Skip to main content
SpringerLink
Log in

Sliding Mode Robust Control of Hydraulic Drive Unit of Hydraulic Quadruped Robot

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

Abstract

This paper focuses on the position control of the quadruped robot hydraulic drive unit (HDU). The proposed control strategy has the advantages of excellent output tracking performance, strong robustness, no chattering and low computational complexity. HDU has the characteristics of nonlinearity and parameter uncertainty, coupled with unpredictable external interference, which makes it difficult to achieve precise position control. In this paper, we first establish the mathematical model of the HDU based on the actual parameters and obtain the state space of the system. Through the pole placement, the simplified system can easily achieve the expected control goal. Then, the state equation of the error system is constructed, and the nonlinearity, parameter uncertainty and external interference of the HDU are summarized as the matched and unmatched uncertainties of the system. The integral sliding mode control (ISMC) is used to derive the control law, and the response characteristics of the system when pole placement and state feedback H∞ control are used for the nominal control are compared. It can be concluded that the system with state feedback H∞ control for nominal control has stronger robustness and can resist the unmatched uncertainties. Finally, the control law of the simplified system is used as feedforward and combined with the ISMC of the error system, the output tracking control framework of the HDU is proposed. Simulations and experiments show that the proposed control method has excellent tracking performance and strong robustness.

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. J. D. Carlo, P. M. Wensing, and S. Kim, “Dynamic locomotion in the MIT Cheetah 3 through convex model-predictive control,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1–9, October 2018.

  2. B. Katz, J. D. Carlo, and S. Kim, “Mini Cheetah: A platform for pushing the limits of dynamic quadruped control,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), pp. 6295–6301, May 2019.

  3. C. Gehring, S. Coros, and M. Hutter, “Towards automatic discovery of agile gaits for quadrupedal robots,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), pp. 4243–4248, June 2014.

  4. C. Gehring, S. Coros, and R. Siegwart, “Control of dynamic gaits for a quadrupedal robot,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), pp. 3287–3292, January 2013.

  5. S. Niquille, “Regarding the pain of SpotMini: Or what a robot’s struggle to learn reveals about the built environment,” Architectural Design, vol. 89, no. 1, pp. 84–91, January 2019.

    Article  Google Scholar 

  6. M. Raibert, K. Blankepoor, and G. Nelson, “Bigdog, the rough-terrain quadruped robot,” IFAC Proceedings Volumes, vol. 41, no. 2, pp. 10822–10825, July 2008.

    Article  Google Scholar 

  7. D. Wooden, M. Malchano, and K. Blankespoor, “Autonomous navigation for BigDog,” Proc. of IEEE International Conference on Robotics and Automation(ICRA), June 2010.

  8. K. Michael, “Meet Boston dynamics’ LS3 — The latest robotic war machine,” Tedxuwollongong Talk, October 2012.

  9. C. Semini, N. G. Tsagarakis, and D. G. Caldwell, “Design of HyQ — A hydraulically and electrically actuated quadruped robot,” Sage Journals, vol. 225, no. 6, pp. 204–210, August 2011.

    Google Scholar 

  10. T.-W. Ni and Z.-G. Yang, “Failure analysis on unexpected leakage of electro-hydraulic servo valve in digital electric hydraulic control system of 300 MW thermal power plant,” Engineering Failure Analysis, vol. 119, p. 104992, January 2021.

    Article  Google Scholar 

  11. G. Wrat, M. Bhola, and P. Ranjan, “Energy saving and Fuzzy-PID position control of electro-hydraulic system by leakage compensation through proportional flow control valve,” ISA Transactions, vol. 101, pp. 269–280, June 2020.

    Article  Google Scholar 

  12. H. E. Merritt, “Hydraulic control systems,” Journal of Applied Mechanics, 1967.

  13. M. Focchi, E. Guglielmino, and C. Semini, “Control of a hydraulically-actuated quadruped robot leg,” Proc. of IEEE International Conference on Robotics and Automation, June 2020.

  14. T. B. Cunha, C. Semini, and E. Guglielmino, “Gain scheduling control for the hydraulic actuation of the HyQ robot leg,” Proc. of the 20th International Congress of Mechanical Engineering, pp. 523–530, January 2009.

  15. T. Boaventura, M. Focchi, and M. Frigerio, “On the role of load motion compensation in high-performance force control,” Proc. of 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4066–4071, October 2012.

  16. Q. J. Yang, Z. Rui, and N. Zhenguo, “Natural frequency analysis of hydraulic quadruped robot and structural optimization of the leg,” Journal of Dynamic Systems, Measurement and Control, vol. 142, no. 1, p. 011009, 2019.

    Article  Google Scholar 

  17. Z. Rui, Q. J. Yang, and J. X. Song, “Research and improvement on active compliance control of hydraulic quadruped robot,” International Journal of Control, Automation, and Systems, vol. 19, pp. 1931–1943, 2021.

    Article  Google Scholar 

  18. R. Freeman and L. Praly, “Integrator backstepping for bounded controls and control rates,” IEEE Transactions on Automatic Control, vol. 43, no. 2, pp. 258–262, March 1998.

    Article  MathSciNet  Google Scholar 

  19. K. K. Ahn, D. N. C. Nam, and M. Jin, “Adaptive backstepping control of an electrohydraulic actuator,” IEEE/ASME Transactions on Mechatronics, vol. 19, no. 3, pp. 987–995, June 2014.

    Article  Google Scholar 

  20. M. Chen and S. S. Ge, “Adaptive neural output feedback control of uncertain nonlinear systems with unknown hysteresis using disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 62, no. 12, pp. 7706–7716, December 2015.

    Article  Google Scholar 

  21. H. Yudong, W. Junzheng, and H. Renjian, “Adaptive robust dead-zone compensation control of electro-hydraulic servo systems with load disturbance rejection,” Journal of Systems Science & Complexity, vol. 28, no. 2, pp. 341–359, 2015.

    Article  MathSciNet  Google Scholar 

  22. H. Yudong, W. Junzheng, and W. Shen, “Indirect adaptive robust dynamic surface control of electro-hydraulic fatigue testing system with huge elastic load,” Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering, vol. 230, no. 2, pp. 115–129, December 2015.

    Google Scholar 

  23. J. Na, Y. Li, and Y. Huang, “Output feedback control of uncertain hydraulic servo systems,” IEEE Transactions on Industrial Electronics, vol. 67, no. 1, pp. 490–500, January 2020.

    Article  Google Scholar 

  24. W. F. Bin, L. Jie, and C. Z. Kun, “RBF parameter identification of valve-controlled cylinder system for excavator robot,” Journal of Northeastern University, vol. 31, no. 10, pp. 1475–1478, 2010.

    Google Scholar 

  25. W. He, Z. Yan, C. Sun, and Y. Chen, “Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer,” IEEE Transactions on Cybernetics, vol. 47, no. 10, pp. 3452–3465, October 2017.

    Article  Google Scholar 

  26. Y. Shtessel, C. Edwards, and L. Fridman, Sliding Mode Control and Observation, Springer, New York, 2014.

    Book  Google Scholar 

  27. A. Bonchis, P. L. Corke, and D. C. Rye, “Variable structure methods in hydraulic servo systems control,” Automatica, vol. 37, no. 4, pp. 589–595, April 2001.

    Article  MathSciNet  Google Scholar 

  28. W. M. Bessa, M. Dutra, and E. J. Kreuzer, “An adaptive fuzzy dead-zone compensation scheme and its application to electro-hydraulic systems,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 32, no. 1, pp. 1–7, 2010.

    Article  Google Scholar 

  29. N. M. H. Norsahperi and K. A. Danapalasingam, “An improved optimal integral sliding mode control for uncertain robotic manipulators with reduced tracking error, chattering, and energy consumption,” Mechanical Systems and Signal Processing, vol. 142, p. 106747, August 2020.

    Article  Google Scholar 

  30. V. Utkin and J. Shi, “Integral sliding mode in systems operating under uncertainty conditions,” Proc. of 35th IEEE Conference on Decision and Control, pp. 4591–4596, December 1996.

  31. G. P. Matthews and R. A. DeCarlo, “Decentralized tracking for a class of interconnected nonlinear systems using variable structure control,” Automatica, vol. 24, no. 2, pp. 187–193, March 1988.

    Article  MathSciNet  Google Scholar 

  32. L. Fridman, A. Poznyak, and F. J. Bejarano, Robust Output LQ Optimal Control via Integral Sliding Modes, Springer, New York, 2014.

    Book  Google Scholar 

  33. J. C. Doyle, K. Glover, and P. P. Khargonekar, “State-space solutions to standard H2 and H∞ control problems,” IEEE Transactions on Automatic Control, vol. 43, no. 8, pp. 831–847, August 1989.

    Article  Google Scholar 

  34. W. Junxiao, L. Shihua, and Y. Jun, “Extended state observer-based sliding mode control for PWM-based DC-DC buck power converter systems with mismatched disturbances,” IET Control Theory & Applications, vol. 9, no. 4, pp. 579–586, February, 2015.

    Article  MathSciNet  Google Scholar 

  35. W. Junxiao, Z. Lei, and Y. Li, “Adaptive terminal sliding mode control for magnetic levitation systems with enhanced disturbance compensation,” IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 756–766, February, 2020.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China

    Rui Zhu, Qingjun Yang, Yudong Liu, Rizhi Dong & Chunli Jiang

  2. Nanjing Chenguang Group Co.Ltd, Nanjing, China

    Jiaxing Song

Authors
  1. Rui Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingjun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yudong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rizhi Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chunli Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jiaxing Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qingjun Yang.

Additional information

Rui Zhu received his B.S. degree in mechanical engineering from Taiyuan University of Technology, China, in 2017. He is currently pursuing a Ph.D. degree in mechatronics engineering from Harbin Institute of Technology, China. His research interests include quadruped robot, electrohydraulic servo control, and nonlinear control.

Qingjun Yang received his B.S., M.S., and Ph.D. degrees in mechatronics engineering from Harbin Institute of Technology, China, in 1995, 1997, and 2003, respectively. He has been with the mechatronics engineering at Harbin Institute of Technology since 2003 and promoted to the rank of associate professor in 2006. His research interests include fluid control and flow field analysis, hydraulic and pneumatic components design, nonlinear control, and adaptive control.

Yudong Liu received his M.S. degree in mechatronics engineering from Harbin Institute of Technology, China, in 2019, and received a B.S. degree in mechanical engineering from Yanshan University, China, in 2017. He is currently pursuing a Ph.D. degree in mechatronics engineering from Harbin Institute of Technology. His research interests include hydraulic components and systems and electro-hydraulic control.

Rizhi Dong received his M.S. degree in mechatronics engineering from Northeast Petroleum University, China, in 2018, and received a B.S. degree in mechanical engineering from Northeast Petroleum University, China, in 2015. He is currently pursuing a Ph.D. degree in mechatronics engineering from Harbin Institute of Technology. His research interests include hydraulic components and systems and fluid machinery.

Chunli Jiang received her B.S. degree in mechatronics Engineering from Hefei University of Technology, China, in 2020. She is currently pursuing an M.S. degree in mechatronics engineering from Harbin Institute of Technology. Her research interests include electro-hydraulic control and microfluidic.

Jiaxing Song received her M.S. degree in mechatronics engineering from Harbin Institute of Technology, China, in 2019, and received a B.S. degree in mechanical engineering from Taiyuan University of Technology, China, in 2017. She works in China Aerospace Science & Industry Nanjing Chenguang Group as an electrical engineer at present. Her research interests include servo valve driver by piezoelectric ceramic and hydraulic control system.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, R., Yang, Q., Liu, Y. et al. Sliding Mode Robust Control of Hydraulic Drive Unit of Hydraulic Quadruped Robot. Int. J. Control Autom. Syst. 20, 1336–1350 (2022). https://doi.org/10.1007/s12555-021-0235-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-021-0235-5

Keywords

Search

Navigation