Advertisement

Stability and Variability in Skilled Rhythmic Action—A Dynamical Analysis of Rhythmic Ball Bouncing

  • Dagmar Sternad
Chapter

Abstract

The task of rhythmically bouncing a ball in the air serves as a model system that addresses many fundamental questions of coordination and perceptual control of actions. The task is simplified such that ball and racket movements are constrained to the vertical direction and the ball cannot be lost. As such, a discrete nonlinear model for the kinematics of periodic racket motions and ballistic ball flight between ball-racket contacts was formulated which permitted a set of analyses and predictions. Most centrally, linear stability analysis predicts that the racket trajectory should be decelerating prior to ball contact in order to guarantee dynamically stable performance. Such solutions imply that small perturbations need not be explicitly corrected for and therefore provide a computationally efficient solution. Four quantitative predictions were derived from a deterministic and a stochastic version of the model and were experimentally tested. Results support that human actors sense and make use of the stability properties of task. However, when single larger perturbations arise, human actors are able to adjust their racket trajectory to correct for errors and maintain a stable bouncing pattern.

Keywords

Rhythmic Action Large Perturbation Stochastic Version Passive Stability Ball Contact 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beek, P. J. (1989). Juggling dynamics. Unpublished Doctoral Dissertation, Free University Press, Amsterdam.Google Scholar
  2. Beek, P. J., & Turvey, M. T. (1992). Temporal patterning in cascade juggling. Journal of Experimental Psychology: Human Perception and Performance, 18,4, 934–947.PubMedCrossRefGoogle Scholar
  3. Beek, P. J., & van Santvoord, A. A. M. (1996). Dexterity in cascade juggling. In M. L. Latash & M. T. Turvey (Eds.), Dexterity and its development (pp. 377–392). Mahwah, NJ: Erlbaum.Google Scholar
  4. Bühler, M., & Koditschek, D. E. (1990). From stable to chaotic juggling: Theory, simulation, and experiments. Proceedings at the IEEE International Conference on Robotics and Automation, Cincinnati, OH, 1976–1981.Google Scholar
  5. Bühler, M., Koditschek, D. E., & Kindlmann, P. J. (1994). Planning and control of robotic juggling and catching tasks. International Journal of Robotics Research, 13, 101–118.Google Scholar
  6. de Rugy, A., Wei, K., Müller, H., & Sternad, D. (2003). Actively tracking “passive” stability. Brain Research, 982,1, 64–78.PubMedCrossRefGoogle Scholar
  7. Dijkstra, T. M. H., Katsumata, H., de Rugy, A., & Sternad, D. (2004). The dialogue between data and model: Passive stability and relaxation behavior in a ball bouncing task. Journal of Nonlinear Studies, 3, 319–345.Google Scholar
  8. Guckenheimer, J., & Holmes, P. (1983). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. New York: Springer.Google Scholar
  9. Raibert, M. (1986). Legged robots that balance. Cambridge, MA: MIT Press.Google Scholar
  10. Schaal, S., Sternad, D., & Atkeson, C. G. (1996). One-handed juggling: A dynamical approach to a rhythmic movement task. Journal of Motor Behavior, 28,2, 165–183.PubMedCrossRefGoogle Scholar
  11. Sim, M., Shaw, R. E., & Turvey, M. T. (1997). Intrinsic and required dynamics of a simple bat-ball skill. Journal of Experimental Psychology: Human Perception and Performance, 23,1, 101–115.PubMedCrossRefGoogle Scholar
  12. Sternad, D., & Dijkstra, T. M. H. (2004). Dynamical stability in the acquisition and performance of rhythmic ball manipulation: Theoretical insights with a clinical slant. Journal of Clinical Neurophysiology, 3,11, 215–227.CrossRefGoogle Scholar
  13. Sternad, D., Duarte, M., Katsumata, H., & Schaal, S. (2001). Bouncing a ball: Tuning into dynamic stability. Journal of Experimental Psychology: Human Perception and Performance, 27,5, 1163–1184.PubMedCrossRefGoogle Scholar
  14. Tufillaro, N. B., Abbott, T., & Reilly, J. (1992). An experimental approach to nonlinear dynamics and chaos. Redwood City, CA: Addison-Wesley.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Dagmar Sternad
    • 1
  1. 1.Department of KinesiologyThe Pennsylvania State UniversityUSA

Personalised recommendations