A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation

Jinwoo Hwang; Ilseung Park; Changseob Song; Vu Phan; Eni Halilaj; Inseung Kang

cs.ROOct 6, 2026

A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation

Authors: Jinwoo Hwang, Ilseung Park, Changseob Song, Vu Phan, Eni Halilaj, Inseung Kang

Organizations: Carnegie Mellon University, Pittsburgh, PA, USA

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 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.

Figures & tables

Fig. 1: Overview of the proposed kinematics-based framework for reusable biological joint moment estimation across wearable systems. (a) Open-source biomechanics datasets are aggregated and processed using OpenSim inverse kinematics and inverse dynamics to obtain reference lower-body kinematics and joint moments for model training. The resulting models are then applied to wearable-derived kinematics from (b) a hip exoskeleton, using hip angle and angular velocity ( $\theta_{Hip}$ , $\omega_{Hip}$ ) to estimate the hip moment ( $T_{Hip}$ ); (c) a knee exoskeleton, using knee angle and angular velocity ( $\theta_{Knee}$ , $\omega_{Knee}$ ) to estimate the knee moment ( $T_{Knee}$ ); and (d) an inertial measurement unit (IMU) sensor suite, using multi-joint lower-body angles and angular velocities to simultaneously estimate hip, knee, and ankle moments ( $T_{Hip}$ , $T_{Knee}$ , and $T_{Ankle}$ ).

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.

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.

Fig. 4: Comparison of multi-joint and single-joint kinematic inputs for biological joint moment estimation using the IMU sensor suite. (a) Mass-normalized RMSE and (b) $R^{2}$ for hip, knee, and ankle moment estimates. The multi-joint model used hip, knee, and ankle angles and angular velocities as inputs, whereas each single-joint model used only the angle and angular velocity of the target joint. Multi-joint inputs resulted in lower RMSE and higher $R^{2}$ across all three joints. Asterisks indicate significant paired differences between input configurations ( $**p<0.01$ , $***p<0.001$ ).

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Fig. S1: Overview of the wearable systems and embedded computing architecture used in this study. (a) Bilateral robotic hip exoskeleton, including the onboard computing unit, battery, pelvis IMU, bilateral hip actuators, and thigh IMUs. (b) Robotic knee exoskeleton configuration used during data collection, including the onboard computing unit, battery, thigh IMU, knee actuator, and shank IMU. (c) Embedded co-processor architecture. Separate inference and input/output processes exchange data through input and output queues. IMU measurements are received through I 2 C, and actuator commands are transmitted through CAN. (d) Placement of the sternum, pelvis, bilateral thigh, bilateral shank, and bilateral foot IMUs in the Xsens Awinda sensor suite.

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Mar 12, 2026, cs.ROJ/K move · Enter open · S save

Human Motion Data Alone Does Not Guarantee Plausible Gait Biomechanics

Xinyi Liu, Jangwhan Ahn, Edgar Lobaton, Jennie Si+1

Department of Biomedical Engineering, University of North Carolina-Chapel Hill, Chapel Hill, NC, USA · Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC, USA · School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, USA

Gait Dynamics Motion Imitation Human Motion Latent Motion Imitation Learning Motion

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Motion imitation learning (IL) is increasingly used in robotics and human gait modeling, yet its ability to recover biomechanically consistent joint moments without explicit kinetic information remains unclear. In this study, we examined whether motion imitation alone can estimate reasonable biological joint moments. We compare motion-only IL (MOIL) against a kinetics-aware IL (KAIL) framework that incorporates ground reaction forces (GRF) and center of pressure (CoP) in imitation rewards, with an ablation study to examine the contribution of each kinetic term. Experiments were conducted using walking data from a non-disabled participant at three speeds (0.9, 1.2, and 1.5 m/s). While both MOIL and KAIL achieved comparable kinematic tracking accuracy, MOIL exhibited substantially larger errors in GRF, CoP, and joint moment estimates relative to inverse dynamics references. In contrast, KAIL produced kinetics more consistent with biomechanical values. These findings highlight a fundamental limitation of MOIL approaches, which may lead to erroneous interpretations of gait biomechanics and downstream applications by failing to estimate consistent human-like gait kinetics.

Abstract

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