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ExoLaN: Physics-Consistent Context-Aware Dynamics Learning for Exoskeletons

Lucas Schulze, Maximilian Schwarz, Jona Hoppe, Jan Peters, Oleg Arenz

arXiv:2609.31434v1cs.ROcs.SYeess.SY

TL;DR

Exoskeleton assistance based on human intention could be more flexible than control tied to predefined tasks, but existing approaches do not adapt to user-dependent dynamics or intermittent contact. ExoLaN learns coupled human-exoskeleton dynamics using temporal context and insole contact measurements. It improves torque estimation on unseen tasks and its learned context contains task information.

  • Problem

    Existing approaches do not adapt to user-dependent human-exoskeleton dynamics or account for intermittent contact during locomotion, limiting task-agnostic torque estimation.

    Source: §I · p. 1

  • Method

    ExoLaN uses a TCN-based context encoder and Learned Insole Mapping to learn full coupled human-exoskeleton dynamics from temporal context and partial contact-force measurements.

    Source: §I · p. 2, A. Contributions · p. 2, D. Learned Insole Mapping (LIM) · p. 4

  • Results

    On unseen tasks, ExoLaN reduces torque-estimation MSE by 7% versus MLP-TCN and 9% versus TCN.

    Source: B. Human Intention Estimation · p. 5

  • Takeaways & Limitations

    The learned latent representation contains task-related information that is proposed as a signal for task-adaptive assistive control.

    Source: §I · p. 2

Abstract

from arXiv · show

Task-agnostic assistive exoskeleton control based on human intention offers greater flexibility than conventional approaches that rely on predefined tasks or motion patterns. Human joint torque estimation enables task-agnostic assistance by characterizing user actions. Physics-consistent methods such as Deep Lagrangian Networks (DeLaN) have been applied to estimate the human torques in multi-user settings, but existing approaches cannot adapt to a specific user without retraining, and do not account for intermittent contacts during locomotion. We propose ExoLaN, a Context-Aware DeLaN for human-exoskeleton interaction that learns the full coupled system dynamics while adapting to changes in interaction context. ExoLaN combines temporal context with partial contact-force measurements from force-sensitive insoles to infer latent dynamics embeddings and estimate generalized contact torques. On seven unseen users performing 21 unseen tasks, ExoLaN reduces torque estimation MSE by 7% compared to a black-box baseline. Beyond inverse dynamics, ExoLaN serves as a unified model that also enables accurate forward prediction: training with a multi-step prediction loss reduces acceleration MSE by 59% and long-horizon position and velocity errors by 60% and 93%, respectively, compared with a single-step loss. Moreover, the learned latent context captures task information without explicit task labels, making it a promising signal for task-aware assistive control.

I. INTRODUCTION

Task-agnostic assistance can use estimated human torques, but existing approaches face challenges with user-dependent dynamics, intermittent contact, and generalization beyond training. ExoLaN learns coupled human-exoskeleton dynamics with context and contact information, and reports improved torque estimation on unseen tasks.

I. INTRODUCTION

  • Task-agnostic assistance can estimate human intended torques, whereas conventional control relies on predefined tasks, task-specific modules, switching, and user-specific tuning,.Torque estimation characterizes user actions and can guide assistance toward the intended action.Source: §I · p. 1
  • Rigid-body models require assumptions about geometry, inertial parameters, coordinates, and sensors, while black-box models may generalize poorly to unseen users and tasks and offer limited physical interpretability.Human muscular actuation and compliance make accurate coupled-system modeling challenging and can require user-specific calibration.Source: §I · p. 1
  • ExoLaN learns full coupled human-exoskeleton dynamics and maps partial contact-force measurements to generalized contact torques, adapting across users and task conditions.Unlike Context-Aware DeLaN, which uses a nominal robot model to learn residual dynamics, ExoLaN models the full system.Source: §I · p. 2

A. Contributions

ExoLaN combines temporal context, partial contact-force mapping, and one DeLaN model for inverse and forward dynamics. The paper considers a 2-DoF lower-limb exoskeleton with sensing and actuation at the hip and knee.

A. Contributions

  • ExoLaN uses a TCN to capture temporal context and estimate human joint torques across users and tasks.A Learned Insole Mapping (LIM) maps partial contact-force measurements to generalized contact torques.Source: A. Contributions · p. 2
  • A single trained DeLaN supports both inverse and forward dynamics, while multi-step prediction loss improves long-horizon prediction.The learned latent representation also contains task-related information that may serve as a signal for task-adaptive assistive control.Source: A. Contributions · p. 2

II. LOWER-LIMB EXOSKELETON

  • The considered 2-DoF lower-limb exoskeleton has hip and knee encoders, six IMUs, wireless force-sensitive insoles, and four actuators providing up to 15 Nm per joint.The semi-rigid exoskeleton supports cyclic and non-cyclic motor tasks.Source: §II · p. 2, Figure 2 · p. 2

A. Dynamical model

The paper models each leg of the physically coupled human-exoskeleton as a mechanical system with hip and knee coordinates. Its dynamics include human, exoskeleton, and intermittent-contact torques.

A. Dynamical model

  • Each leg is modeled independently using hip and knee positions as generalized coordinates; a whole-body model is omitted because it would require additional sensing of pelvis pose and motion.The human and exoskeleton are treated as one mechanically coupled system.Source: A. Dynamical model · p. 3
  • The coupled system's Lagrangian is formed from kinetic and potential energy, and its equations of motion are obtained using the Euler-Lagrange equation.The inertia matrix and generalized forces describe the system dynamics.Source: A. Dynamical model · p. 3
  • Generalized forces are decomposed into human torques, exoskeleton torques, and contact torques arising from intermittent ground contact.The equation of motion also includes Coriolis and centrifugal forces and gravity.Source: A. Dynamical model · p. 3

III. CONTEXT-AWARE DELAN FOR EXOSKELETON

  • ExoLaN extends Context-Aware DeLaN to learn the full coupled human-exoskeleton dynamics under intermittent contact.Source: §III · p. 3

A. Deep Lagrangian Networks

DeLaN learns inertia and potential-energy functions within a Lagrangian model, yielding inverse and forward dynamics. Context-Aware DeLaN conditions one model on an inferred latent context to represent varying systems.

A. Deep Lagrangian Networks

  • DeLaN estimates the inertia matrix and potential energy with neural networks, then uses automatic differentiation and the Euler-Lagrange equation to obtain equations of motion and both inverse and forward dynamics.Its inertia matrix is parameterized through a Cholesky factor to guarantee positive definiteness.Source: A. Deep Lagrangian Networks · p. 3

B. Context-Aware DeLaN

  • A single DeLaN represents one mechanical system, while a latent variable z can parameterize a family of dynamics when held constant over a time horizon.This representation incorporates z into the Lagrangian without changing the Euler-Lagrange formulation.Source: B. Context-Aware DeLaN · p. 3
  • Context-Aware DeLaN conditions its dynamics on latent context inferred by an LSTM from historical states and residual torques from a nominal model, enabling one model to represent multiple systems.The approach is integrated with MPC for adaptive robot manipulation.Source: B. Context-Aware DeLaN · p. 3
  • The paper compares a TCN as a context encoder with recurrent networks such as LSTM.Source: B. Context-Aware DeLaN · p. 3

C. Learning Full Dynamics

ExoLaN learns the full human-exoskeleton dynamics using insole measurements to infer latent context. Its Learned Insole Mapping (LIM) maps partial contact measurements to contact torques conditioned on the joint configuration and context.

C. Learning Full Dynamics

  • Without joint torque sensors or nominal models, the approach uses vertical ground-reaction force and two-dimensional center of pressure to inform contact state, human inertia, and a latent representation.The measurements come from pressure insoles.Source: C. Learning Full Dynamics · p. 3

D. Learned Insole Mapping (LIM)

  • For a single contact, contact torque is expressed using the contact Jacobian and contact force.The passage defines the Jacobian as the contact Jacobian and the force as the contact force.Source: D. Learned Insole Mapping (LIM) · p. 3
  • LIM learns to map measured vertical ground-reaction force to contact torque, conditioned on joint configuration and context.The force is only a partial observation of contact force; force-plate measurements are described as restricting measurement to laboratory environments.Source: D. Learned Insole Mapping (LIM) · pp. 3–4
  • The learnable LIM parameters are optimized jointly with the other model parameters.Source: D. Learned Insole Mapping (LIM) · p. 4

IV. EXPERIMENTS

The experiments evaluate ExoLaN for human intention and trajectory estimation and task identification using a multi-user, multi-task exoskeleton dataset. The evaluation holds out users and tasks to test performance on trained and excluded activities.

IV. EXPERIMENTS

  • The experiments assess human intention estimation, human trajectory estimation, and task information in the learned latent representation.Source: §IV · p. 4

A. Dataset and Training Procedure

  • The dataset contains 21 users performing 28 tasks at 200 Hz, with OpenSim-derived human joint torques used as training and evaluation targets.Tasks are categorized as cyclic, impedance-like, or unstructured movements.Source: A. Dataset and Training Procedure · p. 4
  • Training uses 14 users and seven selected tasks; the remaining seven users are held out, and evaluation includes both those tasks and the other 21 activities.The selected tasks were reported to provide approximately 95% of the performance obtained using all 28 tasks.Source: A. Dataset and Training Procedure · p. 4
  • The same user and task splits are used across intention estimation, forward prediction, and task identification.Source: A. Dataset and Training Procedure · p. 4
  • Data from both legs are combined to train a single model, with latent context z encoding task-, user-, and leg-specific information.Source: A. Dataset and Training Procedure · p. 4

B. Human Intention Estimation

ExoLaN combines a physics-based DeLaN with temporal context and LIM for human intention estimation. Its advantage is most pronounced on unseen tasks, while results also vary with task type and context encoder.

B. Human Intention Estimation

  • Across the seven trained tasks, adding LIM consistently improves torque estimation, and ExoLaN variants outperform corresponding MLP baselines.Source: Figure 3 · p. 4, B. Human Intention Estimation · p. 4
  • On 21 unseen tasks, ExoLaN reduces torque-estimation MSE by 7% versus MLP-TCN and 9% versus TCN.Source: Figure 4 · p. 5, B. Human Intention Estimation · p. 5
  • On trained tasks, ExoLaN with DeLaN-TCN achieves the lowest MSE, improving by 2% versus TCN with LIM and 4% versus MLP-TCN with LIM.Context conditioning improves both DeLaN and MLP performance, and TCN variants generally outperform LSTM counterparts.Source: B. Human Intention Estimation · pp. 4–5
  • For cyclic tasks, TCN reaches 464 N2m2 MSE and ExoLaN DeLaN-TCN reaches 468 N2m2; for non-cyclic tasks, ExoLaN reaches 411 N2m2 versus TCN at 450 N2m2.The passage attributes additional information in non-cyclic tasks to learned dynamical structure beyond temporal history alone.Source: B. Human Intention Estimation · p. 5
  • Torque trajectories show more accurate amplitude estimates from ExoLaN, particularly for knee torque in unseen tasks, while hip torque estimates remain reasonable.Only calisthenics among the four illustrated tasks was included in training.Source: B. Human Intention Estimation · p. 5

C. Human Trajectory Estimation

ExoLaN is trained for forward prediction using forward-dynamics and multi-step losses in addition to inverse dynamics. Multi-step training improves acceleration estimates and long-horizon rollouts, while forward-dynamics training trades a small increase in torque error for better prediction.

C. Human Trajectory Estimation

  • The objective combines inverse- and forward-dynamics losses with multi-step position and velocity losses, using autoregressive state predictions integrated by semi-implicit Euler.The rollout horizon is H = 4, with Ns = 256 randomly sampled starting points per update.Source: C. Human Trajectory Estimation · p. 5
  • Inverse-dynamics-only training gives the lowest torque MSE but poor forward prediction, partly because torque and acceleration targets are not guaranteed to be physically consistent.The passage also notes that torque-only training does not explicitly constrain the learned inertia matrix to be well-conditioned for forward dynamics.Source: C. Human Trajectory Estimation · p. 5
  • Adding forward-dynamics loss reduces acceleration MSE by more than six orders of magnitude and improves rollouts, with a 9% increase in torque MSE.Source: C. Human Trajectory Estimation · p. 6
  • Multi-step training reduces acceleration MSE by approximately 59%; versus wfd-only, it cuts velocity MSE by 57%, 63%, and 93% at steps 4, 10, and 20, and position MSE by 60% at step 20.The multi-step training horizon is four steps, while the latter two comparisons are at longer horizons.Source: C. Human Trajectory Estimation · p. 6
  • For the Run task, adding the multi-step loss keeps predicted trajectories close to ground truth for approximately 60 ms, versus divergence after approximately 30 ms with forward-dynamics loss alone.Source: C. Human Trajectory Estimation · p. 6

D. Task Identification

The learned latent representations contain task information, with ExoLaN achieving the highest reported classification accuracy. The analysis uses classifiers trained on representations from the seven training tasks.

  • The task-classification analysis trains a separate three-hidden-layer MLP classifier on each model’s inferred representations, using an 80/20 train-test split.The classifiers identify the seven training tasks, with class weighting to address task imbalance.Source: D. Task Identification · p. 6
  • ExoLaN’s latent representation reached 67.3% test accuracy, versus 64.2% for MLP-TCN and 31.0% for the majority-class baseline.The majority-class baseline corresponds to jumping in place.Source: D. Task Identification · pp. 6–7
  • The authors suggest that the higher ExoLaN accuracy may reflect more task-discriminative representations and support using latent context as a signal for task-adaptive assistance.Source: D. Task Identification · pp. 6–7

V. CONCLUSIONS

ExoLaN is presented as a model for human-exoskeleton dynamics evaluated for torque estimation and forward prediction. The authors report improved generalization across users and tasks and propose future extensions to assistive control and learning.

V. CONCLUSIONS

  • ExoLaN showed improved generalization across users and tasks for inverse dynamics, while highlighting the benefits of physical structure and learned insole mapping.Evaluation included seven unseen users and both training-seen and previously unseen tasks.Source: §V · p. 7
  • The learned dynamics can be used for forward prediction, providing one model for both inverse and forward dynamics.The Run-task joint-state rollouts recursively integrate estimated accelerations from an initial state without further measurement correction.Source: §V · p. 7, Figure 7 · p. 7
  • Future work will integrate ExoLaN with computed-torque assistive control and investigate whole-body formulations and physics-based simulation for imitation and reinforcement learning.Source: §V · p. 7

APPENDIX

The appendix reports training hyperparameters for human intention and trajectory estimation, as well as task classification from inferred latent representations.

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