Predicting walking response to ankle exoskeletons using data-driven models

TL;DR: The ability of subject-specific phase-varying models to predict kinematic and myoelectric responses to ankle exoskeletons during walking, without requiring prior knowledge of specific user characteristics, is evaluated.

Abstract: II Abstract Despite recent innovations in exoskeleton design and control, predicting subject-specific impacts of exoskeletons on gait remains challenging We evaluated the ability of three classes of subject-specific phase-varying models to predict kinematic and myoelectric responses to ankle exoskeletons during walking, without requiring prior knowledge of specific user characteristics Each model – phase-varying (PV), linear phase-varying (LPV), and nonlinear phase-varying (NPV) – leveraged Floquet Theory to predict deviations from a nominal gait cycle due to exoskeleton torque, though the models differed in complexity and expected prediction accuracy For twelve unimpaired adults walking with bilateral passive ankle exoskeletons, we predicted kinematics and muscle activity in response to three exoskeleton torque conditions The LPV model’s predictions were more accurate than the PV model when predicting less than 125% of a stride in the future and explained 49–70% of the variance in hip, knee, and ankle kinematic responses to torque The LPV model also predicted kinematic responses with similar accuracy to the more-complex NPV model Myoelectric responses were challenging to predict with all models, explaining at most 10% of the variance in responses This work highlights the potential of data-driven phase-varying models to predict complex subject-specific responses to ankle exoskeletons and inform device design and control

Summary

Introduction

• The authors expected the NPV model’s prediction accuracy to meet or exceed that of the 192 LPV model.
• The amount of data required to accurately predict response to exoskeletons will restrict the settings in which 252 phase-varying models are practical, such as in clinical gait analysis where datasets typically contain only a 253 few gait cycles [2, 8].
• To test each model’s generalizability across a range of exoskeleton torque conditions, the authors separately predicted 261 responses to torque in the K1, K2, and K3 datasets, termed held-out conditions, at a 12.5% stride prediction 262 horizon (1/8th of a stride).

VI. DISCUSSION 336

• The authors evaluated the ability of subject-specific phase-varying models to predict kinematic and myoelectric 337 responses to ankle exoskeleton torques during treadmill walking.
• 351 the LPV model’s predictions explained more of the variance in kinematic responses to exoskeletons than the 352 PV model, regardless of whether predictions interpolated (K1 and K2) or extrapolated (K3) relative to the 353 training set.

VII. CONCLUSION 459

• To their knowledge, this is the first study to predict subject-specific responses to ankle exoskeletons using 460 phase-varying models.
• Without making assumptions about individual physiology or motor control, an LPV 461 model predicted short-time kinematic responses to bilateral passive ankle exoskeletons, though predicting 462 myoelectric responses remains challenging.
• Results support the utility of LPV models for studying and 463 predicting response to exoskeleton torque.

Figures

Fig. 4. Average (±1SD) prediction accuracies for all participants and held-out conditions at a prediction horizon of 12.5% of a stride. Gray dots represent individual legs. Colored brackets denote statistically significant differences between held-out conditions for each model. Black horizontal bars denote significant differences between models across all three (solid) or two (dashed) held-out conditions. The large variance in the LPV model’s predictions of rectus femoris and gastrocnemius responses in the held-out K3 condition were due to bad predictions (RRV > 2) in a small number of legs. All comparisons used paired t-tests (α = 0.05) with a Holm-Sidak step-down correction for multiple comparisons.

Fig. 1. Left box: Data were collected during treadmill walking with bilateral ankle exoskeletons that used linear springs to

Fig. 3. Kinematic and myoelectric experimental (black) and predicted (colors) responses to torque for one participant who exhibited large responses to the exoskeletons (P03). Predictions are shown for a prediction horizon of 12.5% of a stride for the PV (green), LPV (orange), and NPV (purple) models. The three held-out conditions are denoted with solid (K1), dashed (K2), and dotted (K3) lines. Lines represent the average (±1SD; shaded region) data and predictions over all gait cycles in the corresponding validation dataset. The experimental data show that the K2 and K3 responses to torque were more similar to each other than to the K1 response. The PV model predictions were similar across heldout conditions, while the LPV and NPV models scaled with exoskeleton torque. Full joint trajectories may be reproduced by rescaling and adding the average unperturbed gait cycle to the predictions. All comparisons used paired t-tests (α = 0.05) with a Holm-Sidak step-down correction for multiple comparisons.

Fig. 6. Average (±1SD; shaded region) prediction accuracy of kinematic (left) and myoelectric (right) outputs for the PV (green), LPV (orange), and NPV (purple) models over training set sizes ranging from 24 to 240 cycles (RRVfull). Prediction accuracies were reported at a 12.5% stride prediction horizon. Orange (LPV) and purple (NPV) horizontal bars denote the training set sizes that yielded significantly worse predictions than those of the full training set. The PV model’s prediction accuracies were not significantly different from RRVfull at any training set size.

Fig. 2. Top: Average kinematic (left) and EMG (right) data for one participant who exhibited large, repeatable responses to exoskeleton torque and high model prediction accuracies (P03). Black lines show the zero-torque condition (K0) that was subtracted from all conditions to reflect responses to exoskeleton torque. Bottom: Average (±1SD) kinematic and myoelectric responses for all participants in each torque condition. Brackets denote significant differences between exoskeleton conditions according to post-hoc paired t-tests (α = 0.05) and a Holm-Sidak step-down correction. Thin gray lines represent individual legs.

Table I: Summary of model structures and expected prediction accuracies. 195

Full text

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Predicting walking response to ankle
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exoskeletons using data-driven models
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Michael C. Rosenberg
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, Bora S. Banjanin
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, Samuel A. Burden
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, Katherine M. Steele
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Department of Mechanical Engineering, University of Washington, Seattle, WA, USA
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Department of Electrical and Computer Engineering, University of Washington, Seattle, WA, USA
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Correspondence: mcrosenb@uw.edu
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I. KEYWORDS
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Ankle exoskeleton; data-driven modeling; locomotion; prediction; joint kinematics; muscle activity
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II. ABSTRACT
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Despite recent innovations in exoskeleton design and control, predicting subject-specific impacts of
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exoskeletons on gait remains challenging. We evaluated the ability of three classes of subject-specific phase-
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varying models to predict kinematic and myoelectric responses to ankle exoskeletons during walking, without
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requiring prior knowledge of specific user characteristics. Each model – phase-varying (PV), linear phase-
15
varying (LPV), and nonlinear phase-varying (NPV) – leveraged Floquet Theory to predict deviations from a
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nominal gait cycle due to exoskeleton torque, though the models differed in complexity and expected
17
prediction accuracy. For twelve unimpaired adults walking with bilateral passive ankle exoskeletons, we
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predicted kinematics and muscle activity in response to three exoskeleton torque conditions. The LPV
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model’s predictions were more accurate than the PV model when predicting less than 12.5% of a stride in
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the future and explained 49–70% of the variance in hip, knee, and ankle kinematic responses to torque. The
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LPV model also predicted kinematic responses with similar accuracy to the more-complex NPV model.
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Myoelectric responses were challenging to predict with all models, explaining at most 10% of the variance
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in responses. This work highlights the potential of data-driven phase-varying models to predict complex
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subject-specific responses to ankle exoskeletons and inform device design and control.
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted September 21, 2020. ; https://doi.org/10.1101/2020.06.18.105163doi: bioRxiv preprint

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III. INTRODUCTION
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Ankle exoskeletons are used to improve kinematics and reduce the energetic demands of locomotion in
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unimpaired adults and individuals with neurologic injuries [1-5]. Customizing exoskeleton properties to
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improve an individual’s gait is challenging and accelerating the iterative experimental process of device
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optimization is an active area of research [6, 7]. Studies examining the effects of exoskeleton properties –
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sagittal-plane ankle stiffness or equilibrium ankle angle for passive exoskeletons and torque control laws for
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powered exoskeletons – on kinematics, motor control, and energetics have developed design and control
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principles to reduce the energetic demand of walking and improve the quality of gait [1, 6, 8, 9]. Predicting
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how an individual’s gait pattern responds to ankle exoskeletons across stance may inform exoskeleton design
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by enabling rapid evaluation of exoskeleton properties not tested experimentally. Additionally for powered
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exoskeletons, which prescribe torque profiles using feedforward or feedback (e.g. kinematic or myoelectric)
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control laws, predicting responses over even 10–20% of a stride may improve tracking performance or
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transitions between control modes [4, 10-12]. However, predicting subject-specific responses to exoskeletons
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remains challenging for unimpaired individuals and those with motor impairments [2, 12, 13].
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Common physics-based models, including simple mechanical models and more physiologically-detailed
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musculoskeletal models, use principles from physics and biology to analyze and predict exoskeleton impacts
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on gait. For example, one lower-limb mechanical walking model predicted that an intermediate stiffness in a
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passive exoskeleton would minimize the energy required to walk, a finding that was later observed
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experimentally in unimpaired adults [1, 14]. More physiologically-detailed musculoskeletal models have
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been used to predict the impacts of exoskeleton design on muscle activity during walking in children with
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cerebral palsy and running in unimpaired adults [15, 16]. While these studies identified hypothetical
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relationships between kinematics and the myoelectric impacts of exoskeleton design parameters, their
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predictions were not evaluated against experimental data.
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted September 21, 2020. ; https://doi.org/10.1101/2020.06.18.105163doi: bioRxiv preprint

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Challenges to accurately predicting responses to ankle exoskeletons with physics-based models largely stem
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from uncertainty in adaptation, musculoskeletal physiology, and motor control, which vary between
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individuals and influence response to exoskeletons. While individuals explore different gait patterns to
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identify an energetically-optimal gait, exploration does not always occur spontaneously, resulting in sub-
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optimal gait patterns for some users [17]. Popular physiologically-detailed models of human gait typically
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assume instantaneous and optimal adaptation, which do not reflect how experience and exploration may
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influence responses to exoskeletons, possibly reducing the accuracy of predicted responses [18, 19].
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Additionally, when specific measurement sets are unavailable for model parameter tuning, population-
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average based assumptions about musculoskeletal properties and motor control are required [17, 20-22].
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However, musculoskeletal properties and motor control are highly uncertain for individuals with motor
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impairments, today’s most ubiquitous ankle exoskeleton users [19, 20, 22, 23]. Musculotendon dynamics and
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motor complexity are known to explain unintuitive exoskeleton impacts on gait energetics, suggesting that
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uncertain musculotendon parameters and motor control may limit the accuracy of predicted changes in gait
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with ankle exoskeletons [19, 21, 24]. Predictions of exoskeleton impacts on gait using physiological models,
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therefore, require accurate estimates of adaptation, musculotendon parameters, and motor control.
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Conversely, data-driven approaches address uncertainty in user-exoskeleton dynamics by representing the
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system entirely from experimental data. For instance, human-in-the-loop optimization provides a model-free
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alternative to physics-based prediction of exoskeleton responses by automatically exploring different
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exoskeleton torque control strategies for an individual [6, 7]. This experimental approach requires no prior
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knowledge about the individual: optimization frameworks identify torque control laws that decrease
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metabolic rate relative to baseline for an individual using only respiratory data and exoskeleton torque
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measurements. However, experimental approaches to exoskeleton optimization require the optimal design to
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be tested, potentially making the search for optimal device parameters time-intensive. Alternatively, machine
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learning algorithms, such as the Random Forest Algorithm, have used retrospective gait analysis and clinical
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted September 21, 2020. ; https://doi.org/10.1101/2020.06.18.105163doi: bioRxiv preprint

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exam data to predict changes in joint kinematics in response to different ankle-foot orthosis designs in
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children with cerebral palsy [8]. This study reported good classification accuracy, though predictions may
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not generalize to new orthosis designs. Unlike physiologically-detailed or physics-based models, human-in-
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the-loop optimization and many machine learning models are challenging to interpret, limiting insight into
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how a specific individual’s physiology influences response to exoskeleton torque. A balance between
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physiologically-detailed and model-free or black-box data-driven approaches may facilitate the prediction
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and analysis of responses to ankle exoskeletons without requiring extensive knowledge of an individual’s
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physiology.
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In this work, we investigated a subject-specific data-driven modeling framework – phase-varying models –
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that may fill the gap between physiologically-detailed model-based and model-free experimental approaches
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for predicting gait with exoskeletons. Phase-varying models typically have linear structure whose parameters
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are estimated from data, enabling both prediction and analysis of gait with exoskeletons [25, 26]. Unlike
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physiologically-detailed models, phase-varying models do not require knowledge of the physics or control
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of the underlying system. Unlike experimental approaches, the model-based framework enables prediction
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of responses to untested exoskeleton designs or control laws.
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Phase-varying models leverage dynamical properties of stable gaits derived from Floquet Theory, which
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ensures that the convergence of a perturbed trajectory to a stable limit cycle may be locally approximated
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using time-varying linear maps [27]. Similar principles have been shown to generalize to limit cycles in non-
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smooth or hybrid systems, such as human walking [28]. Moreover, phase-varying modeling principles have
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been applied to biological systems, identifying linear phase-varying dynamics to investigate gait stability and
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predict changes in kinematics in response to perturbations [25, 26, 29-31]. Responses to ankle exoskeleton
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torques may be similarly defined as perturbations off an unperturbed (i.e. zero torque) gait cycle, suggesting
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that the principles of phase-varying models will generalize to walking with exoskeletons. To the best of our
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted September 21, 2020. ; https://doi.org/10.1101/2020.06.18.105163doi: bioRxiv preprint

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knowledge, phase-varying models have never been used to study walking with exoskeletons and the extent
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to which the principles underlying phase-varying models of locomotion generalize to walking with
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exoskeletons is unknown.
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To determine if phase-varying models represent useful predictive tools for locomotion with exoskeletons, the
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purpose of this research was to evaluate the ability of subject-specific phase-varying models to predict
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kinematic and myoelectric responses to ankle exoskeleton torque during walking. We predicted responses to
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exoskeletons in unimpaired adults walking with passive ankle exoskeletons under multiple dorsiflexion
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stiffness conditions. We focused on three related classes of phase-varying models with different structures,
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complexity, and expected prediction accuracies: a phase-varying (PV), a linear phase-varying (LPV), and a
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nonlinear phase-varying (NPV) model. Since passive exoskeletons typically elicit small changes in joint
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kinematics and muscle activity, we expected the validity of Floquet Theory for human gait to extend to gait
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with exoskeletons, indicating that the LPV model should accurately predict responses to passive exoskeleton
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torque [1, 25-27, 29]. We, therefore, hypothesized that the LPV models would predict kinematic and
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myoelectric responses to torque more accurately than the PV model and as accurately as the NPV model. To
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exemplify the potential utility of subject-specific phase-varying models in gait analysis with ankle
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exoskeletons, we show how varying the length of model prediction time horizon may inform measurement
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selection for exoskeleton design and control. To assess the viability of data-driven phase-varying models in
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gait analysis settings, we evaluated the effect of limiting the size of the training dataset on prediction
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accuracy.
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IV. METHODS
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A. Experimental protocol
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We collected kinematic and electromyographic (EMG) data from 12 unimpaired adults (6 female / 6 male;
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age = 23.9 ± 1.8 years; height = 1.69 ± 0.10 m; mass = 66.5 ± 11.7 kg) during treadmill walking with bilateral
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted September 21, 2020. ; https://doi.org/10.1101/2020.06.18.105163doi: bioRxiv preprint

Frequently asked questions

Q1. What are the contributions in "Predicting walking response to ankle exoskeletons using data-driven models" ?

In this paper, the authors predict subject-specific responses to ankle exoskeletons using 460 phase-varying models. 

Q2. What are the future works in "Predicting walking response to ankle exoskeletons using data-driven models" ?

Improving data-driven models and experimental protocols to study 464 and predict myoelectric responses to exoskeletons represents an important direction for future research. 465 Modeling responses to exoskeletons or other assistive devices using a phase-varying perspective has the 466 potential to inform exoskeleton design for a range of user groups.