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

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

cs.ROSep 25, 2026

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

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

Organizations: Department of Computer Science, Technical University of Darmstadt, Germany · Robotics Institute Germany (RIG) · German Research Center for AI (DFKI), Research Department: Systems AI for Robot Learning

Abstract

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.

Figures & tables

Fig. 1 : Overview of ExoLaN for human-exoskeleton dynamics modeling. Contextual DeLaN denotes the context-conditioned DeLaN proposed in [ 23 ] . The exoskeleton diagram is adapted from [ 18 ] .

Fig. 2 : Considered 2-DoF Lower-limb exoskeleton. Diagram adapted from [ 18 ] .

Fig. 3 : Torque estimation MSE on seven unseen users across the seven tasks seen during training, averaged over five random seeds, comparing models with and without LIM. DeLaN-TCN and DeLaN-LSTM, both with LIM, are two variants of ExoLaN.

Fig. 4 : Torque estimation MSE on seven unseen users across 21 tasks not seen during training, averaged across the evaluation samples and five random training seeds, comparing models with and without LIM. DeLaN-TCN and DeLaN-LSTM, both with LIM, are two variants of ExoLaN.

Panel of Figure 5 — Fig. 5 : Human intention estimation on unseen users across four tasks, using MLP-TCN and ExoLaN, both with LIM. The MSE values are reported as MLP-TCN vs. ExoLaN in $\text{N}^{2}\text{m}^{2}$ : calisthenics ( $1130$ vs. $\mathbf{1104}$ ), running ( $4680$ vs. $\mathbf{2875}$ ), squats ( $441$ vs. $\mathbf{146}$ ), and ball toss ( $605$ vs. $\mathbf{300}$ ). Only calisthenics was included in the training set.

Panel of Figure 6 — Fig. 6 : Human acceleration prediction for two tasks. MSE values are reported as MLP-TCN vs. ExoLaN in $\text{rad}^{2}\text{s}^{-4}$ : running ( $2841$ vs. $\mathbf{1394}$ ) and squats ( $194$ vs. $\mathbf{68}$ ).

Model	$\boldsymbol{\tau}$	$\ddot{\mathbf{q}}$	$\mathbf{q}_{4}$	$\dot{\mathbf{q}}_{4}$	$\mathbf{q}_{10}$	$\dot{\mathbf{q}}_{10}$	$\mathbf{q}_{20}$	$\dot{\mathbf{q}}_{20}$
Model	[ $\text{N}^{2}\text{m}^{2}$ ]	[ $\text{rad}^{2}\text{s}^{-4}$ ]	[ $\text{rad}^{2}$ ]	[ $\text{rad}^{2}\text{s}^{-2}$ ]	[ $\text{rad}^{2}$ ]	[ $\text{rad}^{2}\text{s}^{-2}$ ]	[ $\text{rad}^{2}$ ]	[ $\text{rad}^{2}\text{s}^{-2}$ ]
ExoLaN	434	4.97 $\mathrm{e}{8}$	2.78 $\mathrm{e}{\text{-}1}$	2352	16.6	3.68 $\mathrm{e}{4}$	459	2.55 $\mathrm{e}{5}$
ExoLaN ( $w_{\mathrm{fd}}$ )	475	337	1.41 $\mathrm{e}{\text{-}3}$	0.184	7.63 $\mathrm{e}{\text{-}3}$	2.42	0.0817	79.7
ExoLaN ( $w_{\mathrm{fd}}$ , $w_{\mathrm{ms}}$ )	507	139	1.38 $\mathbf{\boldsymbol{\mathrm{e}}\textbf{-}3}$	0.0787	6.62 $\mathbf{\boldsymbol{\mathrm{e}}\textbf{-}3}$	0.900	0.0329	5.79

TABLE I : Forward dynamics evaluation on seven unseen users across all 28 tasks for ExoLaN trained with inverse dynamics only, with single-step forward dynamics loss

w_{\mathrm{fd}}=0.01

; and

w_{\mathrm{fd}}=0.01

combined with multi-step loss

w_{\mathrm{ms}}=1

(

H=4

Panel of Figure 8 — Fig. 7 : Open-loop autoregressive prediction of human joint states in the Run task for ExoLaN with only $w_{\mathrm{fd}}$ and ExoLaN with both $w_{\mathrm{fd}}$ and $w_{\mathrm{ms}}$ . The predicted joint positions and velocities are obtained by recursively integrating the estimated accelerations from an initial state, without further correction from measurements.

Model	Majority Guess	Test Accuracy
ExoLaN	0.310	0.673 $\pm$ 0.023
MLP-TCN	0.310	0.642 $\pm$ 0.021

TABLE II : Task classification accuracy from the learned latent representations, averaged over five random seeds.

Parameter	Value	Parameter	Value
Activation	Tanh	TCN Kernel Size	2
Batch Size	8192	LSTM Hidden Layers	$16\times 5$
Learning Rate	$1\times 10^{-3}$	History Length	63
Weight Decay	$1\times 10^{-3}$	Context Dim. ( $\mathbf{z}$ )	16
TCN Hidden Layers	$16\times 5$	Training Samples	1.4M

TABLE III : Training hyperparameters for human intention and trajectory training.

Parameter	Value	Parameter	Value
Activation	ReLU	Epochs	1000
Batch Size	4096	Hidden Layers	$64\times 3$
Learning Rate	$1\times 10^{-3}$	Class Weighting	Inv. Train Freq.
Weight Decay	$1\times 10^{-4}$	Training Samples	1.1M

TABLE IV : Training hyperparameters for task classification using inferred latent representations.

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General Performance Guarantee for Human Torque Estimation-Based Task-Agnostic Assistive Exoskeleton Control
Sep 30, 2026Duy Hoang, Bastien Berret, Olivier Bruneau +1Robotic Control Hip Exoskeleton Control
Universit´e Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, 91190 Gif-sur-Yvette, France · Universit´e Paris-Saclay, Inria, CIAMS, 91190 Gif-sur-Yvette, France · Universit´e Paris-Saclay, ENS Paris-Saclay, LURPA, 91190 Gif-Sur-Yvette, France
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Sep 14, 2026Xiao-Yin Liu, Guotao Li, Weiqun Wang +1Data-Driven Control Ankle Exoskeleton Control
State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China. · The School of Artificial Intelligence, University of Chinese Academy Sciences, Beijing, China.

Jun 15, 2026J/K move · Enter open · S save

ExoTraj: A General Lower-limb Exoskeleton Assistance Policy for Complex Environments

Xiao-Yin Liu, Guotao Li, Long Sun, Xu Liang+1

The State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, China · The School of Artificial Intelligence, University of Chinese Academy of Sciences, China · The School of Automation and Intelligence, Beijing Jiaotong University, China+1

Upper-Limb Exoskeletons Assistive Robotics Human Motion Prediction Multimodal Trajectory Prediction Trajectory Prediction

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Adaptive torque prediction in dynamic exoskeleton scenarios requires expensive motion capture systems, which are infeasible in complex outdoor environments. Trajectory prediction has emerged as one of the effective approaches to address such an issue. However, the core challenges of exoskeleton trajectory prediction are twofold: establishing the mapping from multi-modal features to trajectory information; constructing the mapping from trajectory to torque. For the former, most existing methods perform only single-step prediction and neglect inter-subject trajectory variability, thereby limiting the trajectory optimization space and prediction generalization. To address this, this paper proposes a fast flow matching method that enables accurate trajectory prediction and better generalization for real-time performance, where trajectory generation errors and encoded observations are used to guide the training direction. For the second challenge, due to the high dynamics of the human-robot system and the strong coupling between perception and control, simple control methods struggle to achieve efficient assistance based on the predicted trajectory. This paper utilizes model predictive control and designs a novel optimization objective to optimize torque, ensuring the exoskeleton achieves comfortable and robust assistance. By integrating the above two components, the unified policy, denoted as ExoTraj, is developed to enable adaptive assistance in complex outdoor scenarios without high data acquisition cost. Experimental results show that compared to traditional methods, ExoTraj reduces cross-subject prediction error by 14.0% during the online phase and maintains robustness against external noise. Relative to the zero torque condition, ExoTraj decreases metabolic rate by 11.5-24.4%, heart rate by 1.7-19.5%, and peak muscle activation levels by 10.9-41.3%, respectively.

Abstract

Lagrangian Neural Networks

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