Kinetic Energy Analysis Module

Overview

The Kinetic Energy module provides a real-time computation of weighted kinetic energy from joint velocities.

Theoretical Interpretation

  • Input Requirements: This feature inherently tracks movement magnitude derived from the speed of the body segments over time. Therefore, it requires velocity inputs rather than raw positions.
  • Value Interpretation:
    • Higher total kinetic energy corresponds to faster, more expansive, and high-effort movements involving heavily weighted joints.
    • Component kinetic energy (energy_x, energy_y, energy_z) allows isolation of explosive movements along specific canonical axes (e.g., determining if the effort is lateral versus vertical).
    • The weights array allows the model to approximate true physical mass by treating the limbs with anatomically correct inertial weightings.

Velocity Derivation

If you only have raw positional data, you must apply a derivative operator such as extract_velocity_from_position before passing the data to this module.

Algorithm Details & Mathematics

The kinetic energy \(E_k\) of the full body is computed as the sum of translational kinetic energy over all constituent joints.

\[ E_k = \frac{1}{2} \cdot \sum_{i=1}^{N} w_i \cdot \|v_i\|^2 \]

where:

  • \(w_i\) is the configured weight (mass multiplier) of the \(i\)-th joint.
  • \(N\) is the total number of joints.
  • \(v_i\) is the velocity vector of the \(i\)-th joint supplied in the input frame.

The algorithm returns:

  1. total_energy: The scalar sum \(E_k\).
  2. component_energy: Energy isolated by orthogonal vectors (e.g., separating \(v_x^2\) from \(v_y^2\)).
  3. joints: Independent kinetic energy breakdowns for every single tracked joint.

References

  1. Glowinski, D., Dael, N., Camurri, A., Volpe, G., Mortillaro, M., & Scherer, K. (2011). Toward a minimal representation of affective gestures. IEEE Transactions on Affective Computing, 2(2), 106-118. ↩

  2. Camurri, A., Lagerlöf, I., & Volpe, G. (2003). Recognizing emotion from dance movement: comparison of spectator recognition and automated techniques. International journal of human-computer studies, 59(1-2), 213-225. ↩