Skip to main content

Operational Space Consensus in Networks of Robots: The Leader-Follower Case

  • Conference paper
ROBOT2013: First Iberian Robotics Conference

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 253))

  • 2965 Accesses

Abstract

This paper provides a solution to the leader-follower consensus problem in networks composed of multiple heterogeneous robots, modeled in the operational space. Using a simple distributed proportional controller and without using velocity measurements, the paper shows that all the robots in the network asymptotically reach a given leader pose (position and orientation) provided that, at least, one follower robot has access to the leader pose. The singularity-free unit quaternions are used to describe the orientation of the robots manipulators. The effectiveness of the theoretical results is validated through numerical simulations of a network composed of ten robots with 6-Degrees-of-Freedom (DoF).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Liu, Y., Chopra, N.: Controlled synchronization of heterogeneous robotic manipulators in the task space. IEEE Trans. Robot. 28(1), 268–275 (2012)

    Article  Google Scholar 

  2. Aldana, C., Nuño, E., Basañez, L.: Bilateral teleoperation of cooperative manipulators. In: IEEE Int. Conf. Robot. Autom, pp. 4274–4279 (May 2012)

    Google Scholar 

  3. Rodriguez-Angeles, A., Nijmeijer, H.: Mutual synchronization of robots via estimated state feedback: A cooperative approach. IEEE Trans. Control Syst. Technol. 12(4), 542–554 (2004)

    Article  Google Scholar 

  4. Nuño, E., Ortega, R., Basañez, L., Hill, D.: Synchronization of networks of nonidentical Euler-Lagrange systems with uncertain parameters and communication delays. IEEE Trans. Autom. Control 56(4), 935–941 (2011)

    Article  Google Scholar 

  5. Hatanaka, T., Fujita, Y.I.M., Spong, M.: Passivity-based pose synchronization in three dimensions. IEEE Trans. Autom. Control 57(2), 360–375 (2012)

    Article  MathSciNet  Google Scholar 

  6. Lee, D., Spong, M.: Stable Flocking of Multiple Inertial Agents on Balanced Graphs. IEEE Trans. Autom. Control 52(8), 1469–1475 (2007)

    Article  MathSciNet  Google Scholar 

  7. Gu, D.-B., Wang, Z.: Leader-follower flocking: Algorithms and experiments. IEEE Trans. Control Syst. Technol. 17(5), 1211–1219 (2009)

    Article  Google Scholar 

  8. Wang, X., Yu, C., Lin, Z.: A Dual Quaternion Solution to Attitude and Position Control for Rigid-Body Coordination. IEEE Trans. Robot. 28(5), 1162–1170 (2012)

    Article  Google Scholar 

  9. Qin, J., Zheng, W., Gao, H.: Coordination of Multiple Agents With Double-Integrator Dynamics Under Generalized Interaction Topologies. IEEE Trans. Syst., Man, Cybern. B 42(1), 44–57 (2012)

    Article  Google Scholar 

  10. Zhua, W., Cheng, D.: Leader-following consensus of second-order agents with multiple time-varying delays. Automatica 46(12), 1994–1999 (2010)

    Article  MathSciNet  Google Scholar 

  11. Nuño, E., Sarras, I., Panteley, E., Basañez, L.: Consensus in networks of nonidentical Euler-Lagrange systems with variable time-delays. In: 51st IEEE Conf. on Decision and Control, Maui, Hawaii, USA, pp. 4721–4726 (December 2012)

    Google Scholar 

  12. Abdessameud, A., Tayebi, A.: On consensus algorithms design for double integrator dynamics. Automatica 49(1), 253–260 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, Z., Duan, Z., Huang, L.: Leader-follower consensus of multi-agent systems. In: Proc. Amer. Contr. Conf, pp. 3256–3261 (2009)

    Google Scholar 

  14. Ren, W.: Distributed attitude alignment in spacecraft formation flying. Int. J. Adapt. Contr. Signal Process. 21(2-3), 95–113 (2007)

    Article  MATH  Google Scholar 

  15. Ren: Distributed cooperative attitude synchronization and tracking for multiple rigid bodies. IEEE Trans. Control Syst. Technol. 18(2), 383–392 (2010)

    Article  Google Scholar 

  16. Abdessameud, A., Tayebi, A., Polushin, I.-G.: Attitude synchronization of multiple rigid bodies with communication delays. IEEE Trans. Autom. Control 57(9), 2405–2411 (2012)

    Article  MathSciNet  Google Scholar 

  17. Abdessameud, A., Tayebi, A.: Formation control of VTOL unmanned aerial vehicles with communication delays. Automatica 47(11), 2383–2394 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Spong, M., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley (2005)

    Google Scholar 

  19. Caccavale, F., Siciliano, B., Villani, L.: The role of Euler parameters in robot control. Asian J. Control 1(1), 25–34 (1999)

    Article  Google Scholar 

  20. Chou, J.: Quaternion kinematic and dynamic differential equations. IEEE Trans. Robot. Autom. 8(1), 53–64 (1992)

    Article  Google Scholar 

  21. Kuipers, J.B.: Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality. Princeton University Press (2002)

    Google Scholar 

  22. Wen, J.-Y., Kreutz-Delgado, K.: The attitude control problem. IEEE Trans. Autom. Control 36(10), 1148–1162 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  23. Fjellstad, O.: Control of unmanned underwater vehicles in six degrees of freedom: a quaternion feedback approach. Ph.D. dissertation, Norwegian Institute of Technology, University of Trondheim (1994)

    Google Scholar 

  24. Campa, R., Camarillo, K.: Unit quaternions: A mathematical tool for modeling, path planning and control of robot manipulators. In: Robot manipulators, pp. 21–48. InTech (2008)

    Google Scholar 

  25. Hu, J., Hong, Y.: Leader-following coordination of multi-agent systems with coupling time delays. Phys. A Stat. Mech. Appl. 374(2), 853–863 (2007)

    Article  Google Scholar 

  26. Serre, D.: Matrices: Theory and Applications. Springer (2010)

    Google Scholar 

  27. Kelly, R., Santibáñez, V., Loria, A.: Control of robot manipulators in joint space. Advanced textbooks in control and signal processing. Springer (2005)

    Google Scholar 

  28. Corke, P.I.: Robotics, Vision & Control: Fundamental Algorithms in Matlab. Springer (2011)

    Google Scholar 

  29. Spurrier, R.A.: Comment on singularity-free extraction of a quaternion from a direction-cosine matrix. J. Spacecraft and Rockets 15(4), 255 (1978)

    Article  Google Scholar 

  30. Mazo, F.: Modelado dinámico y simulación del robot industrial stäubli TX90. Masters thesis (2011), http://upcommons.upc.edu/e-prints/handle/2117/520

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlos I. Aldana .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Aldana, C.I., Romero, E., Nuño, E., Basañez, L. (2014). Operational Space Consensus in Networks of Robots: The Leader-Follower Case. In: Armada, M., Sanfeliu, A., Ferre, M. (eds) ROBOT2013: First Iberian Robotics Conference. Advances in Intelligent Systems and Computing, vol 253. Springer, Cham. https://doi.org/10.1007/978-3-319-03653-3_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03653-3_42

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03652-6

  • Online ISBN: 978-3-319-03653-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics