Skip to main content
Log in

Variable Impedance Control for a Single Leg of a Quadruped Robot Based on Contact Force Estimation

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

Abstract

A quadruped robot interacts with the ground during the stance phase. This interaction will have a great impact on the feet, torso and joints of the robot, thus affecting the stability of its movement and reducing its adaptability in complex environments with features such as uneven terrain. The contact between each foot of the quadruped robot and the ground should not only control the movement trajectory of the leg but also control the force between the leg and the ground to comply with the environmental constraints. In general, the environment is constantly changing, whereas the traditional impedance control parameters are fixed and thus impose fixed-point constraints. To improve the compliance of the feet of a robot and achieve flexible interactions with the ground in various complex environments, such as pipelines, ruins and forests, variable impedance control is proposed. Based on variable inertia, damping and stiffness parameters, a new Lyapunov function is selected to analyse the stability of the closed-loop system. Furthermore, a force estimator is applied to estimate the contact forces, thereby reducing the burden of structural design and the cost of the robot. The effectiveness of the proposed variable impedance control scheme and contact force estimator is verified through numerical simulations in MATLAB.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Y. Farid, V. J. Majd, and A. Ehsani-Seresht, “Dynamic-free robust adaptive intelligent fault-tolerant controller design with prescribed performance for stable motion of quadruped robots,” Adaptive Behavior, vol. 29, no. 3, pp. 233–252, 2021.

    Article  Google Scholar 

  2. Y. Tan, Z. Chao, and S. Han, “Trotting control of load-carrying quadruped walking vehicle with load variations based on the centroidal dynamics and adaptive sliding mode control,” Mathematical Problems in Engineering, vol. 2020, Article ID 7154254, 2020.

  3. L. Wang, L. Meng, and R. Kang, “Design and dynamic locomotion control of quadruped robot with perception-less terrain adaptation,” Cyborg and Bionic Systems, vol. 2022, ArticlelD 9816495, 2022.

  4. N. Hu, S. Li, and F. Gao, “Multi-objective hierarchical optimal control for quadruped rescue robot,” International Journal of Control, Automation, and Systems, vol. 16, no. 4, pp. 1866–1877, 2018.

    Article  Google Scholar 

  5. S. Seok, A. Wang, and M. Y. Chuah, “Design principles for energy-efficient legged locomotion and implementation on the MIT Cheetah robot,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 3, pp. 1117–1129, 2014.

    Article  Google Scholar 

  6. R. Zhu, Q. Yang, and Y. Liu, “Sliding mode robust control of hydraulic drive unit of hydraulic quadruped robot,” International Journal of Control, Automation, and Systems, vol. 20, no. 4, pp. 1336–1350, 2022.

    Article  Google Scholar 

  7. V. G. Loc, S. Roh, and I. M. Koo, “Sensing and gait planning of quadruped walking and climbing robot for traversing in complex environment,” Robotics and Autonomous Systems, vol. 58, no. 5, pp. 666–675, 2010.

    Article  Google Scholar 

  8. M. Hutter, C. Gehring, and D. Jud, “Anymal-a highly mobile and dynamic quadrupedal robot,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 38–44, 2016.

  9. M. Li, Z. Jiang, and P. Wang, “Control of a quadruped robot with bionic springy legs in trotting gait,” Journal of Bionic Engineering, vol. 11, no. 1, pp. 188–198, 2014.

    Article  Google Scholar 

  10. M. H. Raibert, and J. J. Craig, “Hybrid position/force control of manipulators,” Journal of Dynamic Systems, Measurement, and Control, vol. 103, no. 2, pp. 188–198, 2014.

    Google Scholar 

  11. N. Hogan, “Impedance control: An approach to manipulation: Part I-Theory,” Dynamic Systems, Measurement and Control, vol. 107, no. 1, pp. 1–7, 1985.

    Article  Google Scholar 

  12. S. Yi, “Stable walking of quadruped robot by impedance control for body motion,” International Journal of Control and Automation, vol. 6, no. 2, pp. 99–110, 2013.

    Google Scholar 

  13. L. Xiao, T. Yang, and B. Huo, “Impedance control of a robot needle with a fiber optic force sensor,” Proc. of IEEE 13th International Conference on Signal Processing (ICSP), pp. 1379–1383, 2016.

  14. E. Akdogan, M. E. Aktan, and A. T. Koru, “Hybrid impedance control of a robot manipulator for wrist and forearm rehabilitation: Performance analysis and clinical results,” Mechatronics, vol. 49, pp. 77–91, 2018.

    Article  Google Scholar 

  15. W. Huo, S. Mohammed, and Y. Amirat, “Active impedance control of a lower limb exoskeleton to assist sit-to-stand movement,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), pp. 3530–3536, 2016.

  16. H. Ochoa and R. Cortesao, “Impedance control architecture for robotic-assisted mold polishing based on human demonstration,” IEEE Transactions on Industrial Electronics, pp. 1–9, 2021.

  17. K. Lee and M. Buss, “Force tracking impedance control with variable target stiffness,” Proc. of the 17th World Congress, vol. 41, no. 2, pp. 6751–6756, 2008.

    Google Scholar 

  18. M. Bednarczyk, H. Omran, and B. Bayle, “Passivity filter for variable impedance control,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 7159–7164, 2020.

  19. J. Wei, D. Yi, and X. Bo, “Adaptive variable parameter impedance control for apple harvesting robot compliant picking,” Complexity, pp. 1–15, 2020.

  20. K. Ba, G. Ma, and B. Yu, “A nonlinear model-based variable impedance parameters control for position-based impedance control system of hydraulic drive unit,” International Journal of Control, Automation, and Systems, vol. 18, no. 7, pp. 1806–1817, 2020.

    Article  Google Scholar 

  21. F. Ferraguti, C. Secchi, and C. Fantuzzi, “A tank-based approach to impedance control with variable stiffness,” Proc. of IEEE International Conference on Robotics and Automation, pp. 4948–4953, 2013.

  22. A. Dietrich, X. Wu, and K. Bussmann, “Passive hierarchical impedance control via energy tanks,” IEEE Robotics and Automation Letters, vol. 2, no. 2, pp. 522–529, 2016.

    Article  Google Scholar 

  23. J. Park and Y. Choi, “Input-to-state stability of variable impedance control for robotic manipulator,” Applied Sciences, vol. 12, no. 4, pp. 522–529, 2016.

    Google Scholar 

  24. K. Kronander and A. Billard, “Stability considerations for variable impedance control,” IEEE Transactions on Robotics, vol. 32, no. 5, pp. 1298–1305, 2016.

    Article  Google Scholar 

  25. L. P. J. Selen, D. W. Franklin, and D. M. Wolpert, “Impedance control reduces instability that arises from motor noise,” Journal of Neuroscience, vol. 29, no. 40, pp. 12606–12616, 2009.

    Article  Google Scholar 

  26. K. Ba, B. Yu, and Z. Gao, “Parameters sensitivity analysis of position-based impedance control for bionic legged robots’ HDU,” Applied Sciences, vol. 7, no. 10, pp. 1–20, 2017.

    Article  Google Scholar 

  27. G. Peng, C. Yang, W. He, and C. L. P. Chen, “Force sensorless admittance control with neural learning for robots with actuator saturation,” IEEE Transactions on Industrial Electronics, vol. 67, no. 40, pp. 1–10, 2019.

    Article  Google Scholar 

  28. A. Mohammadi, M. Tavakoli, and H. J. Marquez, “Nonlinear disturbance observer design for robotic manipulators,” Control Engineering Practice, vol. 21, no. 3, pp. 253–267, 2013.

    Article  Google Scholar 

  29. R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction Torobotic Manipulation, CRC press, Boca Raton, 1994.

    Google Scholar 

  30. A. B. Tatar, B. Taşar, and O. Yakut, “A shooting and control application of four-legged robots with a gun turret,” Arabian Journal for Science and Engineering, vol. 45, no. 7, pp. 5191–5206, 2020.

    Article  Google Scholar 

  31. Y. T. Dong and B. B. Ren, “UDE-based variable impedance control of uncertain robot systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 12, pp. 1–12, 2017.

    Google Scholar 

  32. D. Luca, A. Albu-Schaffer, and S. Haddadin, “Collision detection and safe reaction with the DLR-III lightweight manipulator arm,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1623–1630, 2006.

  33. P. J. Hacksel, and S. E. Salcudean, “Estimation of environment forces and rigid-body velocities using observers,” Proc. of the 1994 IEEE International Conference on Robotics and Automation, pp. 1623–1630, 1994.

  34. K. S. Eom, I. H. Suh, and W. K. Chung, “Disturbance observer based path tracking control of robot manipulator considering torque saturation,” Proc. of 1997 8th International Conference on Advanced Robotics, pp. 651–657, 1997.

  35. N. Dini and V. J. Majd, “Sliding-Mode tracking control of a walking quadruped robot with a push recovery algorithm using a nonlinear disturbance observer as a virtual force sensor,” Iranian Journal of Science and Technology, Transactions of Electrical Engineering, vol. 44, no. 3, pp. 1033–1057, 2020.

    Article  Google Scholar 

  36. A. Shiva, A. Stilli, and Y. Noh, “Tendon-based stiffening for a pneumatically actuated soft manipulator,” IEEE Robotics and Automation Letters, vol. 1, no. 2, pp. 632–637, 2016.

    Article  Google Scholar 

  37. G. P. He, Y. N. Fan, and T. T. Su, “Variable impedance control of cable actuated continuum manipulators” International Journal of Control, Automation, and Systems, vol. 18, no. 7, pp. 1839–1852, 2020.

    Article  Google Scholar 

  38. T. T. Su, L. Z. Niu, G. P. He, X. Liang, L. Zhao, and Q. Zhao, “Coordinated variable impedance control for multisegment cable-driven continuum manipulators,” Mechanism and Machine Theory, vol. 153, 103969, 2020.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yanan Fan.

Ethics declarations

The authors declare that there is no competing financial interest or personal relationship that could have appeared to influence the work reported in this paper.

Additional information

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

Yanan Fan received her M.S. degree from the Department of Mechanical and Materials Engineering, North China University of Technology, Beijing, China. Currently she is a doctor in the School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China. Her research interests in dynamics and control of robot.

Zhongcai Pei received his B.S., M.S., and Ph.D. degrees in mechanical and electrical engineering from Harbin Institute of Technology University of China, Haerbin, China, in 1991, 1994, and 1997, respectively. He is currently with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His current research interests include robot technology and electro-hydraulic servo control.

Zhiyong Tang received his B.S. degree in fluid power transmission and control from Beihang University in 1997 and his Ph.D. degree in mechanical and electrical engineering from Beihang University in 2003. He is currently with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His research interests include electro-hydraulic servo control and intelligent robot system.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, Y., Pei, Z. & Tang, Z. Variable Impedance Control for a Single Leg of a Quadruped Robot Based on Contact Force Estimation. Int. J. Control Autom. Syst. 22, 1360–1370 (2024). https://doi.org/10.1007/s12555-022-0601-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-022-0601-y

Keywords

Navigation