Skip to main content
SpringerLink
Log in

Lyapunov and Sliding Mode Based Leader-follower Formation Control for Multiple Mobile Robots with an Augmented Distance-angle Strategy

  • Regular Papers
  • Intelligent Control and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, a new two-layer control strategy which combines Kinematic Controller based on Lyapunov Theory (KCLT) with Dynamic Controller based on Sliding Mode (DCSM) is proposed to solve the problem of leader-follower formation control for multiple wheeled mobile robots (M-WMR). An augmented distance-angle leader-follower formation kinematic is constructed to describe the formation states, and a 2D LiDAR sensor is utilized to measure the states instead of using camera and image processing on each follower. Instead of transferring the measured formation states into reference position command for each follower, KCLT is designed to generate follower’s velocity command. By taking the velocity command of followers as reference signals, DCSM is implemented to realize formation control. Lyapunov stability theory verifies that with the designed controller all the error signals can converge to 0 theoretically, which implies formation control of M-WMR under the proposed method can be realized. Real experiments with one leader and two followers are carried out to demonstrate the effectiveness of the proposed control schema. In order to verify the robustness of the proposed method, the reference rotational velocity of the leader robot is designed to change between +0:2 rad/s and -0:2 rad/s at some specified position. And the experimental results are compared with that of traditional proportional-integral-derivative (PID) method.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Sugiyama, T. Tsujioka, and M. Murata, “Real-time exploration of a multi-robot rescue system in disaster areas,” Advanced Robotics, vol. 27, no. 17, pp. 13131323, October 2013.

    Article  Google Scholar 

  2. A. G. Barrientos, J. L. López, and E. S. Espinoza, “Object transportation using a cooperative mobile multi-robot system,” IEEE Latin America Transactions, vol. 14, no. 3, pp. 1184–1191, March 2016.

    Article  Google Scholar 

  3. G. Droge, “Distributed virtual leader moving formation control using behavior-based MPC,” Proc. of American Control Conference, Palmer House Hilton, pp. 2323–2328, July 2015.

    Google Scholar 

  4. B. Shahbazi, M. Malekzadeh, and H. R. Koofigar, “Robust constrained attitude control of spacecraft formation flying in the presence of disturbances,” IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no. 5, pp. 2534–2543, October 2017.

    Article  Google Scholar 

  5. S. Yin, H. Yang, and O. Kaynak, “Coordination task triggered formation control algorithm for multiple marine vessels,” IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 4984–4993, June 2017.

    Article  Google Scholar 

  6. S. J. Yoo and B. S. Park, “Formation tracking control for a class of multiple mobile robots in the presence of unknown skidding and slipping,” IET Control Theory & Applications, vol. 7, no. 5, pp. 635–645, March 2013.

    Article  MathSciNet  Google Scholar 

  7. H. Wang, D. Guo, and X. Liang, “Adaptive vision-based leaderfollower formation control of mobile robots,” IEEE Transactions on Industrial Electronics, vol. 64, no. 4, pp. 2893–2902, April 2017.

    Article  Google Scholar 

  8. K. Shojaei, “Neural adaptive output feedback formation control of type (m, s) wheeled mobile robots,” IET Control Theory & Applications, vol. 11, no. 4, pp. 504–515, February 2017.

    Article  MathSciNet  Google Scholar 

  9. H. Xiao, Z. Li, and C. L. Philip Chen, “Formation control of leaderfollower mobile robots’ systems using model predictive control based on neural-dynamic optimization,” IEEE Transactions on Industrial Electronics, vol. 63, no. 9, pp. 5752–5762, September 2016.

    Article  Google Scholar 

  10. B. S. Park, J. B. Park, and Y. H. Choi, “Adaptive formation control of electrically driven nonholonomic mobile robots with limited information,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 41, no. 4, pp. 1061–1075, August 2011.

    Article  Google Scholar 

  11. M. H. Rezaei, M. B. Menhaj, “Stationary average consensus for high-order multi-agent systems,” IET Control Theory and Applications, vol. 11, no. 5, pp. 723–731, March 2017.

    Article  MathSciNet  Google Scholar 

  12. A. Loria, J. Dasdemir, and N. A. Jarquin, “Leaderfollower formation and tracking control of mobile robots along straight paths,” IEEE Transactions on Control Systems Technology, vol. 24, no. 2, pp. 727–732, March 2016.

    Article  Google Scholar 

  13. X. Liang, Y. Liu, and H. Wang, “Leader-following formation tracking control of mobile robots without direct position measurements,” IEEE Transactions on Automatic Control, vol. 61, no. 12, pp. 4131–4137, December 2016.

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Herrera, F. Roberti, and M. Toibero, “Human interaction dynamics for its use in mobile robotics: impedance control for leader-follower formation,” IEEE/CAA Journal of Automatica Sinica, vol. 4, no. 4, pp. 696–703, September 2017.

    Article  Google Scholar 

  15. K. Sakurama, Y. Kosaka, and S. Nishida, “Formation control of swarm robots with multiple proximity distance sensors,” International Journal of Control, Automation and System, vol. 16, no. 1, pp. 16–26, Jan. 2018.

    Article  Google Scholar 

  16. N. Soltani, A. Shahmansoorian, and M. A. Khosravi, “Robust distance-angle leader-follower formation control of non-holonomic mobile robots,” Proceeding of the 2nd RSI/ISM International Conference on Robotics and Mechatronics, pp. 24–28, October 2014.

    Google Scholar 

  17. D. Qian, C. Li, and S. Tong, “Integral sliding mode-based formation control of multiple uncertain robots via nonlinear disturbance observer,” International Journal of Advanced Robotics System, vol. 2, no. 1, pp. 1–11, December 2016.

    Google Scholar 

  18. F.Wu, J. Chen, and Y. Liang, “Leader-following formation control for quadrotors,” Proc. of IOP Conference Series: Materials Science and Engineering, pp. 1–7, January 2016.

    Google Scholar 

  19. D. Qian, S. Tong, and C. Xu, “Robust multi-robot formations via sliding mode controller and fuzzy compensator,” Automatika, vol. 57, no. 4, pp. 1007–1019, 2017.

    Article  Google Scholar 

  20. Y. H. Chang, C. Y. Yang, and W. S. Chan, “Adaptive fuzzy sliding-mode formation controller design for multi-robot dynamic systems,” International Journal of Fuzzy System, vol. 16, 1, pp. 121–131, March 2014.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics Engineering, Pusan National University, 63-2 Jangjeon-dong, Geumjeong-gu, Busan, 46241, Korea

    Yudong Zhao, Yueyuan Zhang & Jangmyung Lee

Authors
  1. Yudong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yueyuan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jangmyung Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jangmyung Lee.

Additional information

Recommended by Editor Fumitoshi Matsuno. This research was funded and conducted under the Cooperative Development on Medical Robot System between DAKEWE and PNU (CDMRSDP), operated by DAKEWE-PNU Research Institute of Medical Robot (DPRIMR). (No. 201738260001, cooperative development on medical robot system).

Yudong Zhao received his B.S. and M.S. degrees in Mechanical Design, Manufacturing and Automation and Electronics Engineering from Henan Polytechnic University and Pusan National University, China and Korea, in 2014 and 2016, respectively. Now he is pursing a doctoral degree in Pusan National University, Korea, and his research interest includes computer vision, adaptive control theory, terminal sliding mode control, and collaboration robotics.

Yueyuan Zhang received her B.S. degree in Communication Engineering from Yanbian University, China in 2013. Now she is pursing a master degree in Pusan National University, Korea, and her research interests include robot control, visual servoing and haptic technology.

Jangmyung Lee received his B.S. and M.S. degrees in Electronics Engineering from Seoul National University, Seoul, Korea, in 1980 and 1982, respectively, and his Ph.D. in Computer Engineering from the University of Southern California (USC), Los Angeles, in 1990. Since 1992, he has been a professor with the Intelligent Robot Laboratory, Pusan National University, Busan, Korea. His current research interests include intelligent robotic systems, ubiquitous ports, and intelligent sensor. Prof. Lee is a past president of the Korean Robotics Society, and a Vice president of ICROS. He is also the head of National Robotics Research Center, SPENALO.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Y., Zhang, Y. & Lee, J. Lyapunov and Sliding Mode Based Leader-follower Formation Control for Multiple Mobile Robots with an Augmented Distance-angle Strategy. Int. J. Control Autom. Syst. 17, 1314–1321 (2019). https://doi.org/10.1007/s12555-018-0194-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-018-0194-7

Keywords

Search

Navigation