Inference of analytical functions modeling human finger movement using symbolic regression

Question of interest

Can we infer functionally accurate mathematical regression functions modeling human finger movement directly from data?

Background

A paper that I published that forms a prequel to this work can be found here.

  • Control of finger movement and force is made possible by a complex network of tendons.
  • Analytical functions modeling tendon excursions are useful for building robotic and prosthetic hands and understanding control of finger movement.
  • Hypothesis: Simultaneous extraction of form and parameters of functions directly from experimental data will give us more functionally accurate representations as opposed to assumption of form for the expression apriori.
  • Experimental data

    Cadaver setup
    A dataset consisting of tendon excursions(output variable) and joint angles (features) were obtained using human cadaveric hands: Tendon excursions were recorded and joint angles calculated from 3D positions of motion capture markers.

    Regression: Model inference

    Symbolic regression as implemented in the software Eureqa was used to regress mathematical functions of the form s = f(theta1, theta2, theta3 and theta4) for each tendon. The functional accuracy of the models was compared to that of vanilla polynomial regression and Landsmeer models on cross-validation datasets.

    Results

    Below is a comparison of prediction accuracy and number of parameters on cross-validation datasets: Symbolic regression vs. Polynomial vs. Landsmeer model
    Results: comparison against poly 1
    a) Mean of normalized RMS errors of the different models across two movement trials from the same cadaveric specimen. The best symbolic regression function (picked from the family of functions generated) had lower errors across the two trials compared to the polynomial regressions and the Landsmeer based models. (b) Normalized RMS errors vs. the number of parameters in the functions generated using the different techniques. Symbolic regression expressions had fewer parameters and lower RMS errors compared to the other functions.
    Cadaver setup
    (a) Mean of normalized RMS errors of the different regressions across two movement trials from two different cadaveric specimens. The models were all trained on dataset from one specimen but uniformly scaled when tested on the other specimen. The best symbolic regression model (picked from the family of functions generated) had lower mean errors across the specimens, compared to the other functions. (b) Normalized RMS errors vs. the number of parameters in the models generated using the different techniques. Symbolic regression expressions had fewer parameters and lower RMS errors compared to the other models.

    Contact information

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