Hybrid Consensus-Based Formation Control of Nonholonomic Mobile Robots

  • Haci M. GuzeyEmail author
  • Travis Dierks
  • Sarangapani Jagannathan
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 42)


In this chapter, a hybrid consensus-based formation controller is designed for mobile robots. First, omnidirectional (holonomic) robots are considered in the controller development to create a hybrid automaton, which drives the robots to their goal positions while maintaining a specified formation. The controller consists of two discrete modes, each with continuous dynamics: a regulation mode and a formation keeping mode. The controller in the regulation mode is designed to drive the robot to a goal position, while the formation keeping controller ensures that the robots achieve a specified geometric formation prior to reaching their goal-position. The proposed approach is subsequently extended to include formation control of nonholonomic mobile robots. Lyapunov methods are used to demonstrate that the formation errors converge to a small bounded region around the origin; moreover, the size of the bound can be adjusted by using the switching conditions. Convergence to goal position while in formation is also demonstrated in the same Lyapunov analysis, and simulation results verify the theoretical conjectures.


Mobile Robot Formation Error Formation Control Switching Condition Nonholonomic Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Andreasson M, Dimarogonas DV, Johansson KH (2012) Undamped nonlinear consensus using integral Lyapunov functions. In: Proceedings of the American control conference, 27–29 June 2012, pp 6644Google Scholar
  2. Arranz L, Seuret A, de Wit CC (2009) Translation control of a fleet circular formation of AUVs under finite communication range. In: Proceedings of IEEE conference on decision and control and Chinese control conference, 16–18 Dec 2009, pp 8345–8350Google Scholar
  3. Balch T, Arkin RC (1998) Behavior-based formation control for multi-robot teams. IEEE Trans Robot Autom 14(6):926–939CrossRefGoogle Scholar
  4. Bauso D, Giarre L, Pesenti R (2009) Consensus for networks with unknown but bounded disturbances. SIAM J Control Optim 48(3):1756–1770CrossRefMathSciNetzbMATHGoogle Scholar
  5. Branicky MS (1998) Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Control 43(4):475–482CrossRefMathSciNetzbMATHGoogle Scholar
  6. Dierks T, Jagannathan S (2009) Neural network control of mobile robot formations using rise feedback. IEEE Trans Syst Man Cybern Part B: Cybern 39(2):332–347CrossRefGoogle Scholar
  7. Dong-Jing L, Li W (2008) Small-signal stability analysis of an autonomous hybrid renewable energy power generation/energy storage system part i: time-domain simulations. IEEE Trans Energy Convers 23(1):311–320CrossRefGoogle Scholar
  8. Fierro R, Lewis FL (1998) Control of a nonholonomic mobile robot using neural networks. IEEE Trans Neural Netw 8:589–600CrossRefGoogle Scholar
  9. Guzey HM, Jagannathan S (2013) Adaptive neural network consensus based control of robot formations. Proc SPIE 8741:87410Google Scholar
  10. Low CB (2011) A dynamic virtual structure formation control for fixed-wing UAVs. In: 9th IEEE international conference on control and automation (ICCA), pp 627–632Google Scholar
  11. Luca AD, Oriolo G, Vendittelli M (2001) Control of wheeled mobile robots: an experimental overview. In: Nicosia S, Siciliano B, Bicchi A (eds) RAMSETE-articulated and mobile robotics for services and technologies, vol 270. Springer, New York, pp 181–223Google Scholar
  12. Olfati-Saber R, Murray RM (2004) Consensus problems in networks of robot switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533CrossRefMathSciNetGoogle Scholar
  13. Papachristodoulou A, Prajna S (2009) Robust stability analysis of nonlinear hybrid systems. IEEE Trans Autom Control 54(5):1035–1041CrossRefMathSciNetGoogle Scholar
  14. Ren W, Atkins E (2007) Distributed multi-vehicle coordinated control via local information exchange. Int J Robust Nonlinear Control 17(10–11):1002–1033CrossRefMathSciNetzbMATHGoogle Scholar
  15. Ren W, Beard R (2005) Consensus seeking in multi-robot systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50(5):655–661CrossRefMathSciNetGoogle Scholar
  16. Ren W, Beard R, Attkins E (2005) A survey of consensus problems in multi-robot coordination. In: Proceedings of the American control conference, 8–10 June 2005, pp 1859Google Scholar
  17. Semsar-Kazerooni E, Khorasani K (2008) Optimal consensus algorithms for cooperative team of robots subject to partial information. Automatica 44(11):2766–2777CrossRefMathSciNetzbMATHGoogle Scholar
  18. Semsar-Kazerooni E, Khorasani K (2009) Analysis of actuator faults in a cooperative team consensus of unmanned systems. In: American control conference (ACC), 10–12 June 2009, pp 2618Google Scholar
  19. Shi P, Zhao Y, Cui Y (2010) Modeling and control of wheeled mobile robot based on hybrid automata. In: Proceedings of the Chinese control and decision conference (CCDC), 26–28 May 2010, pp 3375Google Scholar
  20. Tejada A, Gonzalez OR, Gray WS (2013) Stability analysis of stochastic hybrid jump linear systems using a Markov kernel approach. IEEE Trans Autom Control 58(12):3156–3168CrossRefMathSciNetGoogle Scholar
  21. Tian Y, Liu C (2010) Consensus of multi robot systems with diverse input and communication delays. IEEE Trans Syst Man Cybern Part B 40(2):362–370CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Haci M. Guzey
    • 1
    Email author
  • Travis Dierks
    • 2
  • Sarangapani Jagannathan
    • 1
  1. 1.Department of Electrical and Computer EngineeringMissouri University of Science and TechnologyRollaUSA
  2. 2.DRS Sustainment Systems, Inc.St. LouisUSA

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