Control Theory and Technology

, Volume 14, Issue 2, pp 97–112 | Cite as

Robot impedance control and passivity analysis with inner torque and velocity feedback loops

  • Michele FocchiEmail author
  • Gustavo A. Medrano-Cerda
  • Thiago Boaventura
  • Marco Frigerio
  • Claudio Semini
  • Jonas Buchli
  • Darwin G. Caldwell


Impedance control is a well-established technique to control interaction forces in robotics. However, real implementations of impedance control with an inner loop may suffer from several limitations. In particular, the viable range of stable stiffness and damping values can be strongly affected by the bandwidth of the inner control loops (e.g., a torque loop) as well as by the filtering and sampling frequency. This paper provides an extensive analysis on how these aspects influence the stability region of impedance parameters as well as the passivity of the system. This will be supported by both simulations and experimental data. Moreover, a methodology for designing joint impedance controllers based on an inner torque loop and a positive velocity feedback loop will be presented. The goal of the velocity feedback is to increase (given the constraints to preserve stability) the bandwidth of the torque loop without the need of a complex controller.


Impedance control torque control passivity and stability analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. A. Pratt. Low impedance walking robots. Annual Meeting of the Society-for-Integrative-and-Comparative-Biolog, Chicago: Oxford University Press, 2002: 174–181.Google Scholar
  2. [2]
    J. Buchli, M. Kalakrishnan, M. Mistry, et al. Compliant quadruped locomotion over rough terrain. IEEE/RSJ International Conference on Intelligent Robots and Systems, St Louis: IEEE, 2009: 814–820.Google Scholar
  3. [3]
    N. Tsagarakis, S. Morfey, G. Medrano-Cerda, et al. Compliant humanoid COMAN: Optimal joint stiffness tuning for modal frequency control. IEEE International Conference on Robotics and Automation, Karlsruhe: IEEE, 2013: 673–678.Google Scholar
  4. [4]
    N. Paine, S. Oh, L. Sentis. Design and control considerations for high-performance series elastic actuators. IEEE/ASME Transactions on Mechatronics, 2014, 19(3): 1080–1091.CrossRefGoogle Scholar
  5. [5]
    A. Albu-Schäffer, S. Haddadin, C. Ott, et al. The DLR lightweight robot: Design and control concepts for robots in human environments. Industrial Robot: An International Journal, 2007, 34(5): 376–385.CrossRefGoogle Scholar
  6. [6]
    D. P. Ferris, M. Louie, C. T. Farley. Running in the real world: adjusting leg stiffness for different surfaces. Proceedings of the Royal Society B: Biological Sciences, 1998, 265(1400): 989–994.CrossRefGoogle Scholar
  7. [7]
    N. Hogan. Impedance control: An approach to manipulation–Part II: Implementation. Journal of Dynamic Systems, Measurement, and Control, 1985, 107(1): 8–16.CrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    O. Khatib. A unified approach for motion and force control of robot manipulators: The operational space formulation. Journal of Robotics and Automation. 1987: 43–53.Google Scholar
  9. [9]
    M. H. Raibert, J. J. Craig. Hybrid position/force control of manipulators. Journal of Dynamic Systems, Measurement, and Control, 1981, 103(2): 126–133.CrossRefGoogle Scholar
  10. [10]
    J. Pratt, C. Chew, A. Torres, et al. Virtual model control: An intuitive approach for bipedal locomotion. International Journal of Robotics Research, 2001, 20(2): 129–143.CrossRefGoogle Scholar
  11. [11]
    W. Bosworth, S. Kim, N. Hogan. The effect of leg impedance on stability and efficiency in quadrupedal trotting. IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago: IEEE, 2014: 4895–4900.Google Scholar
  12. [12]
    G. Pratt, M. Williamson. Series elastic actuators. IEEE/RSJ International Conference on Intelligent Robots and Systems, Pittsburgh: IEEE Computer Society, 1995: 399–406.Google Scholar
  13. [13]
    T. Boaventura, C. Semini, J. Buchli, et al. Dynamic torque control of a hydraulic quadruped robot. International Conference on Robotics and Automation, St. Paul: IEEE, 2012: 1889–1894.Google Scholar
  14. [14]
    M. Hutter, M. Hoepflinger, C. Gehring. Hybrid operational space control for compliant legged systems. Proceedings of Robotics: Science and Systems, Sydney: MIT Press, 2012: 150–157.Google Scholar
  15. [15]
    J. Mehling, J. Colgate, M. Peshkin. Increasing the impedance range of a haptic display by adding electrical damping. The 1st Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, Pisa: IEEE Computer Society, 2005: 257–262.CrossRefGoogle Scholar
  16. [16]
    J. E. Colgate. Coupled stability of multiport systems–theory and experiments. Journal of Dynamic Systems, Measurement and Control, 1994, 116(3): 419–428.CrossRefzbMATHGoogle Scholar
  17. [17]
    G. Ellis. Control System Design Guide. 2nd ed. London: Academic Press, 2000.Google Scholar
  18. [18]
    F. Janabi-Sharifi, V. Hayward, C.-S. Chen. Discrete-time adaptive windowing for velocity estimation. IEEE Transactions on Control Systems Technology, 2000, 8(6): 1003–1009.CrossRefGoogle Scholar
  19. [19]
    A. Albu-Schaffer, C. Ott, G. Hirzinger. A unified passivity-based control framework for position, torque and impedance control of flexible joint robots. The 12th International Journal of Robotics Research, San Francisco: SAGE Publications Ltd., 2007: 23–39.Google Scholar
  20. [20]
    A. Albu-Schaffer, C. Ott, G. Hirzinger. A passivity based Cartesian impedance controller for flexible joint robots–Part II: Full state feedback, impedance design and experiments. International Conference on Robotics and Automation, New Orleans: IEEE, 2004: 2666–2672.Google Scholar
  21. [21]
    N. Hogan, E. Colgate. Stability problems in contact tasks. Robotics Review, Cambridge: MIT Press, 2004: 339–348.Google Scholar
  22. [22]
    H. Karerooni, T. B. Sheridan, P. K. Houpt. Robust compliant motion for manipulators–Part I: The fundamental concepts of compliant motion, Part II: Design method. Journal of Robotics and Automation, 1986, 2(2): 83–105.CrossRefGoogle Scholar
  23. [23]
    D. A. Lawrence. Impedance control stability properties in common implementations. International Conference on Robotics and Automation, Philadelphia: IEEE Computer Society, 1988: 1185–1190.Google Scholar
  24. [24]
    S. P. Buerger, N. Hogan. Complementary stability and loop shaping for improved human-robot interaction. IEEE Transactions on Robotics, 2007, 23(2): 232–244.CrossRefGoogle Scholar
  25. [25]
    H. Mehdi, O. Boubaker. Stiffness and impedance control using Lyapunov theory for robot-aided rehabilitation. International Journal of Social Robotics, 2011, 4(1): 107–119.Google Scholar
  26. [26]
    N. Yasrebi, D. Constantinescu. Extending the Z-width of a haptic device using acceleration feedback. Proceedings of the 6th EuroHaptics International Conference, Madrid: Springer, 2008: 157–162.Google Scholar
  27. [27]
    C. Semini, N. G. Tsagarakis, E. Guglielmino, et al. Design of HyQ–a hydraulically and electrically actuated quadruped robot. Journal of Systems and Control Engineering, 2011, 225(I6): 831–849.Google Scholar
  28. [28]
    M. Focchi, T. Boaventura, C. Semini, et al. Torque-control based compliant actuation of a quadruped robot. Proceedings of the 12th IEEE International Workshop on Advanced Motion Control, Sarajevo: IEEE, 2012: DOI 10.1109/AMC.2012.6197133.Google Scholar
  29. [29]
    Y. Hori, H. Iseki, K. Sugiura. Basic consideration of vibration suppression and disturbance rejection control of multi-inertia system using SFLAC (state feedback and load acceleration control). IEEE Transactions on Industry Applications, 1994, 30(4): 889–896.CrossRefGoogle Scholar
  30. [30]
    M. Focchi. Strategies to Improve the Impedance Control Performance of a Quadruped Robot. Ph.D. thesis. Italy: Istituto Italiano di Tecnologia, 2013.Google Scholar
  31. [31]
    T. Boaventura, M. Focchi, M. Frigerio, et al. On the role of load motion compensation in high-performance force control. IEEE/RSJ International Conference on Intelligent Robots and Systems, Algarve: IEEE, 2012: 4066–4071.Google Scholar
  32. [32]
    E. Colgate, N. Hogan. An analysis of contact instability in terms of passive physical equivalents. IEEE International Conference on Robotics and Automation, Scottsdale: IEEE Computer Society, 1989: 404–409.Google Scholar
  33. [33]
    B. D. O. Anderson, S. Vongpanitlerd. Network Analysis and Synthesis: A Modern Systems Theory Approach. New York: Dover Publications, 2006.Google Scholar
  34. [34]
    J. E. Colgate. The Control of Dynamically Interacting Systems. Ph.D. thesis. Cambridge: Massachusetts Institute of Technology, 1986.zbMATHGoogle Scholar
  35. [35]
    J. E. Colgate, G. G. Schenkel. Passivity of a class of sampleddata systems: Application to haptic interfaces. Journal of Robotic Systems, 1997, 14(1): 37–47.CrossRefGoogle Scholar

Copyright information

© South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Michele Focchi
    • 1
    Email author
  • Gustavo A. Medrano-Cerda
    • 1
  • Thiago Boaventura
    • 2
  • Marco Frigerio
    • 1
  • Claudio Semini
    • 1
  • Jonas Buchli
    • 2
  • Darwin G. Caldwell
    • 1
  1. 1.Department of Advanced RoboticsIstituto Italiano di Tecnologia (IIT)GenovaItaly
  2. 2.Agile & Dexterous Robotics Lab, ETH ZürichZürichSwitzerland

Personalised recommendations