Flocking Behavior via Leader’s Backstepping on Nonholonomic Robot Group

  • Lei ChengEmail author
  • Jun Wang
  • Huaiyu Wu
  • Wenxia Xu
  • Wenhao Zhang
  • Pian Jin
  • Quanmin Zhu
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 452)


This chapter aims to improve flocking control for a group of nonholonomic robots. It introduces a new flocking control algorithm with potential-based flocking as its foundation. By incorporating Leader’s Backstepping algorithm into the flocking strategy, an improved flocking performance is obtained, which leads the flock to the target point swiftly in a smoothed trajectory. Simulations in this chapter test and verify the effectiveness of the algorithm, in which key parameters’ influences on system performance are discussed.


Flocking Backstepping Nonholonomic robot 



This work was supported by the National Natural Science Foundation in China (Grant No. 60705035, 61075087, 61203331, 61005065), Key Program of Hubei Province Natural Science Foundation of China (Grant No. 2010CDA005), Key Program of Open Foundation of Hubei Province Key Laboratory of Systems Science in Metallurgical Process of China (Grant No. Z201102), Open Foundation of Henan Provincial Open Laboratory for Control Engineering Key Disciplines (Grant No. KG2011-01), Scientific Research Plan Key Project of Hubei Provincial Department of Education (Grant No. D20131105). This is greatly acknowledged.


  1. 1.
    Xiao BJ, Su HM, Zhao YL, Chen X (2013) Ant colony optimisation algorithm-based multi-robot exploration. Int J Model Ident Control 18(1):41–46CrossRefGoogle Scholar
  2. 2.
    Rigatos G (2008) Multi-robot motion planning using swarm intelligence. Int J Adv Rob Syst 5(2):139–144MathSciNetGoogle Scholar
  3. 3.
    Zhang XY, Peng J, Hu HS, Lin K, Wang J (2012) Target attraction-based ant colony algorithm for mobile robots in rescue missions. Int J Model Ident Control 17(2):133–142CrossRefGoogle Scholar
  4. 4.
    Reynolds C (1987) Flocks, birds, and schools: a distributed behaviour model. Comput Graphics 21(4):25–34CrossRefGoogle Scholar
  5. 5.
    Chen SM (2007) Review of the modeling and control of swarm behaviours. Comput Eng Sci 29(7):102–105Google Scholar
  6. 6.
    Jadbabaie A, Lin J, Morse AS (2002) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001CrossRefMathSciNetGoogle Scholar
  7. 7.
    Tanner HG, Jadbabaie A, Pappas GJ (2007) Flocking in fixed and switching networks. IEEE Trans Autom Control 52(5):863–868CrossRefMathSciNetGoogle Scholar
  8. 8.
    Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533CrossRefMathSciNetGoogle Scholar
  9. 9.
    Ji M, Egerstedt M (2007) Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Rob 23(4):693–703CrossRefGoogle Scholar
  10. 10.
    Li SQ, Shuai L, Cheng XY, Tang ZM, Yang JY (2005) A descriptive model of robot team and the dynamic evolution of robot team cooperation. Int J Adv Rob Syst 2(2):139–143Google Scholar
  11. 11.
    Zavlanos MM, Tanner HG, Jadbabaie A, Pappas GJ (2009) Hybrid control for connectivity preserving flocking. IEEE Trans Autom Control 54(12):2869–2875CrossRefMathSciNetGoogle Scholar
  12. 12.
    Ekanayake SW, Pathirana PN (2010) Formations of robotic swarm: an artificial force based approach. Int J Adv Rob Syst 7(3):173–190Google Scholar
  13. 13.
    Dimarogonas D, Kyriakopoulos KJ (2007) On the rendezvous problem for multiple nonholonomic agents. IEEE Trans Autom Control 52(5):916–922CrossRefMathSciNetGoogle Scholar
  14. 14.
    Cheng L, Yu H, Wu HY, Wang YJ (2008) A sequential flocking control system for multiple mobile robots. Control Theory Appl/Kongzhi Lilun yu Yingyong 25(6):1117–1120Google Scholar
  15. 15.
    Tran VH, Lee SG (2011) A stable formation control using approximation of translational and angular accelerations. Int J Adv Rob Syst 8(1):65–75Google Scholar
  16. 16.
    Saber RO (2006) Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Control 51(3):401–420CrossRefMathSciNetGoogle Scholar
  17. 17.
    Li W, Chen Z, Liu Z (2009) Formation control of multi-agent system based on potential function in complex environment. Int J Syst Control Commun 1(4):525–539CrossRefGoogle Scholar
  18. 18.
    Cheng L, Cao L, Wu HY (2011) Trajectory tracking control of nonholonomic mobile robots by Backstepping. In: Proceedings of 2011 international conference on modelling, identification and control, pp 134–139Google Scholar
  19. 19.
    Yang JH, Wu J, Hu YM (2002) Backstepping method and its applications to nonlinear robust control. Control Decis 17:641–647Google Scholar
  20. 20.
    Saberi A, Kokotovic PV, Sussmam HJ (1990) Global stabilization of partially linear composite systems. SIAM J Control Optim 28:1491–1503Google Scholar
  21. 21.
    Zohar I, Ailon A, Rabinovici R (2011) Mobile robot characterized by dynamic and kinematic equations and actuator dynamics: trajectory tracking and related application. Rob Auton Syst 59:343–353CrossRefGoogle Scholar
  22. 22.
    Bouteraa Y, Ghommam J, Derbel N (2011) Coordinated Backstepping control of multiple robot system of the leader-follower structure. In: International multi-conference on systems, signals and devices, pp 1–5Google Scholar
  23. 23.
    Aguiar AP, Hespanha JP (2007) Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty. IEEE Trans Autom Control 52(8):1362–1379CrossRefMathSciNetGoogle Scholar
  24. 24.
    Ghommam J, Saad M, Mnif, F (2010) Robust adaptive formation control of fully actuated marine vessels using local potential functions. In: 2010 IEEE international conference on robotics and automation anchorage convention district, Anchorage, Alaska, USA, pp 3001–3007Google Scholar
  25. 25.
    Chiu CH, Peng YF, Lin YW (2011) Intelligent Backstepping control for wheeled inverted pendulum. Expert Syst Appl 38:3364–3371CrossRefGoogle Scholar
  26. 26.
    Li XH, Xiao J, Cai ZJ (2005) Backstepping based multiple mobile robots formation control. In: IEEE/RSJ international conference on intelligent robots and systems, City University of New York, NY, USA, pp 887–892Google Scholar
  27. 27.
    Castro R, Álvarez J, Martínez J (2009) Robot formation control using Backstepping and sliding mode techniques. In: International conference on 6th electrical engineering, computing science and automatic control, Mexico City, Mexico, pp 1–6Google Scholar
  28. 28.
    Dong WJ (2010) Formation control of multiple wheeled mobile robots with uncertainty. In: 49th IEEE conference on decision and control, Hilton Atlanta Hotel, Atlanta, GA, USA, pp 4492–4497Google Scholar
  29. 29.
    Dong WJ (2011) Flocking of multiple mobile robots based on Backstepping. IEEE Trans Syst Man Cybern Part B Cybern 41(2):414–424Google Scholar
  30. 30.
    Chen YY, Tian YP (2008) A Backstepping design for directed formation control of three-coleader agents in the plane. Int J Robust Nonlinear Control 19:729–745CrossRefMathSciNetGoogle Scholar
  31. 31.
    Do KD (2008) Formation tracking control of unicycle-type mobile robots With limited sensing ranges. IEEE Trans Control Syst Technol 16(3):527–538CrossRefGoogle Scholar
  32. 32.
    Li Q, Jiang ZP (2008) Formation tracking control of unicycle teams with collision avoidance. In: Proceedings of the 47th IEEE conference on decision and control, Cancun, Mexico, pp 496–501Google Scholar
  33. 33.
    Han TT, Ge SS (2011) Cooperative control design for circular flocking of underactuated hovercrafts. In: 50th IEEE conference on decision and control and European control conference (CDC-ECC), Orlando, FL, USA, pp 4891–4896Google Scholar
  34. 34.
    Cheng L, Xu WX, Wu HY, Zhu QM, Wang YJ, Nouri H (2012) A new procedure for multi-mode sequential flocking with application to multiple non-holonomic mobile robot motion control: mode description and integration principle. Int J Model Ident Control 15(1):39–47CrossRefGoogle Scholar
  35. 35.
    Cheng L, Zheng XJ, Wu HY, Zhu QM, Wang YJ, Nouri H (2012) A new procedure for multi-mode sequential flocking with application to multiple non-holonomic mobile robot motion control: implementation and analysis. Int J Model Ident Control 16(1):50–59CrossRefGoogle Scholar
  36. 36.
    Chaimowicz L (2002) Dynamic coodination of cooperative robots: a hybrid system approach. Doctoral Thesis, University of Minas Gerais, Collaborated with GRASP Laboratory at University of PennsylvaniaGoogle Scholar
  37. 37.
    Tanner HG, Jadbabaie A, Pappas GJ (2003) Stable flocking of mobile agents, part I: fixed topology. In: Proceedings of IEEE conference on decision and control conference proceedings, Maui, HI, USA, pp 2010–2015Google Scholar
  38. 38.
    Yu H, Wang YJ, Cheng L (2005) Control of stable flocking motion of multiply-agent with a leader. J Huazhong Univ Sci Technol. Nat Sci Ed 33(8):56–58Google Scholar
  39. 39.
    Siegwart R, Nourbakhsh IR (2006) Introduction to autonomous mobile robots. LI Ren-hou Translation. Xi’an Jiaotong University Press, Xi’anGoogle Scholar
  40. 40.
    Min YY, Liu YG (2007) Barbalat Lemma and its applicatioin in analysis of system stability. J Shandong Univ 37(1):51–55MathSciNetGoogle Scholar
  41. 41.

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Lei Cheng
    • 1
    • 2
    Email author
  • Jun Wang
    • 1
  • Huaiyu Wu
    • 1
  • Wenxia Xu
    • 3
  • Wenhao Zhang
    • 1
    • 4
  • Pian Jin
    • 3
  • Quanmin Zhu
    • 4
  1. 1.Engineering Research Center of Metallurgical Automation and Measurement Technology, Ministry of EducationWuhan University of Science and TechnologyWuhanChina
  2. 2.Henan Provincial Open Laboratory for Control Engineering Key DisciplinesHenan Polytechnic UniversityJiaozuoChina
  3. 3.School of AutomationHuazhong University of Science and TechnologyWuhanChina
  4. 4.Faculty of Environment and TechnologyUniversity of the West of EnglandBristolUK

Personalised recommendations