE/RSJ international conference on intelligent robots and systems, pp 2509–2514Google Scholar
  15. 15.
    Mahmood A, Kim Y (2014) Leader-following formation and heading control of networked quadcopters. In: 14th international conference on control, automation and systems, pp 919–921Google Scholar
  16. 16.
    Wang X, Ni W, Wang X (2012) Leader-following formation of switching multirobot systems via internal model. IEEE Trans Syst Man Cybern B Cybern 42(3):817–826MathSciNetCrossRefGoogle Scholar
  17. 17.
    Montijano E, Cristofalo E, Zhou D, Schwager M, Sagüés C (2016) Vision-based distributed formation control without an external positioning system. IEEE Trans Robot 32(2):339–351CrossRefGoogle Scholar
  18. 18.
    Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95:215–233CrossRefzbMATHGoogle Scholar
  19. 19.
    Dörfler F, Francis B (2010) Geometric analysis of the formation problem for autonomous robots. Autom Control IEEE Trans 55(10):2379–2384MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Fax JA, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49(9):1465–1476MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Satici AC, Poonawala H, Eckert H, Spong MW (2013) Connectivity preserving formation control with collision avoidance for nonholonomic wheeled mobile robots. In: IEEE/RSJ international conference on intelligent robots and systems, pp 5080–5086Google Scholar
  22. 22.
    Listmann KD, Masalawala MV, Adamy J (2009) Consensus for formation control of nonholonomic mobile robots. In: IEEE international conference on robotics and automation. IEEE, pp 3886–3891Google Scholar
  23. 23.
    Xie G, Wang L (2006) Consensus control for a class of networks of dynamic agents: switching topology. In: American control conference, 2006. IEEE, p 6Google Scholar
  24. 24.
    Storms JG., Tilbury DM (2014) Blending of human and obstacle avoidance control for a high speed mobile robot. In: American control conference. IEEE, pp 3488–3493Google Scholar
  25. 25.
    Jin J, Kim Ygu, Wee, Sgil, Gans, N (2015) Consensus based attractive vector approach for formation control of nonholonomic mobile robots. In: IEEE/ASME international conference on advanced intelligent mechatronics, pp 977–983Google Scholar
  26. 26.
    Jin, J, Green, A, Gans, N (2014) A stable switched-system approach to obstacle avoidance for mobile robots in se(2). In: IEEE/RSJ international conference on intelligent robots and systems, pp 1533–1539Google Scholar
  27. 27.
    Klancar G, Skrjanc I (2007) Tracking-error model-based predictive control for mobile robots in real time. Robot Auton Syst 55:460–469CrossRefGoogle Scholar
  28. 28.
    Ren W (2008) Collective motion from consensus with cartesian coordinate coupling-part I: Single-integrator kinematics. In: 47th IEEE conference on decision and control, pp 1006–1011Google Scholar
  29. 29.
    Ren W (2008) On consensus algorithms for double-integrator dynamics. IEEE Trans Autom Control 53(6):1503–1509MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Biggs N (1993) Algebra graph theory. Cambridge University Press, CambridgeGoogle Scholar
  31. 31.
    Moshtagh N, Jadbabaie A (2007) Distributed geodesic control laws for flocking of nonholonomic agents. IEEE Trans Autom Control 52(4):681–686MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Jadbabaie A, Lin J, Morse A (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48:988–1001MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Ren W, Sorensen N (2008) Distributed coordination architecture for multi-robot formation control. Robot Auton Syst 56(4):324–333CrossRefzbMATHGoogle Scholar
  34. 34.
    Liberzon D (2003) Switching in systems and control. Birkhauser, BaselCrossRefzbMATHGoogle Scholar
  35. 35.
    Bacciotti A, Mazzi L (2005) An invariance principle for nonlinear switched systems. Syst Control Lett 54(11):1109–1119MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Antonelli G, Arrichiello F, Caccavale F, Marino A (2013) A decentralized controller-observer scheme for multi-agent weighted centroid tracking. IEEE Trans Autom Control 58(5):1310–1316MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Antonelli G, Arrichiello F, Caccavale F, Marino A (2014) Decentralized time-varying formation control for multi-robot systems. Int J Robot Res 33(7):1029–1043CrossRefGoogle Scholar
  38. 38.
    Liberzon D (2012) Switching in systems and control. Springer, New YorkzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Autonomous Vehicle Systems Engineering, General MotorsWarrenUSA
  2. 2.Department of Electrical EngineeringUniversity of Texas at DallasRichardsonUSA
  3. 3.Department of Electronics EngineeringUniversity of GuanajuatoGuanajuatoMexico
  4. 4.Convergence Research Center for WellnessDaegu Gyeongbuk Institute of Science and TechnologyDaeguSouth Korea

Personalised recommendations