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A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation

A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation

Jinwoo Hwang, Ilseung Park, Changseob Song, Vu Phan, Eni Halilaj, Inseung Kang · N/A · 2026

locomotion reinforcement-learning control benchmark
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Summary

Objective: Data-driven models that estimate physiological states, particularly biological joint moments, are widely used in exoskeleton control.

Abstract Summary

Objective: Data-driven models that estimate physiological states, particularly biological joint moments, are widely used in exoskeleton control. However, these estimators are often coupled to device-specific sensor configurations, limiting controller transfer and the use of open-source biomechanics datasets. Methods: We proposed joint kinematics as an intermediate representation that decouples hardware-specific sensing from downstream biological joint moment estimation. A joint-moment estimator using joint angles and angular velocities was trained exclusively on open-source biomechanics data and evaluated using kinematics from a hip exoskeleton, knee exoskeleton, and inertial measurement unit (IMU) sensor suite during level-ground, ramp-ascent, and ramp-descent walking. Results: The estimator achieved an root mean square error (RMSE) of 0.17 Nm/kg and coefficient of determination (R2) of 0.79 using hip exoskeleton kinematics, 0.19 Nm/kg and 0.62 using knee exoskeleton kinematics, and 0.15 Nm/kg and 0.85 using kinematics derived from IMUs across bilateral hip, knee, and ankle joints. Conclusion: Joint kinematics enabled an estimator trained only on open-source data to operate across distinct wearable platforms. Significance: This framework may reduce target-device data collection and support transferable biological joint moment estimation for exoskeleton control and wearable biomechanics.

Key Points

  • Objective: Data-driven models that estimate physiological states, particularly biological joint moments, are widely used in exoskeleton control.
  • However, these estimators are often coupled to device-specific sensor configurations, limiting controller transfer and the use of open-source biomechanics datasets.
  • Methods: We proposed joint kinematics as an intermediate representation that decouples hardware-specific sensing from downstream biological joint moment estimation.
  • A joint-moment estimator using joint angles and angular velocities was trained exclusively on open-source biomechanics data and evaluated using kinematics from a hip exoskeleton, knee exoskeleton, and inertial measurement unit (IMU) sensor suite during level-ground, ramp-ascent, and ramp-descent walking.
  • Results: The estimator achieved an root mean square error (RMSE) of 0.17 Nm/kg and coefficient of determination (R2) of 0.79 using hip exoskeleton kinematics, 0.19 Nm/kg and 0.62 using knee exoskeleton kinematics, and 0.15 Nm/kg and 0.85 using kinematics derived from IMUs across bilateral hip, knee, and ankle joints.

Methods

All biological joint-moment estimators were trained using publicly available biomechanics data (Fig. 1 (a)). The curated database combined level-ground, ramp-ascent, and ramp-descent walking trials from the datasets used in Camargo et al. [ 21 ] , Scherpereel et al. [ 16 ] , and Molinaro et al. [ 9 , 15 ] .

Acyclic activities, such as squatting, and stair-negotiation trials were excluded because they were outside the scope of the present evaluation.

Methods — A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation
Fig. 2: Wearable-derived biological joint-moment estimates across the gait cycle for the hip and knee exoskeletons. (a) Hip results during level-ground walking at 0.8, 1.2, and 1.6 m/s and ramp ascent at 0.8 m/s (hip flexion moment is positive). (b) Knee results during ramp ascent and descent at 0.8 m/s (knee extension moment is positive). Black curves show motion-capture-derived inverse-dynamics reference biological moments, and blue curves show biological joint moments estimated from the wearable-derived kinematics. Solid curves represent mean trajectories, and shaded regions denote one standard deviation across participants. Gait cycles are segmented by heel-strike gait events.

Results

The kinematics-based estimator accurately tracked biological hip moments across level-ground walking speeds and ramp ascent using motor-encoder hip angles and IMU-derived angular velocities (Fig. 2 (a)). Across all four conditions, mean RMSE ranged from $0.12\pm 0.04$ to $0.25\pm 0.08$ Nm/kg, and mean $R^{2}$ ranged from $0.76\pm 0.10$ to $0.84\pm 0.09$.

During level-ground walking, mean RMSE increased with speed from $0.12\pm 0.04$ Nm/kg at 0.8 m/s to $0.25\pm 0.08$ Nm/kg at 1.6 m/s.

Results — A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation
Fig. 3: Lower-body biological joint-moment estimates across the gait cycle using the IMU sensor suite. Results are shown for the hip, knee, and ankle during level-ground walking at 0.8, 1.2, and 1.6 m/s and ramp ascent and descent at 0.8 m/s. Black curves show inverse-dynamics reference biological moments. Blue curves show biological joint moments estimated from the IMU-derived kinematics. Hip flexion, knee extension, and ankle dorsiflexion moments are positive. Solid curves represent mean trajectories, and shaded regions denote one standard deviation across participants.

Sources and Demonstrations

Figures are reproduced from Hwang et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.

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