Skip to main content
Log in

Novel strategies in feedforward adaptation to a position-dependent perturbation

  • Research Article
  • Published:
Experimental Brain Research Aims and scope Submit manuscript


To investigate the control mechanisms used in adapting to position-dependent forces, subjects performed 150 horizontal reaching movements over 25 cm in the presence of a position-dependent parabolic force field (PF). The PF acted only over the first 10 cm of the movement. On every fifth trial, a virtual mechanical guide (double wall) constrained subjects to move along a straight-line path between the start and target positions. Its purpose was to register lateral force to track formation of an internal model of the force field, and to look for evidence of possible alternative adaptive strategies. The force field produced a force to the right, which initially caused subjects to deviate in that direction. They reacted by producing deviations to the left, “into” the force field, as early as the second trial. Further adaptation resulted in rapid exponential reduction of kinematic error in the latter portion of the movement, where the greatest perturbation to the handpath was initially observed, whereas there was little modification of the handpath in the region where the PF was active. Significant force directed to counteract the PF was measured on the first guided trial, and was modified during the first half of the learning set. The total force impulse in the region of the PF increased throughout the learning trials, but it always remained less than that produced by the PF. The force profile did not resemble a mirror image of the PF in that it tended to be more trapezoidal than parabolic in shape. As in previous studies of force-field adaptation, we found that changes in muscle activation involved a general increase in the activity of all muscles, which increased arm stiffness, and selectively-greater increases in the activation of muscles which counteracted the PF. With training, activation was exponentially reduced, albeit more slowly than kinematic error. Progressive changes in kinematics and EMG occurred predominantly in the region of the workspace beyond the force field. We suggest that constraints on muscle mechanics limit the ability of the central nervous system to employ an inverse dynamics model to nullify impulse-like forces by generating mirror-image forces. Consequently, subjects adopted a strategy of slightly overcompensating for the first half of the force field, then allowing the force field to push them in the opposite direction. Muscle activity patterns in the region beyond the boundary of the force field were subsequently adjusted because of the relatively-slow response of the second-order mechanics of muscle impedance to the force impulse.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others


  • Brown SH, Cooke D (1990) Movement-related phasic muscle activation. I. Relations with temporal profile of movement. J Neurophysiol 63:455–465

    CAS  PubMed  Google Scholar 

  • Burdet E, Osu R, Franklin DW, Milner TE, Kawato M (2001) The central nervous system stabilizes unstable dynamics by learning optimal impedance. Nature 414: 446–449

    Article  CAS  PubMed  Google Scholar 

  • Donchin O, Francis JT, Shadmehr R (2003) Quantifying generalization from trial-by-trial behaviour of adaptive systems that learn with basis functions: theory and experiments in human motor control. J Neurosci 23:9032–9045

    CAS  PubMed  Google Scholar 

  • Flanagan JR, Wing AM (1997) The role of internal models in motion planning and control: evidence from grip force adjustments during movements of hand-held loads. J Neurosci 17:1519–1528

    CAS  PubMed  Google Scholar 

  • Franklin DW, Osu R, Burdet E, Kawato M, Milner TE (2003a) Adaptation to stable and unstable dynamics as achieved by combined impedance control and inverse dynamics model. J Neurophysiol 90:3270–3282

    Google Scholar 

  • Franklin DW, Burdet E, Osu R, Kawato M, Milner TE (2003b) Functional significance of stiffness in adaptation to stable and unstable dynamics. Exp Brain Res 151:145–157

    Article  Google Scholar 

  • Franklin DW, So U, Kawato M, Milner TE (2004) Impedance control balances stability with metabolically costly muscle activation. J Neurophysiol 92:3097–3105

    Article  PubMed  Google Scholar 

  • Gomi H, Kawato M (1996) Equilibrium-point control hypothesis examined by measured arm stiffness during multijoint movement. Science 272:117–120

    CAS  PubMed  Google Scholar 

  • Gomi H, Kawato M (1997) Human arm stiffness and equilibrium-point trajectory during multi-joint movement. Biol Cybern 76:163–171

    Article  CAS  PubMed  Google Scholar 

  • Kawato M (1990) Feedback-error-learning network for supervised motor learning. In: Eckmiller R (eds) Advanced neural computers. North-Holland/Elsevier, Amsterdam, pp 365–372

    Google Scholar 

  • Lackner JR, Dizio P (1994) Rapid adaptation to coriolis force perturbations of arm trajectory. J Neurophysiol 72:299–313

    CAS  PubMed  Google Scholar 

  • Lai EJ, Hodgson AJ, Milner TE (2003) Influence of interaction force levels on degree of motor adaptation in a stable dynamic force field. Exp Brain Res 153:76–83

    Article  CAS  PubMed  Google Scholar 

  • Osu R, Gomi H (1999) Multijoint muscle regulation mechanisms examined by measured human arm stiffness and EMG signals. J Neurophysiol 81:1458–1468

    CAS  PubMed  Google Scholar 

  • Osu R, Franklin DW, Kato H, Gomi H, Domen K, Yoshioka T, Kawato M (2002) Short- and long-term changes in joint co-contraction associated with motor learning as revealed from surface EMG. J Neurophysiol 88:991–1004

    PubMed  Google Scholar 

  • Osu R, Franklin DW, Kato H, Gomi H, Domen K, Yoshioka T, Kawato M (2003) Different mechanisms involved in adaptation to stable and unstable dynamics. J Neurophysiol 90:3255–3269

    PubMed  Google Scholar 

  • Perreault EJ, Kirsch RF, Crago PE (2004) Multijoint dynamics and postural stability of the human arm. Exp Brain Res 157:507–517

    Article  PubMed  Google Scholar 

  • Scheidt RA, Reinkensmeyer DJ, Conditt MA, Rymer WZ, Mussa-Ivaldi FA (2000) Persistence of motor adaptation during constrained, multi-joint, arm movements. J Neurophysiol 84:853–862

    CAS  PubMed  Google Scholar 

  • Scheidt RA, Dingwell JB, Mussa-Ivaldi FA (2001) Learning to move amid uncertainty. J Neurophysiol 86:971–985

    CAS  PubMed  Google Scholar 

  • Shadmehr R, Mussa-Ivaldi FA (1994) Adaptive representation of dynamics during learning of a motor task. J Neurosci 14:3208–3224

    CAS  PubMed  Google Scholar 

  • Takahashi CD, Scheidt RA, Reinkensmeyer DJ (2001) Impedance control and internal model formation when reaching in a randomly varying dynamical environment. J Neurophysiol 86:1047–1051

    CAS  PubMed  Google Scholar 

  • Tee KP, Burdet E, Chew CM, Milner TE (2004) A model of force and impedance in human arm movements. Biol Cybern 90:368–375

    Article  CAS  PubMed  Google Scholar 

  • Thoroughman KA, Shadmehr R (2000) Learning of action through adaptive combination of motor primitives. Nature 407:742–747

    Article  CAS  PubMed  Google Scholar 

Download references


This work was conducted while M.R. Hinder worked as a student intern in the Computational Neuroscience Laboratories at Advanced Telecommunications Research Institute International, Kyoto, Japan. We thank Dr. M. Kawato for this opportunity. We also thank D. Franklin and T. Yoshioka for assistance in conducting experiments at ATR, and D. Franklin for providing an earlier version of Figure 1. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada and the Gordon Diewert Memorial Scholarship.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Theodore E. Milner.



Simulations to determine how the impedance of the arm transformed the force impulse of the PF into lateral displacement were carried out using a second-order model of the limb mechanics driven by joint torques, τr, derived from null-field movements such that

$$I(\theta)\ddot\theta + C(\theta,\dot\theta)\dot\theta+ B_{j} \dot\theta+ K_{j} (\theta- \theta_{\rm r}) = \tau_{\rm r} + \tau_{\text {PF}} $$

where I represents the inertia of the arm determined from anthropometric estimates, C represents Coriolis and centrifugal terms, Bj is the joint damping matrix, Kj is the joint stiffness matrix, θr(t) is the null field trajectory and τPF represents the joint torques imposed by the PF. Joint stiffness terms were scaled as a function of joint torque, corresponding to measurements made by Osu and Gomi (1999) and Perreault et al. (2004). Joint damping was proportional to joint stiffness and inversely proportional to joint velocity (Tee et al. 2004), with a proportionality constant chosen such that the damping ratio was approximately equal to that measured by Perreault et al. (2004). Joint torques, τr, were computed from inverse dynamics, using the trajectories and the hand forces recorded during null-field movements as in Franklin et al. (2003a). The above differential equation was solved using the Matlab function ode45.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hinder, M.R., Milner, T.E. Novel strategies in feedforward adaptation to a position-dependent perturbation. Exp Brain Res 165, 239–249 (2005).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: