Biological Cybernetics

, Volume 90, Issue 5, pp 368–375 | Cite as

A model of force and impedance in human arm movements

  • K. P. Tee
  • E. Burdet
  • C. M. Chew
  • T. E. Milner


This paper describes a simple computational model of joint torque and impedance in human arm movements that can be used to simulate three-dimensional movements of the (redundant) arm or leg and to design the control of robots and human-machine interfaces. This model, based on recent physiological findings, assumes that (1) the central nervous system learns the force and impedance to perform a task successfully in a given stable or unstable dynamic environment and (2) stiffness is linearly related to the magnitude of the joint torque and increased to compensate for environment instability. Comparison with existing data shows that this simple model is able to predict impedance geometry well.


Motor adaptation Impedance Force Stable and unstable interactions 


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  1. 1.
    Bennett DJ, Hollerbach JM, Xu Y, Hunter IW (1992) Time-varying of human elbow joint during cyclic voluntary movement. Exp Brain Res 88(2): 433–442Google Scholar
  2. 2.
    Bennett DJ (1993) Torques generated at the human elbow joint in response to constant position errors imposed during voluntary movement. Exp Brain Res 95(3): 488–498Google Scholar
  3. 3.
    Bicchi A, Rizzini SL, Tonietti G (2001) Compliant design for intrinsic safety: general issues and preliminary design. In: Proceedings of IEEE/RSJ international conference of intelligent robots and systems, pp 1864–1869Google Scholar
  4. 4.
    Burdet E, Osu R, Franklin DW, Milner TE, Kawato M (1999) Measuring endpoint stiffness during multi-joint arm movements. In: Proceedings of ASME symposium on haptic interfaces and virtual environments for teleoperator systems, pp 421–428Google Scholar
  5. 5.
    Burdet E, Osu R, Franklin DW, Yoshioka T, Milner TE, Kawato M (2000) A method for measuring endpoint stiffness during multi-joint arm movements. J Biomech 33(12): 1705–1709Google Scholar
  6. 6.
    Burdet E, Osu R, Franklin DW, Milner TE, Kawato M (2001) The central nervous system skillfully stabilizes unstable dynamics by learning optimal impedance. Nature 414: 446–449Google Scholar
  7. 7.
    Burdet E, Franklin DW, Osu R, Tee KP, Kawato M, Milner TE (2004) How are internal models of unstable tasks formed? In: Proceedings of IEEE international conference on engineering in medicine and biologyGoogle Scholar
  8. 8.
    Colgate JE and Hogan N (1988) Robust control of dynamically interacting systems. Int J Control 48: 65–88Google Scholar
  9. 9.
    Conditt MA, Mussa-Ivaldi FA (1997) The motor system does not learn the dynamics of the arm by rote memorization of past experience. J Neurophysiol 78(1): 554–560Google Scholar
  10. 10.
    De Wit CC, Siciliano B, Bastin G (1996) Theory of robot control. Springer, Berlin Heidelberg New YorkGoogle Scholar
  11. 11.
    Flash T, Hogan N (1985) The co-ordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5: 1688–1703Google Scholar
  12. 12.
    Flash T, Mussa-Ivaldi FA (1990) Human arm stiffness characteristics during the maintenance of posture. Exp Brain Res 82(2): 315–326Google Scholar
  13. 13.
    Franklin DW, Milner TE (2003a) Adaptive control of stiffness to stabilize hand position with large loads. Exp Brain Res 152(2): 211–220Google Scholar
  14. 14.
    Franklin DW, Burdet E, Osu R, Kawato M, Milner TE (2003b) Functional significance of stiffness in adaptation of multijoint arm movements to stable and unstable dynamics. Exp Brain Res 151: 145–157Google Scholar
  15. 15.
    Franklin DW, Osu R, Burdet E, Kawato M, Milner TE (2003c) Adaptation to stable and unstable dynamics achieved by combined impedance control and inverse dynamics model. J Neurophysiol 90: 3270–3282Google Scholar
  16. 16.
    Gomi H, Kawato M (1997) Human arm stiffness and equilibrium point trajectory during multi-joint movement. Biol Cybern 76(3): 163–171Google Scholar
  17. 17.
    Gomi H, Osu R (1998) Task-dependent viscoelasticity of human multijoint arm and its spatial characteristics for interaction with environments. J Neurosci 18: 8965–8978Google Scholar
  18. 18.
    Kawato M (1999) Internal models for motor control and trajecotry planning. Curr Opin Neurobiol 9: 718–727Google Scholar
  19. 19.
    Lackner JR, Dizio P (1994) Rapid adaptation to Coriolis force perturbations of arm trajectory. J Neurophysiol 72: 299–313Google Scholar
  20. 20.
    Milner TE (1993) Dependence of elbow viscoelastic behaviour on speed and loading in voluntary movements. Exp Brain Res 93(1): 177–180Google Scholar
  21. 21.
    Milner TE, Cloutier C (1993) Compensation for mechanically unstable loading in voluntary wrist movement. Exp Brain Res 94: 522–532Google Scholar
  22. 22.
    Mussa-Ivaldi FA, Hogan N, Bizzi E (1985) Neural, mechanical, and geometric factors subserving arm posture in humans. J Neurosci 5(10): 2732–2743Google Scholar
  23. 23.
    Osu R, Burdet E, Franklin DW, Milner TE, Kawato M (2003) Different mechanisms involved in adaptation to stable and unstable dynamics. J Neurophysiol 90: 3255–3269Google Scholar
  24. 24.
    Perreault EJ, Kirsch RF, Crago PE (2001) Effects of voluntary force generation on the elastic components of endpoint stiffness. Exp Brain Res 141(3): 312–323Google Scholar
  25. 25.
    Perreault EJ, Kirsch RF, Crago PE (2002) Voluntary control of static endpoint stiffness during force regulation tasks. J Neurophysiol 87(6): 2808–2816Google Scholar
  26. 26.
    Rancourt D, Hogan N (2001) Dynamics of pushing. J Mot Behav 33(4): 351–362Google Scholar
  27. 27.
    Schmidt RA, Zelaznik H, Hawkins B, Frank JS, Quinn JT (1979) Motor output variability: a theory for the accuracy of rapid motor acts. Psychol Rev 47: 415–451Google Scholar
  28. 28.
    Shadmehr R, Mussa-Ivaldi FA (1994) Adaptive representation of dynamics during learning of motor tasks. J Neurosci 14(5): 3208–3224Google Scholar
  29. 29.
    Shadmehr R, Holcomb HH (1997) Neural correlates of motor memory consolidation. Science 277: 821–825Google Scholar
  30. 30.
    Slifkin AB, Newell KM (1999) Noise, information transmission, and force variability. J Exp Psychol Hum Percept Perform 25(3): 837–851Google Scholar
  31. 31.
    Surgical robots (2004) productsandsolutions/products/zeus/index. cfm; Scholar
  32. 32.
    Thoroughman KA, Shadmehr R (1999) Electromyographic correlates of learning an internal model of reaching movements. J Neurosci 19(19): 8573–8588Google Scholar
  33. 33.
    Tsuji T, Morasso PG, Goto K, Ito K (1995) Human hand impedance characteristics during maintained posture. Biol Cyber 72(6): 475–485Google Scholar
  34. 34.
    Zhang H, Burdet E, Hutmacher DW, Poo AN, Bellouard Y, Clavel R, Sidler T (2002) Robotic micro-assembly of scaffold/cell constructs with a shape memory alloy gripper. In: Proceedings of the IEEE international conference on robotics and automation, pp 1483–1488Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • K. P. Tee
    • 1
  • E. Burdet
    • 1
    • 2
  • C. M. Chew
    • 1
  • T. E. Milner
    • 3
  1. 1.Department of Mechanical EngineeringNational University
  2. 2.Division of BioengineeringNational University
  3. 3.School of KinesiologySimon Fraser UniversityCanada

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