Experimental Brain Research

, Volume 151, Issue 2, pp 145–157 | Cite as

Functional significance of stiffness in adaptation of multijoint arm movements to stable and unstable dynamics

  • David W. FranklinEmail author
  • Etienne Burdet
  • Rieko Osu
  • Mitsuo Kawato
  • Theodore E. Milner
Research Article


This study compared the mechanisms of adaptation to stable and unstable dynamics from the perspective of changes in joint mechanics. Subjects were instructed to make point to point movements in force fields generated by a robotic manipulandum which interacted with the arm in either a stable or an unstable manner. After subjects adjusted to the initial disturbing effects of the force fields they were able to produce normal straight movements to the target. In the case of the stable interaction, subjects modified the joint torques in order to appropriately compensate for the force field. No change in joint torque or endpoint force was required or observed in the case of the unstable interaction. After adaptation, the endpoint stiffness of the arm was measured by applying displacements to the hand in eight different directions midway through the movements. This was compared to the stiffness measured similarly during movements in a null force field. After adaptation, the endpoint stiffness under both the stable and unstable dynamics was modified relative to the null field. Adaptation to unstable dynamics was achieved by selective modification of endpoint stiffness in the direction of the instability. To investigate whether the change in endpoint stiffness could be accounted for by change in joint torque or endpoint force, we estimated the change in stiffness on each trial based on the change in joint torque relative to the null field. For stable dynamics the change in endpoint stiffness was accurately predicted. However, for unstable dynamics the change in endpoint stiffness could not be reproduced. In fact, the predicted endpoint stiffness was similar to that in the null force field. Thus, the change in endpoint stiffness seen after adaptation to stable dynamics was directly related to changes in net joint torque necessary to compensate for the dynamics in contrast to adaptation to unstable dynamics, where a selective change in endpoint stiffness occurred without any modification of net joint torque.


Stability Motor learning Impedance control Endpoint stiffness Inverse dynamics model 



The experiments were performed at ATR. We thank T. Yoshioka for his technical assistance. The manipulandum was setup by T. Yoshioka and H. Gomi. This research was supported by the Telecommunications Advancement Organization of Japan, the Natural Sciences and Engineering Research Council of Canada, the Swiss National Science Foundation, and the Human Frontier Science Program


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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  • David W. Franklin
    • 1
    • 2
    Email author
  • Etienne Burdet
    • 3
  • Rieko Osu
    • 1
  • Mitsuo Kawato
    • 1
  • Theodore E. Milner
    • 2
  1. 1.ATR Computational Neuroscience LaboratoriesKyotoJapan
  2. 2.School of KinesiologySimon Fraser UniversityBurnabyCanada
  3. 3.Department of Mechanical Engineering and Division of BioengineeringNational University of Singapore119260 Singapore

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