Decentralized Formation Control in Fleets of Nonholonomic Robots with a Clustered Pattern

  • Marcos Cesar BragagnoloEmail author
  • Irinel-Constantin Morărescu
  • Lucian Buşoniu
  • Pierre Riedinger
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 42)


In this work we consider a fleet of non-holonomic robots that has to realize a formation in a decentralized and collaborative manner. The fleet is clustered due to communication or energy-saving constraints. We assume that each robot continuously measures its relative distance to other robots belonging to the same cluster. Due to this, the robots communicate on a directed connected graph within each cluster. On top of this, in each cluster there exists one robot called leader that receives information from other leaders at discrete instants. In order to realize the formation we propose a two-step strategy. First, the robots compute reference trajectories using a linear consensus protocol. Second, a classical tracking control strategy is used to follow the references. Overall, formation realization is obtained. Numerical simulations with robot teams illustrate the effectiveness of this approach.



This work was supported by a Programme Hubert Curien-Brancusi cooperation grant (CNCS-UEFISCDI contract no. 781/2014 and Campus France grant no. 32610SE) and by the PICS project No 6614 “Artificial-Intelligence-Based Optimization for the Control of Networked and Hybrid Systems”. Additionally, the work of L. Buşoniu was supported by the Romanian National Authority for Scientific Research, CNCS-UEFISCDI (No. PNII-RU-TE-2012-3-0040). The work of I.-C. Morărescu was partially funded by the National Research Agency (ANR) project “Computation Aware Control Systems” (No. ANR-13-BS03-004-02).


  1. Anta A, Tabuada P (2010) To sample or not to sample: self-triggered control for nonlinear systems. IEEE Trans Autom Control 55(9):2030–2042CrossRefMathSciNetGoogle Scholar
  2. Beard R, Stepanyan V (2003) Information consensus in distributed multiple vehicle coordinated control. In: IEEE conference on decision and control, vol 2, pp 2029–2034Google Scholar
  3. Bertuccelli LF, Choi HL, Cho P, How JP (2009) Real-time multi-UAV task assignment in dynamic and uncertain environments. In: AIAA guidance, navigation, and control conferenceGoogle Scholar
  4. Bragagnolo MC, Morărescu IC, Daafouz J, Riedinger P (2014) LMI sufficient conditions for the consensus of linear agents with nearly-periodic resets. In: American control conference, pp 2575–2580Google Scholar
  5. Brinon Arranz L, Seuret A, Canudas de Wit C (2014) Cooperative control design for time-varying formations of multi-agent systems. IEEE Trans Autom Control 59(8):2283–2288CrossRefMathSciNetGoogle Scholar
  6. Brogliato B, Lozano R, Maschke B, Egeland O (2007) Dissipative systems analysis and control. Theory and applications, 2nd edn. CCES. Springer, LondonGoogle Scholar
  7. Buşoniu L, Morărescu IC (2014) Consensus for black-box nonlinear agents using optimistic optimization. Automatica 50(4):1201–1208CrossRefMathSciNetzbMATHGoogle Scholar
  8. Bullo F, Cortés J, Martinez S (2009) Distributed control of robotic networks. A mathematical approach to motion coordination algorithms. Princeton University Press, PrincetonzbMATHGoogle Scholar
  9. Ding X, Rahmani A, Egerstedt M (2009) Optimal multi-UAV convoy protection. In: Second international conference on robot communication and coordination ROBOCOMM ’09Google Scholar
  10. Fiacchini M, Morărescu IC (2014) Convex conditions on decentralized control for graph topology preservation. IEEE Trans Autom Control 59(6):1640–1645CrossRefGoogle Scholar
  11. Halgamuge MN, Guru SM, Jennings A (2003) Energy efficient cluster formation in wireless sensor networks. In: 10th international conference on telecommunicationsGoogle Scholar
  12. Heemels W, Johansson K, Tabuada P (2012) An introduction to event-triggered and self-triggered control. In: IEEE conference on decision and controlGoogle Scholar
  13. Hetel L, Daafouz J, Tarbouriech S, Prieur C (2013) Stabilization of linear impulsive systems through a nearly-periodic reset. Nonlinear Anal: Hybrid Syst 7:4–15MathSciNetzbMATHGoogle Scholar
  14. Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001CrossRefMathSciNetGoogle Scholar
  15. Jiang ZP, Nijmeijer H (1997) Tracking control of mobile robots: a case study in backstepping. Automatica 33(7):1393–1399CrossRefMathSciNetzbMATHGoogle Scholar
  16. Kanayama Y, Kimura Y, Miyazaki F, Noguchi T (1990) A stable tracking control method for an autonomous mobile robot. In: IEEE international conference on robotics and automationGoogle Scholar
  17. Kolmanovsky H, McClamroch N (1995) Developments in nonholonomic control systems. IEEE Control Syst Mag 15(6):20–36CrossRefGoogle Scholar
  18. Lin X, Cassandras C (2014) Trajectory optimization for multi-agent persistent monitoring in two-dimensional spaces. In: IEEE conference on decision and controlGoogle Scholar
  19. Mahacek P, Kitts C, Mas I (2011) Dynamic guarding of marine assets through cluster control of automated surface vessel fleets. IEEE/ASME Trans Mechatron 17(1):65–75CrossRefGoogle Scholar
  20. Martin S, Girard A (2013) Continuous-time consensus under persistent connectivity and slow divergence of reciprocal interaction weights. SIAM J Control Opt 51(3):2568–2584CrossRefMathSciNetzbMATHGoogle Scholar
  21. McClamroch N, Wang D (1988) Feedback stabilization and tracking of constrained robots. IEEE Trans Autom Control 33:419–426CrossRefMathSciNetzbMATHGoogle Scholar
  22. Michiels W, Morarescu IC, Niculescu SI (2009) Consensus problems with distributed delays, with application to traffic flow models. SIAM J Control Opt 48(1):77–101CrossRefMathSciNetzbMATHGoogle Scholar
  23. Moreau JJ (1988) Unilateral contact and dry friction in finite freedom dynamics. In: Moreau JJ, Panagiotopoulos PD (eds) Nonsmooth mechanics and applications, vol 302. CISM courses and lectures. Springer, New YorkGoogle Scholar
  24. Moreau L (2005) Stability of multiagent systems with time-dependent communication links. IEEE Trans Autom Control 50(2):169–182CrossRefMathSciNetGoogle Scholar
  25. Morărescu IC, Brogliato B (2010a) Passivity-based switching control of flexible-joint complementarity mechanical systems. Automatica 46(1):160–166Google Scholar
  26. Morărescu IC, Brogliato B (2010b) Passivity-based tracking control of multiconstraint complementarity Lagrangian systems. IEEE Trans Autom Control 55(6):1300–1310Google Scholar
  27. Olfati-Saber R, Murray R (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49:1520–1533CrossRefMathSciNetGoogle Scholar
  28. Panteley E, Lefeber E, Loria A, Nijmeijer H (1998) Exponential tracking control of a mobile car using a cascaded approach. In: IFAC workshop on motion controlGoogle Scholar
  29. Postoyan R, Tabuada P, Nesic D, Anta A (2011) Event-triggered and self-triggered stabilization of distributed networked control systems. In: Joint IEEE conference on decision and control and European control conference, pp 2565–2570Google Scholar
  30. Ratliff LJ, Dong R, Ohlsson H, Cárdenas AA, Sastry SS (2014) Privacy and customer segmentation in the smart grid. In: IEEE conference on decision and controlGoogle Scholar
  31. Ren W, Beard R (2004) Formation feedback control for multiple spacecraft via virtual structures. IEEE Proc Control Theory Appl 151:357–368CrossRefGoogle Scholar
  32. Samad T, Bay J, Godbole D (2007) Network-centric systems for military operations in urban terrain: the role of UAVs. Proc IEEE 95(1):92–107CrossRefGoogle Scholar
  33. Samson C, Ait-Abderrahim K (1991) Feedback control of a nonholonomic wheeled cart in Cartesian space. In: IEEE international conference on robotics and automation, pp 1136–1141Google Scholar
  34. Sariel S, Balch T, Stack J (2006) Distributed multi-AUV coordination in naval mine countermeasure missions. Technical report, Georgia Institute of TechnologyGoogle Scholar
  35. Scharf DP, Hadaegh FY, Ploen SR (2003) A survey of spacecraft formation flying guidance and control (part i): guidance. In: American control conference, vol 2, pp 1733–1739Google Scholar
  36. Scharf DP, Hadaegh FY, Ploen SR (2004) A survey of spacecraft formation flying guidance and control (part ii): control. In: American control conference, vol 4. IEEE, pp 2976–2985Google Scholar
  37. Su H, Chen G, Wang X, Lin Z (2011) Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica 47(2):368–375CrossRefMathSciNetzbMATHGoogle Scholar
  38. Sun K, Peng P, Ning P, Wang C (2006) Secure distributed cluster formation in wireless sensor networks. In: 22nd annual computer security applications conferenceGoogle Scholar
  39. Tanner H, Jadbabaie A, Pappas G (2007) Flocking in fixed and switching networks. IEEE Trans Autom Control 52(5):863–867CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marcos Cesar Bragagnolo
    • 1
    • 2
    Email author
  • Irinel-Constantin Morărescu
    • 1
    • 2
  • Lucian Buşoniu
    • 3
  • Pierre Riedinger
    • 1
    • 2
  1. 1.Université de Lorraine, CRAN, UMR 7039NancyFrance
  2. 2.CNRS, CRAN, UMR 7039NancyFrance
  3. 3.Automation DepartmentTechnical University of Cluj-NapocaCluj-NapocaRomania

Personalised recommendations