Tracing curves in the plane: Geometric-invariant learning from human demonstrations

PLoS One. 2024 Feb 28;19(2):e0294046. doi: 10.1371/journal.pone.0294046. eCollection 2024.

Abstract

The empirical laws governing human-curvilinear movements have been studied using various relationships, including minimum jerk, the 2/3 power law, and the piecewise power law. These laws quantify the speed-curvature relationships of human movements during curve tracing using critical speed and curvature as regressors. In this work, we provide a reservoir computing-based framework that can learn and reproduce human-like movements. Specifically, the geometric invariance of the observations, i.e., lateral distance from the closest point on the curve, instantaneous velocity, and curvature, when viewed from the moving frame of reference, are exploited to train the reservoir system. The artificially produced movements are evaluated using the power law to assess whether they are indistinguishable from their human counterparts. The generalisation capabilities of the trained reservoir to curves that have not been used during training are also shown.

MeSH terms

  • Biomechanical Phenomena
  • Generalization, Psychological
  • Humans
  • Mathematics
  • Models, Biological*
  • Movement*

Grants and funding

This research is supported by the National Research Foundation, Singapore, under the NRF Medium Sized Centre scheme (CARTIN). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore. LG thanks the hospitality of the Division of Mathematical Sciences at NTU, Singapore, which funded the visit that made this collaboration possible. We declare that the funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.