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Predicting center of mass position in non-cyclic activities: The influence of acceleration, prediction horizon, and ground reaction forces

Mohsen Alizadeh Noghani, Edgar Bolívar-Nieto

Abstract

The whole-body center of mass (CoM) plays an important role in quantifying human movement. Prediction of future CoM trajectory, modeled as a point mass under influence of external forces, can be a surrogate for inferring intent. Given the current CoM position and velocity, predicting the future CoM position by forward integration requires a forecast of CoM accelerations during the prediction horizon. However, it is unclear how assumptions about the acceleration, prediction horizon length, and information from ground reaction forces (GRFs), which provide the instantaneous acceleration, affect the prediction. We study these factors by analyzing data of 10 healthy young adults performing 14 non-cyclic activities. We assume that the acceleration during a horizon will be 1) zero, 2) remain constant, or 3) converge to zero as a cubic trajectory, and perform predictions for horizons of 125 to 625 milliseconds. We quantify the prediction performance by comparing the position error and accuracy of identifying the main direction of displacement against trajectories obtained from a whole-body marker set. For all the assumed accelerations profiles, position errors grow quadratically with horizon length ($R^2 > 0.930$) while the accuracy of the predicted direction decreases linearly ($R^2>0.615$). Post-hoc tests reveal that the constant and cubic profiles, which utilize the GRFs, outperform the zero-acceleration assumption in position error ($p<0.001$, Cohen's $d>3.23$) and accuracy ($p<0.034$, Cohen's $d>1.44)$ at horizons of 125 and 250$\,ms$. The results provide evidence for benefits of incorporating GRFs into predictions and point to 250$\,ms$ as a threshold for horizon length in predictive applications.

Predicting center of mass position in non-cyclic activities: The influence of acceleration, prediction horizon, and ground reaction forces

Abstract

The whole-body center of mass (CoM) plays an important role in quantifying human movement. Prediction of future CoM trajectory, modeled as a point mass under influence of external forces, can be a surrogate for inferring intent. Given the current CoM position and velocity, predicting the future CoM position by forward integration requires a forecast of CoM accelerations during the prediction horizon. However, it is unclear how assumptions about the acceleration, prediction horizon length, and information from ground reaction forces (GRFs), which provide the instantaneous acceleration, affect the prediction. We study these factors by analyzing data of 10 healthy young adults performing 14 non-cyclic activities. We assume that the acceleration during a horizon will be 1) zero, 2) remain constant, or 3) converge to zero as a cubic trajectory, and perform predictions for horizons of 125 to 625 milliseconds. We quantify the prediction performance by comparing the position error and accuracy of identifying the main direction of displacement against trajectories obtained from a whole-body marker set. For all the assumed accelerations profiles, position errors grow quadratically with horizon length () while the accuracy of the predicted direction decreases linearly (). Post-hoc tests reveal that the constant and cubic profiles, which utilize the GRFs, outperform the zero-acceleration assumption in position error (, Cohen's ) and accuracy (, Cohen's at horizons of 125 and 250. The results provide evidence for benefits of incorporating GRFs into predictions and point to 250 as a threshold for horizon length in predictive applications.

Paper Structure

This paper contains 15 sections, 18 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Data collection and processing
  4. CoM prediction
  5. Statistical analysis
  6. Results
  7. Discussion
  8. Average and maximum error ($AE$ and $ME$)
  9. Average and minimum displacement direction accuracy ($ADA$ and $MDA$)
  10. Recommendations for horizon length acceleration profile
  11. Limitations
  12. Conclusion
  13. Description of the activities
  14. Double-integrator dynamics
  15. Analysis of the quadratic prediction error trend

Figures (4)

  • Figure 1: The activities and statistics of their durations, reported in milliseconds as mean (standard deviation) and minimum-maximum. The numbers 1,2,3 correspond to consecutive snapshots of the movements. One Leg, Squat, and Shoe Lace were split into start (from 1 to 2) and return (from 2 to 3) phases. The activities in the Static group are marked with (*). A written description of each activity is available in \ref{['sect:activities']}.
  • Figure 2: (a) The framework for prediction of CoM position in a horizon, which works in two steps: 1) estimating the current CoM state to supply $x[1]$, and 2) predicting the CoM position over the time horizon by propagating the CoM dynamics. WM refers to the estimate from the whole-body marker set computed by OpenSim. (b) An example of the acceleration profiles for a horizon with the length 625ms. The vertical dashed line shows the start of the horizon.
  • Figure 3: The fitted curves for (a) the average error ($AE$), and (b) the maximum error ($ME$). The solid markers ($\CIRCLE$ for Zero, $\blacksquare$ for Constant, $\blacklozenge$ for Cubic to 0, and $\blacktriangle$ for Oracle) show the mean of the data points, while the hollow markers represent the 95% CIs.
  • Figure 4: The fitted curves for (a) the average direction accuracy ($ADA$), and (b) the minimum direction accuracy ($MDA$). The solid markers ($\CIRCLE$ for Zero, $\blacksquare$ for Constant, $\blacklozenge$ for Cubic to 0, and $\blacktriangle$ for Oracle) show the mean of the data points, while the hollow markers represent the 95% CIs.