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A Unified Kinematic Representation Enables Reusable Biological Joint Moment Estimation

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

arXiv:2610.09150v1cs.RO

TL;DR

Device-specific sensor inputs limit reuse of joint-moment estimators and open-source biomechanics data across wearable platforms. The paper uses joint kinematics as a common interface, demonstrating deployment of open-source-trained estimators across a hip exoskeleton, knee exoskeleton, and IMU suite without target-device training. Knee-estimation performance was comparatively lower than hip-estimation performance.

  • Problem

    Estimators based on device-specific signals are difficult to transfer across sensing configurations, limiting reuse of open-source biomechanics data across wearable systems.

    Source: §I · p. 1

  • Method

    The study trains causal temporal convolutional estimators exclusively on open-source kinematics and inverse-dynamics moments, then applies joint-angle and angular-velocity inputs from wearable platforms without target-device fine-tuning.

    Source: §I · p. 2

  • Results

    Estimators trained entirely on open-source data were deployed across multiple wearable platforms without target-device training, while multi-joint inputs reduced mean RMSE from 0.177 to 0.147 N m/kg, a 17.2% reduction.

    Source: D. Study Impact and Limitations · p. 7, C. Benefits of Multi-Joint Kinematic… · p. 7, §V · p. 7

  • Takeaways & Limitations

    Separating device-specific kinematic reconstruction from downstream moment estimation makes cross-platform reuse depend primarily on sufficiently accurate, consistently defined joint kinematics.

    Source: §IV · p. 5, A. Joint Kinematics as a Common… · p. 6

    Eliminating target-domain adaptation did not ensure equivalent performance across joints and conditions, as knee-estimation R2 values were lower.

    Source: D. Study Impact and Limitations · p. 7

Abstract

from arXiv · show

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.

I. INTRODUCTION

Adaptive exoskeleton control benefits from continuous estimates of biomechanical state, but estimators based on device-specific signals are difficult to transfer and limit reuse of open-source biomechanics data. This study uses joint kinematics as a common representation for models trained on open-source data and applied across wearable platforms without target-device training or adaptation.

I. INTRODUCTION

  • Joint moments provide a continuous, mechanically interpretable measure of locomotor demand, complementing discrete gait-phase or terrain labels.Controllers use biomechanical-state estimates to adjust assistance as users, speeds, terrains, and tasks vary.Source: §I · p. 1
  • Device-specific signals can yield accurate estimates when training and deployment use the same sensing configuration, but sensor differences limit transfer across systems.Differences in modality, placement, orientation, calibration, attachment, and preprocessing can alter the model’s input distribution.Source: §I · p. 1
  • Hardware-specific inputs also prevent open-source biomechanics data from serving as a generalized input source across wearable systems.Those datasets provide lower-limb kinematics, ground-reaction forces, and inverse-dynamics moments, but their wearable signals reflect original sensing configurations.Source: §I · p. 1
  • The study trains estimators on open-source kinematics and inverse-dynamics moments, then applies them without target-device fine-tuning across hip, knee, and IMU platforms.Joint angles and angular velocities form the common representation; the study also evaluates single- and multi-joint estimation and adjacent-joint context.Source: §I · p. 2

II. METHODS

The methods assemble and standardize open-source walking biomechanics data, then train causal temporal convolutional estimators on joint kinematics to predict mass-normalized joint moments.

A. Open-Source Data for Model Training

  • The curated training resource combines walking data from 56 participants, with 51 assigned to training, 2 to validation, and 3 to testing; squatting and stair-negotiation trials were excluded.The training partition contained approximately 15.2 hours of walking data, and the full participant pool contained approximately 20.6 hours.Source: A. Open-Source Data for Model Training · p. 2
  • Before training, limb data were mapped to consistent joint definitions and conventions; kinematics were downsampled to 100 Hz and joint moments normalized by body mass.Angular velocities were derived from filtered angle trajectories, and models used physical-unit inputs and directly predicted Nm/kg moments without input or output normalization.Source: A. Open-Source Data for Model Training · p. 2
  • Condition-based oversampling balanced level-ground, ramp-ascent, and ramp-descent exposure despite their unequal shares of valid training windows.The raw training windows were 84.3%, 10.7%, and 5.0% from those conditions, respectively; no dataset-level ablation evaluated individual source contributions.Source: A. Open-Source Data for Model Training · p. 2

B. Biological Joint-Moment Estimator

  • Causal temporal convolutional networks used a one-second input window to estimate moments from either single-joint or combined hip, knee, and ankle kinematics.The network used five convolutional blocks with 80 hidden channels, kernel size five, and dilation factors 1, 2, 4, 8, and 16.Source: B. Biological Joint-Moment Estimator · pp. 2–3, Figure 1 · p. 3

C. Wearable Sensing and Exoskeleton Platforms

The hip exoskeleton supplies hip kinematics to a shared estimator, and its predicted biological hip moment is used in the per-leg output-torque command.

C. Wearable Sensing and Exoskeleton Platforms

  • The bilateral 4.3 kg hip exoskeleton supplies hip angle and angular velocity from motor encoders and relative pelvis–thigh movement to the shared single-joint estimator.The device was developed for sagittal-plane assistance and included brushless actuators and onboard computing.Source: 1) Robotic Hip Exoskeleton · p. 3
  • Each leg’s commanded output torque uses the predicted biological hip moment, participant body mass, a 0.12 scaling factor, filtering, and a 15 Nm torque limit.The command includes a 120 ms delay, selected based on prior hip assistance work using delays of approximately 100–150 ms.Source: 1) Robotic Hip Exoskeleton · p. 3
  • The hip command delay was chosen to better align assistive torque with hip angular velocity and increase positive mechanical work delivered by the exoskeleton.The cited prior work used delays of approximately 100–150 ms.Source: 1) Robotic Hip Exoskeleton · p. 3

2) Robotic Knee Exoskeleton:

The methods pair a right-leg knee exoskeleton and a bilateral IMU suite with an eight-person participant protocol spanning level and inclined walking conditions.

2) Robotic Knee Exoskeleton:

  • The unilateral right-leg knee exoskeleton measures knee angle with a motor encoder and estimates angular velocity from thigh- and shank-mounted IMUs.Its knee scaling factor was 0.09, with no additional command delay; higher torque behavior was outside the study’s scope.Source: 2) Robotic Knee Exoskeleton · p. 3

3) IMU Sensor Suite:

  • The wireless IMU suite provides bilateral multi-joint kinematics from sensors on the pelvis, thighs, shanks, and feet, using calibrated relative segment orientations.Sensor orientations were estimated by fusing accelerometer, gyroscope, and magnetometer measurements; joint kinematics were calculated between consecutive segments.Source: 3) IMU Sensor Suite · pp. 3–4

D. Participants

  • Eight healthy adults participated, with eligibility exclusions for conditions that could affect walking or safe protocol completion.Participants completed the hip-exoskeleton, knee-exoskeleton, and IMU protocols in one experimental day.Source: D. Participants · p. 4

E. Experimental Protocol

  • The force-instrumented treadmill protocol included level walking at 0.8, 1.2, and 1.6 m/s and ramp ascent and descent at 0.8 m/s.Hip-exoskeleton trials covered level walking and ascent, knee-exoskeleton trials covered ascent and descent, and the IMU suite covered all conditions; analyzed trial counts were 31, 16, and 39, respectively.Source: E. Experimental Protocol · p. 4

F. Reference Biomechanics and Moment Estimation

Reference biological joint moments were derived from optical motion capture and inverse dynamics, and the estimator was evaluated against them using mass-normalized RMSE and R2. With hip-exoskeleton kinematics, it tracked hip moments across level-ground speeds and ramp ascent.

F. Reference Biomechanics and Moment Estimation

  • Reference joint kinematics came from optical motion capture and constrained inverse kinematics; inverse dynamics produced net sagittal-plane moments, with exoskeleton motor torque subtracted for assisted trials.The resulting biological moments were normalized by participant body mass.Source: F. Reference Biomechanics and Moment… · p. 4

G. Model Evaluation

  • Model performance was evaluated using mass-normalized root mean square error (RMSE) and coefficient of determination (R2) between predicted and reference moments.The hip analysis included 31 trials, with one level-ground trial at 1.6 m/s excluded due to failed inverse dynamics from poor marker data. All 16 collected knee trials were included; the IMU analysis included 39 trials, with one level-ground trial at 0.8 m/s excluded for the same reason.Source: G. Model Evaluation · p. 4
  • The IMU multi-joint comparison used 78 paired observations per joint and Holm–Bonferroni correction across six joint-level tests.One-sided paired t-tests evaluated whether the single-joint model had higher RMSE and lower R2 than the multi-joint model.Source: G. Model Evaluation · p. 4

A. Hip Exoskeleton Moment Estimation

  • 0.12 ± 0.04 to 0.25 ± 0.08 Nm/kg was the mean RMSE across four hip-exoskeleton conditions, while mean R2 ranged from 0.76 ± 0.10 to 0.84 ± 0.09.RMSE increased from 0.12±0.04 Nm/kg at 0.8 m/s to 0.25±0.08 Nm/kg at 1.6 m/s; ramp ascent had the highest R2, 0.84 ± 0.09.Source: A. Hip Exoskeleton Moment Estimation · p. 4

B. Knee Exoskeleton Moment Estimation

The knee-exoskeleton estimator predicted moments during ramp ascent and descent, while the IMU suite extended estimation to hip, knee, and ankle moments across walking conditions. The discussion frames cross-device transfer as a shared-kinematics representation problem.

B. Knee Exoskeleton Moment Estimation

  • 0.22 ± 0.03 versus 0.17 ± 0.03 Nm/kg was mean knee RMSE during ramp descent versus ascent, and mean R2 was 0.58 ± 0.14 versus 0.65 ± 0.14.The estimates used knee angle from a motor encoder and angular velocity derived from thigh and shank IMUs.Source: B. Knee Exoskeleton Moment Estimation · p. 4, Figure 2 · p. 5

C. Multi-Joint Moment Estimation Using IMU Sensor Suite Kinematics

IV. DISCUSSION

  • The discussion treats cross-device estimator transfer as a representation problem: a common kinematic interface separates device-specific motion reconstruction from downstream moment estimation.This decomposition allows the downstream estimator to remain unchanged as the sensing platform changes.Source: §IV · p. 5

A. Joint Kinematics as a Common Representation Across Wearable Platforms

The framework routes each platform’s signals through a front end that supplies joint angles and angular velocities to a shared moment estimator. It also compares multi-joint and single-joint inputs and discusses condition-averaged R2 as a proxy for control across walking contexts.

A. Joint Kinematics as a Common Representation Across Wearable Platforms

  • Each platform supplies joint angles and angular velocities to the downstream estimator, using encoder and segment-IMU inputs for the exoskeletons or inertial motion capture for the IMU suite.This let distinct sensing configurations interface with a model trained on open-source biomechanics data.Source: A. Joint Kinematics as a Common… · pp. 5–6
  • Raw-signal models can learn device-specific properties that limit reuse, whereas the proposed framework places those properties in the device-specific front end.Transfer depends primarily on whether the new platform can provide sufficiently accurate and consistently defined joint kinematics.Source: A. Joint Kinematics as a Common… · pp. 5–6
  • Multi-joint inputs resulted in lower RMSE and higher R2 than single-joint inputs for hip, knee, and ankle moment estimates.The multi-joint model used hip, knee, and ankle angles and angular velocities; each single-joint model used only the target joint’s angle and angular velocity.Source: Figure 4 · p. 6
  • Condition-averaged R2 indicates how consistently moment estimates preserve temporal variation across walking contexts, but does not replace evaluation during unconstrained daily activity.It is described as a practical proxy for supporting control across varied locomotor conditions.Source: A. Joint Kinematics as a Common… · p. 6

B. Comparison with Existing Estimation and Domain-Adaptation Approaches

Multi-joint kinematics improved joint-moment estimates, while comparisons with prior work and broader transfer claims remain qualified by differences in evaluation settings and the study’s hardware, assistance, kinematic, and task boundaries.

B. Comparison with Existing Estimation and Domain-Adaptation Approaches

  • No evaluated target-device recordings were used for training, adaptation, fine-tuning, or checkpoint selection, but prior-study comparisons require caution because evaluation settings and metric aggregation differed.Hip-exoskeleton RMSE ranged from 0.12 to 0.25 Nm/kg, compared with 0.15 and 0.13 Nm/kg reported for hip and knee by Molinaro et al. using labeled target-exoskeleton data.Source: B. Comparison with Existing Estimation… · pp. 6–7

C. Benefits of Multi-Joint Kinematic Context

  • 17.2%: multi-joint inputs reduced mean RMSE from 0.177 to 0.147 Nm/kg versus single-joint models, with significantly lower RMSE and higher R2 at all three joints.The multi-joint model uses adjacent-joint kinematics, which provide information about limb configuration and gait progression unavailable from single-joint trajectories alone.Source: C. Benefits of Multi-Joint Kinematic… · p. 7

D. Study Impact and Limitations

  • Lower knee R2 values indicate that eliminating target-domain adaptation does not ensure equivalent performance across all joints and conditions.Hip-estimation performance remained within the range of prior device-specific and domain-adapted approaches.Source: D. Study Impact and Limitations · p. 7
  • Both exoskeletons used quasi-direct-drive actuation and were developed within one laboratory, so broader hardware generalizability requires validation on commercial systems and independently developed devices.The devices share aspects of mechanical design, interfaces, control architecture, and signal processing despite differing in actuated joint and sensing configuration.Source: D. Study Impact and Limitations · p. 7
  • Assistance torques generally peaked at 5–7 Nm, below the devices’ approximate 18 Nm capacity; higher assistance may increase biomechanical changes, interface deformation, and sensor vibration.Source: D. Study Impact and Limitations · p. 7
  • Training/reference kinematics used constrained OpenSim inverse kinematics, whereas IMU evaluation used unconstrained reconstruction with coordinate systems not explicitly aligned; estimates may reflect errors and pipeline differences.The model maintained strong estimation performance despite these sources of mismatch.Source: D. Study Impact and Limitations · p. 7
  • Evaluation covered periodic level-ground, ramp-ascent, and ramp-descent walking; performance should not be assumed to generalize to stairs, transitions, turning, obstacle negotiation, or nonlocomotor activities.The authors suggest that broader training behaviors and complementary measurements such as pressure insoles may broaden the supported task range.Source: D. Study Impact and Limitations · p. 7

V. CONCLUSION

Joint kinematics provided a common intermediate representation for estimating biological joint moments across three wearable platforms without target-device training or fine-tuning. The study’s participant cohort comprised eight healthy adults.

V. CONCLUSION

  • Joint kinematics supported biological joint-moment estimation across a hip exoskeleton, knee exoskeleton, and IMU sensor suite, with open-source-trained estimators applied without target-device training or fine-tuning.Hip performance was within the range of prior device-specific and domain-adapted estimators, while knee performance was comparatively lower; multi-joint inputs improved estimation when more sensing was available.Source: §V · p. 7

PARTICIPANT DEMOGRAPHICS

  • Eight healthy participants were recruited; mean age was 26.3 ± 2.3 years (range 24–30), mean height 1.74 ± 0.06 m, and mean body mass 72.3 ± 13.3 kg.Table S1 provides participant-level physical characteristics.Source: PARTICIPANT DEMOGRAPHICS · p. 9, Table S1 · p. 9

A. Mechatronic and Physical Architecture

The study’s hip and knee exoskeletons use embedded computing and encoder-based actuation, with distinct frames and attachment configurations.

A. Mechatronic and Physical Architecture

  • The bilateral hip exoskeleton uses two brushless DC actuators with integrated motor encoders, an onboard 22.2-V battery, and an embedded Jetson Orin Nano with a custom PCB.The PCB manages sensor feedback and motor commands; the structural frame includes a nylon-based user interface and flexible carbon-fiber joint.Source: A. Mechatronic and Physical Architecture · p. 9
  • The hip system weighs 4.3 kg and fits users through four adjustable attachment locations: a pelvis band, two thigh orthotic shells, and an electronics backpack.Source: A. Mechatronic and Physical Architecture · p. 9
  • The knee exoskeleton used one side during experiments and combines brushless DC actuators, integrated encoders, an onboard 22.2-V battery, and embedded Jetson Orin Nano computing.Its printed frame weighs 2.2 kg, with a waist belt/electronics assembly and unilateral knee attachment.Source: A. Mechatronic and Physical Architecture · p. 9

WEARABLE KINEMATICS SYSTEM

The wearable kinematics setup combines inertial motion capture with device-mounted sensors and embedded computing across the study’s wearable platforms.

A. IMU Sensor Configuration

  • Fig. S1 depicts the hip and knee exoskeleton sensor configurations alongside the sternum, pelvis, thigh, shank, and foot IMU placements.Source: Figure S1 · p. 10
  • The embedded architecture separates inference and input/output processes using queues, receives IMU measurements through I2C, and transmits actuator commands through CAN.Source: Figure S1 · p. 10
  • Full-body inertial motion capture used seven IMUs secured to the pelvis, bilateral thighs, shanks, and feet.Source: A. IMU Sensor Configuration · pp. 9–10

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