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Online Phase Estimation of Human Oscillatory Motions using Deep Learning

Antonio Grotta, Francesco De Lellis

TL;DR

This work introduces a learning-based approach for online phase estimation in three-dimensional motion trajectories, using a Long Short- Term Memory (LSTM) network, and evaluates on motion capture data and in a dynamical system.

Abstract

Accurately estimating the phase of oscillatory systems is essential for analyzing cyclic activities such as repetitive gestures in human motion. In this work we introduce a learning-based approach for online phase estimation in three-dimensional motion trajectories, using a Long Short- Term Memory (LSTM) network. A calibration procedure is applied to standardize trajectory position and orientation, ensuring invariance to spatial variations. The proposed model is evaluated on motion capture data and further tested in a dynamical system, where the estimated phase is used as input to a reinforcement learning (RL)-based control to assess its impact on the synchronization of a network of Kuramoto oscillators.

Online Phase Estimation of Human Oscillatory Motions using Deep Learning

TL;DR

This work introduces a learning-based approach for online phase estimation in three-dimensional motion trajectories, using a Long Short- Term Memory (LSTM) network, and evaluates on motion capture data and in a dynamical system.

Abstract

Accurately estimating the phase of oscillatory systems is essential for analyzing cyclic activities such as repetitive gestures in human motion. In this work we introduce a learning-based approach for online phase estimation in three-dimensional motion trajectories, using a Long Short- Term Memory (LSTM) network. A calibration procedure is applied to standardize trajectory position and orientation, ensuring invariance to spatial variations. The proposed model is evaluated on motion capture data and further tested in a dynamical system, where the estimated phase is used as input to a reinforcement learning (RL)-based control to assess its impact on the synchronization of a network of Kuramoto oscillators.
Paper Structure (12 sections, 14 equations, 4 figures, 1 table)

This paper contains 12 sections, 14 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Data Acquisition
  4. Motion Data Calibration
  5. Centering
  6. Alignment
  7. Training and Validation
  8. Training
  9. Validation
  10. Validation of LSTM Phase Estimation through RL agent
  11. Conclusions
  12. Acknowledgment

Figures (4)

  • Figure 1: Visualization of the experiment, with a screenshot of the setup (a), the corresponding three-dimensional motion trajectories of the participants (b) and the same trajectories after calibration (c).
  • Figure 2: Comparison of the true phase (blue, solid line) of a trajectory from the test set $\mathcal{D}_{\text{test}}$ and the predicted phase (red, dashed line). The lower plot shows the circular error $\Delta \theta_t$.
  • Figure 3: Block diagram of the validation conducted using an RL agent. A synthetic dataset of 3D human motions is generated from pre-computed Kuramoto phases. Our LSTM model then extracts phase estimates online and feeds them to a pre-trained Deep Q-Network agent, which powers the control system (as in GROTTA202437).
  • Figure 4: Top left: Estimation error $\Delta \theta ^{i}$ for each oscillator over time. Top right: Difference between the Kuramoto order parameter $\langle r \rangle$ obtained with and without phase estimation. Bottom left: Control input $\omega_a$ from the DQN agent. Bottom right: Reconstructed 3D trajectory obtained using Eq. \ref{['eq:3Dtransformation']}. Results refers to Group 2 as an exemplificative case.