Computing the Optimal Trajectory of Arm Movement: The TOPS (Task Optimization in the Presence of Signal-Dependent Noise) Model

  • Hiroyuki Miyamoto
  • Daniel M. Wolpert
  • Mitsuo Kawato
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 109)


A new framework is proposed for motor control: the Task Optimization in the Presence of Signal-dependent noise (TOPS) model. By using this model, we need not specify the position, velocity, and acceleration of the hand at the start and end of a movement. We can easily apply this model to any task setting as well as to simple point-to-point reaching movements. Estimation of the optimal trajectories using computer simulations showed that in the case of a moving target, the trajectories estimated by this model are very different from those estimated by the minimum jerk model.


Optimal Trajectory Radial Basis Function Network Goal Area Sigma Point Hand Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kelso JAS, Southard DL, Goodman D (1979) On the nature of human interlimb coordination. Science 203: 1029–1031CrossRefGoogle Scholar
  2. 2.
    Morasso P (1981) Spatial control of arm movements. Exp. Brain Res. 42: 223–227CrossRefGoogle Scholar
  3. 3.
    Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Bain 105: 331–348Google Scholar
  4. 4.
    Flash T, Hogan N (1985) The coordination of arm movements: An experimentally confirmed mathematical model. J. Neurosci. 5: 1688–1703Google Scholar
  5. 5.
    Uno Y, Kawato M, Suzuki, R (1989) Formation and control of optimal trajectory in human multijoint arm movement-minimum torque-change model. Biol. Cybern. 61: 89–101Google Scholar
  6. 6.
    Koike Y, Kawato M (1995) Estimation of dynamic joint torques and trajectory formation from surface electromyography signals using a neural network model. Biol. Cybern. 73: 291–300Google Scholar
  7. 7.
    Bizzi Y, Accornero N, Chapple W, Hogan N (1984) Posture control and trajectory formation during arm movement. J. Neurosci. 4: 2738–2744Google Scholar
  8. 8.
    Kawato M (1992) Optimization and learning in neural networks for formation and control of coordinated movement. In: DE Meyer and S Kornblum (eds). Attention and Performance XIV. Cambridge, MA: MIT Press, pp 225–259Google Scholar
  9. 9.
    Soechting JF, Flanders M (1998) Movement planning: kinematics, dynamics, both or neither? In: LR Harris, M Jenkin (eds) Vision and Action. Cambridge: Cambridge University Press, pp 332–349Google Scholar
  10. 10.
    Harris CM, Wolpert DM (1998) Signal-dependent noise determines motor planning. Nature 394 (20): 780–784CrossRefGoogle Scholar
  11. 11.
    Fitts PM (1954) The information capacity of the human motor system in controlling the amplitude of movements. J. Exp. Psychol. 47: 381–391CrossRefGoogle Scholar
  12. 12.
    Lacquaniti F, Terzuolo CA, Viviani P (1983) The law relating kinematic and figural aspects of drawing movements. Acta Psychologica 54: 115–130CrossRefGoogle Scholar
  13. 13.
    Viviani P, Schneider R (1991) A developmental study of the relationship between geometry and kinematics in drawing movements. J. Exp. Psychol. HPP 17: 198–218Google Scholar
  14. 14.
    Julier SJ, Uhlmann JK, Durrant-Whyte HF (1995) A New Approach for Filtering Nonlinear Systems. Proceedings of the 1995 American Control Conference, Seattle, Washington, pp 1628–1632Google Scholar
  15. 15.
    Hoff B, Arbib MA (1993) Model of Trajectory Formation and Temporal Interaction of Reach and Grasp. Journal of Motor Behavior 25 (3): 175–192CrossRefGoogle Scholar
  16. 16.
    Doya K, Sejnowski TJ (1998) A Computational Model of Birdsong Learning by Auditory Experience and Auditory Feedback. In: Poon, Brugge (eds) Central Auditory Processing and Neural Modeling. Plenum Press, New York, pp 77–88CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hiroyuki Miyamoto
    • 1
  • Daniel M. Wolpert
    • 2
  • Mitsuo Kawato
    • 3
  1. 1.Kawato Dynamic Brain ProjectJapan Science and Technology CorporationKyotoJapan
  2. 2.Sobell Department of Neurophysiology, Institute of NeurologyUniversity College LondonLondonUK
  3. 3.ATR Human Information Processing Research LaboratoriesKyotoJapan

Personalised recommendations