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One-handed juggling: A dynamical approach to a rhythmic movement task




The skill of rhythmic juggling a ball on a racket is investigated from the viewpoint of nonlinear dynamics. The difference equations that model the dynamical system are analyzed by means of local and non-local stability analyses. These analyses yield that the task dynamics offer an economical juggling pattern which is stable even for open-loop actuator motion. For this pattern, two types of pre dictions are extracted: (i) Stable periodic bouncing is sufficiently characterized by a negative acceleration of the racket at the moment of impact with the ball; (ii) A nonlinear scaling relation maps different juggling trajectories onto one topologically equivalent dynamical system. The relevance of these results for the human control of action was evaluated in an experiment where subjects performed a comparable task of juggling a ball on a paddle. Task manipulations involved different juggling heights and gravity conditions of the ball. The predictions were confirmed: (i) For stable rhythmic performance the paddle's acceleration at impact is negative and fluctuations of the impact acceleration follow predictions from global stability analysis; (ii) For each subject, the realizations of juggling for the different experimental conditions are related by the scaling relation. These results allow the conclusion that for the given task, humans reliably exploit the stable solutions inherent to the dynamics of the task and do not overrule these dynamics by other control mechanisms. The dynamical scaling serves as an efficient principle to generate different movement realizations from only a few parameter changes and is discussed as a dynamical formalization of the principle of motor equivalence.

Author(s): Schaal, S. and Sternad, D. and Atkeson, C. G.
Book Title: Journal of Motor Behavior
Volume: 28
Number (issue): 2
Pages: 165-183
Year: 1996

Department(s): Autonomous Motion
Bibtex Type: Article (article)

Cross Ref: p871
Note: clmc
URL: http://www-clmc.usc.edu/publications/S/schaal-JMB1996.pdf


  title = {One-handed juggling: A dynamical approach to a rhythmic movement task},
  author = {Schaal, S. and Sternad, D. and Atkeson, C. G.},
  booktitle = {Journal of Motor Behavior},
  volume = {28},
  number = {2},
  pages = {165-183},
  year = {1996},
  note = {clmc},
  crossref = {p871},
  url = {http://www-clmc.usc.edu/publications/S/schaal-JMB1996.pdf}