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Origins and violations of the 2/3 power law in rhythmic 3D movements




The 2/3 power law, the nonlinear relationship between tangential velocity and radius of curvature of the endeffector trajectory, has been suggested as a fundamental constraint of the central nervous system in the formation of rhythmic endpoint trajectories. However, studies on the 2/3 power law have largely been confined to planar drawing patterns of relatively small size. With the hypothesis that this strategy overlooks nonlinear effects that are constitutive in movement generation, the present experiments tested the validity of the power law in elliptical patterns which were not confined to a planar surface and which were performed by the unconstrained 7-DOF arm with significant variations in pattern size and workspace orientation. Data were recorded from five human subjects where the seven joint angles and the endpoint trajectories were analyzed. Additionally, an anthropomorphic 7-DOF robot arm served as a "control subject" whose endpoint trajectories were generated on the basis of the human joint angle data, modeled as simple harmonic oscillations. Analyses of the endpoint trajectories demonstrate that the power law is systematically violated with increasing pattern size, in both exponent and the goodness of fit. The origins of these violations can be explained analytically based on smooth rhythmic trajectory formation and the kinematic structure of the human arm. We conclude that in unconstrained rhythmic movements, the power law seems to be a by-product of a movement system that favors smooth trajectories, and that it is unlikely to serve as a primary movement generating principle. Our data rather suggests that subjects employed smooth oscillatory pattern generators in joint space to realize the required movement patterns.

Author(s): Schaal, S. and Sternad, D.
Book Title: Experimental Brain Research
Volume: 136
Pages: 60-72
Year: 2001

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

Cross Ref: p1136
Note: clmc
URL: http://www-clmc.usc.edu/publications/S/schaal-EBR2001.pdf; http://www-clmc.usc.edu/publications/S/schaal-EBR2001-reprint.pdf


  title = {Origins and violations of the 2/3 power law in rhythmic 3D movements},
  author = {Schaal, S. and Sternad, D.},
  booktitle = {Experimental Brain Research},
  volume = {136},
  pages = {60-72},
  year = {2001},
  note = {clmc},
  crossref = {p1136},
  url = {http://www-clmc.usc.edu/publications/S/schaal-EBR2001.pdf; http://www-clmc.usc.edu/publications/S/schaal-EBR2001-reprint.pdf}