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Handling Uncertainty and Networked Structure in Robot Control pp 313–333Cite as

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

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Part of the Studies in Systems, Decision and Control book series (SSDC,volume 42)

Abstract

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.

Keywords

  • Reference Trajectory
  • Linear Consensus
  • Reset Sequence
  • Perron Matrix
  • Consensus Algorithm

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.

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References

  • Anta A, Tabuada P (2010) To sample or not to sample: self-triggered control for nonlinear systems. IEEE Trans Autom Control 55(9):2030–2042

    CrossRef  MathSciNet  Google Scholar 

  • Beard R, Stepanyan V (2003) Information consensus in distributed multiple vehicle coordinated control. In: IEEE conference on decision and control, vol 2, pp 2029–2034

    Google Scholar 

  • 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 conference

    Google Scholar 

  • 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 2575–2580

    Google Scholar 

  • 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):2283–2288

    CrossRef  MathSciNet  Google Scholar 

  • Brogliato B, Lozano R, Maschke B, Egeland O (2007) Dissipative systems analysis and control. Theory and applications, 2nd edn. CCES. Springer, London

    Google Scholar 

  • Buşoniu L, Morărescu IC (2014) Consensus for black-box nonlinear agents using optimistic optimization. Automatica 50(4):1201–1208

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Bullo F, Cortés J, Martinez S (2009) Distributed control of robotic networks. A mathematical approach to motion coordination algorithms. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Ding X, Rahmani A, Egerstedt M (2009) Optimal multi-UAV convoy protection. In: Second international conference on robot communication and coordination ROBOCOMM ’09

    Google Scholar 

  • Fiacchini M, Morărescu IC (2014) Convex conditions on decentralized control for graph topology preservation. IEEE Trans Autom Control 59(6):1640–1645

    CrossRef  Google Scholar 

  • Halgamuge MN, Guru SM, Jennings A (2003) Energy efficient cluster formation in wireless sensor networks. In: 10th international conference on telecommunications

    Google Scholar 

  • Heemels W, Johansson K, Tabuada P (2012) An introduction to event-triggered and self-triggered control. In: IEEE conference on decision and control

    Google Scholar 

  • Hetel L, Daafouz J, Tarbouriech S, Prieur C (2013) Stabilization of linear impulsive systems through a nearly-periodic reset. Nonlinear Anal: Hybrid Syst 7:4–15

    MathSciNet  MATH  Google Scholar 

  • Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001

    CrossRef  MathSciNet  Google Scholar 

  • Jiang ZP, Nijmeijer H (1997) Tracking control of mobile robots: a case study in backstepping. Automatica 33(7):1393–1399

    CrossRef  MathSciNet  MATH  Google Scholar 

  • 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 automation

    Google Scholar 

  • Kolmanovsky H, McClamroch N (1995) Developments in nonholonomic control systems. IEEE Control Syst Mag 15(6):20–36

    CrossRef  Google Scholar 

  • Lin X, Cassandras C (2014) Trajectory optimization for multi-agent persistent monitoring in two-dimensional spaces. In: IEEE conference on decision and control

    Google Scholar 

  • 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):65–75

    CrossRef  Google Scholar 

  • Martin S, Girard A (2013) Continuous-time consensus under persistent connectivity and slow divergence of reciprocal interaction weights. SIAM J Control Opt 51(3):2568–2584

    CrossRef  MathSciNet  MATH  Google Scholar 

  • McClamroch N, Wang D (1988) Feedback stabilization and tracking of constrained robots. IEEE Trans Autom Control 33:419–426

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Michiels W, Morarescu IC, Niculescu SI (2009) Consensus problems with distributed delays, with application to traffic flow models. SIAM J Control Opt 48(1):77–101

    CrossRef  MathSciNet  MATH  Google Scholar 

  • 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 York

    Google Scholar 

  • Moreau L (2005) Stability of multiagent systems with time-dependent communication links. IEEE Trans Autom Control 50(2):169–182

    CrossRef  MathSciNet  Google Scholar 

  • Morărescu IC, Brogliato B (2010a) Passivity-based switching control of flexible-joint complementarity mechanical systems. Automatica 46(1):160–166

    Google Scholar 

  • Morărescu IC, Brogliato B (2010b) Passivity-based tracking control of multiconstraint complementarity Lagrangian systems. IEEE Trans Autom Control 55(6):1300–1310

    Google Scholar 

  • Olfati-Saber R, Murray R (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49:1520–1533

    CrossRef  MathSciNet  Google Scholar 

  • 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 control

    Google Scholar 

  • 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 2565–2570

    Google Scholar 

  • 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 control

    Google Scholar 

  • Ren W, Beard R (2004) Formation feedback control for multiple spacecraft via virtual structures. IEEE Proc Control Theory Appl 151:357–368

    CrossRef  Google Scholar 

  • Samad T, Bay J, Godbole D (2007) Network-centric systems for military operations in urban terrain: the role of UAVs. Proc IEEE 95(1):92–107

    CrossRef  Google Scholar 

  • 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 1136–1141

    Google Scholar 

  • Sariel S, Balch T, Stack J (2006) Distributed multi-AUV coordination in naval mine countermeasure missions. Technical report, Georgia Institute of Technology

    Google Scholar 

  • 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 1733–1739

    Google Scholar 

  • 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 2976–2985

    Google Scholar 

  • Su H, Chen G, Wang X, Lin Z (2011) Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica 47(2):368–375

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Sun K, Peng P, Ning P, Wang C (2006) Secure distributed cluster formation in wireless sensor networks. In: 22nd annual computer security applications conference

    Google Scholar 

  • Tanner H, Jadbabaie A, Pappas G (2007) Flocking in fixed and switching networks. IEEE Trans Autom Control 52(5):863–867

    CrossRef  MathSciNet  Google Scholar 

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Acknowledgments

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).

Author information

Authors and Affiliations

  1. Université de Lorraine, CRAN, UMR 7039, 2 Avenue de la Forêt de Haye, Nancy, France

    Marcos Cesar Bragagnolo, Irinel-Constantin Morărescu & Pierre Riedinger

  2. CNRS, CRAN, UMR 7039, Nancy, France

    Marcos Cesar Bragagnolo, Irinel-Constantin Morărescu & Pierre Riedinger

  3. Automation Department, Technical University of Cluj-Napoca, Memorandumului 28, 400114, Cluj-Napoca, Romania

    Lucian Buşoniu

Authors
  1. Marcos Cesar Bragagnolo
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  2. Irinel-Constantin Morărescu
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  3. Lucian Buşoniu
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  4. Pierre Riedinger
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Corresponding author

Correspondence to Marcos Cesar Bragagnolo .

Editor information

Editors and Affiliations

  1. Automation Department, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Lucian Busoniu

  2. Automation Department, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Levente Tamás

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Bragagnolo, M.C., Morărescu, IC., Buşoniu, L., Riedinger, P. (2015). Decentralized Formation Control in Fleets of Nonholonomic Robots with a Clustered Pattern. In: Busoniu, L., Tamás, L. (eds) Handling Uncertainty and Networked Structure in Robot Control. Studies in Systems, Decision and Control, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-26327-4_13

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  • DOI: https://doi.org/10.1007/978-3-319-26327-4_13

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