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A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation

Joint angles and angular velocities serve as a shared intermediate representation, decoupling wearable sensing hardware from downstream biological joint moment estimation.

Jinwoo Hwang1 Ilseung Park1 Changseob Song1 Vu Phan1 Eni Halilaj1 Inseung Kang1

1Carnegie Mellon University, Mechanical Engineering

Paper

Why this matters

Device-agnostic interface

Joint angles and angular velocities form a shared biomechanical input domain, so each wearable only needs to produce compatible kinematics rather than matching another device’s raw sensors.

Open-source training only

Causal TCN estimators are trained exclusively on public biomechanics datasets and applied without target-device training or fine-tuning to hip exo, knee exo, and IMU kinematics.

Multi-joint context helps

On the Awinda IMU suite, multi-joint (3-DoF) inputs cut mean RMSE by 17.2% versus single-joint models, with significant gains at hip, knee, and ankle.

Each wearable converts its sensors into joint kinematics; a shared estimator maps those kinematics to biological joint moments—trained once on open-source data, deployed across platforms.

Abstract

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 a 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.

Presentation video

A short walk-through of the unified kinematic representation and how it transfers across the hip exoskeleton, knee exoskeleton, and IMU sensor suite.

Video summary of the manuscript.

Framework at a glance

Overview of the kinematics-based device-agnostic joint moment estimation framework
Top: open-source biomechanics datasets are processed in OpenSim to yield reference kinematics and dynamics for training.
Bottom: for each deployment setting we train a downstream estimator on the joint channels available at that platform—hip only, knee only, or multi-joint hip/knee/ankle—and apply it directly with no device-specific fine-tuning. Exoskeleton inputs come from onboard encoders and IMUs; the IMU suite inputs come from body-mounted IMU sensor fusion.

Wearable platforms and embedded control

Hip exoskeleton, knee exoskeleton, embedded co-processor architecture, and Xsens Awinda IMU placement
(a) Bilateral robotic hip exoskeleton: onboard computing unit, battery, pelvis IMU, bilateral hip actuators, and thigh IMUs. (b) Robotic knee exoskeleton (one side used in this study): onboard computing unit, battery, thigh IMU, knee actuator, and shank IMU. Both exoskeletons use brushless DC actuators with integrated motor encoders and an embedded Jetson Orin Nano. (c) Embedded co-processor architecture on the exoskeletons: an I/O process reads the IMUs over I2C and the actuators over CAN, passes the data to a separate inference process through an input queue, and sends the estimator's output back to the actuators as CAN commands through an output queue. (d) Xsens MTw Awinda IMU suite with seven sensors on the pelvis and both thighs, shanks, and feet.

Exoskeleton deployment: hip exoskeleton

Hip exoskeleton predicted and reference hip joint moments
Predicted and OpenSim reference hip joint moments across level-ground speeds and ramp ascent (shaded: ±1 SD).

Exoskeleton deployment: knee exoskeleton

Knee exoskeleton predicted and reference knee joint moments
Predicted and OpenSim reference knee joint moments during ramp ascent and descent (shaded: ±1 SD). Performance was generally lower during ramp descent, where the greater variability in the ground-truth profiles also indicates more variable gait across participants.

IMU sensor suite: joint moments

IMU-predicted and reference hip, knee, and ankle joint moments across gait conditions
Predicted and OpenSim reference hip, knee, and ankle joint moments across level-ground and ramp walking (shaded: ±1 SD). Same open-source-trained multi-joint model; no target-device fine-tuning.

Benefit of multi-joint kinematic context

Multi-joint versus single-joint performance comparison
Multi-joint (3-DoF) inputs improve both RMSE and R² relative to single-joint (1-DoF) models across the hip, knee, and ankle, with the strongest gains in the IMU deployment setting.

Main results

0.79 hip exo mean R² (RMSE 0.17 Nm/kg)
0.62 knee exo mean R² (RMSE 0.19 Nm/kg)
0.85 IMU multi-joint mean R² (RMSE 0.15 Nm/kg)
17% lower RMSE vs. single-joint IMU inputs

Citation

BibTeX

@misc{hwang2026unifiedkinematicrepresentationenables,
  title={A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation},
  author={Jinwoo Hwang and Ilseung Park and Changseob Song and Vu Phan and Eni Halilaj and Inseung Kang},
  year={2026},
  eprint={2610.09150},
  archivePrefix={arXiv},
  primaryClass={cs.RO},
  url={https://arxiv.org/abs/2610.09150}
}