Publications

MC Rosenberg, JL Proctor, KM Steele (2024) “Quantifying changes in individual-specific template-based representations of center-of-mass dynamics during walking with ankle exoskeletons using Hybrid-SINDy”

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Journal Article in Scientific Reports

Ankle exoskeletons alter whole-body walking mechanics, energetics, and stability by altering center-of-mass (CoM) motion. Controlling the dynamics governing CoM motion is, therefore, critical for maintaining efficient and stable gait. However, how CoM dynamics change with ankle exoskeletons is unknown, and how to optimally model individual-specific CoM dynamics, especially in individuals with neurological injuries, remains a challenge.

Depictions of walking conditions, phase variables, and example template state variables. (A) Two-dimensional depictions of template model applied to human walking without and with ankle exoskeletons (left). The phase portrait (right) defined a phase variable, , used to cluster kinematically similar measurements for model fitting. Colors denote gait phases corresponding to first and second double-limb support, single-limb support, and swing of the right leg. (B) Stride-averaged global CoM position, velocity, and acceleration for an exemplary unimpaired adult in the anterior–posterior, vertical, and mediolateral directions. The three exoskeleton conditions are shown in panels (B) and (C): shoes-only (solid lines), zero-stiffness exoskeletons (K0; dashed lines), and stiff exoskeletons (KH; dotted lines). (C) Template position and velocity states used to fit the template signatures were defined by sagittal- and frontal-plane leg angles, and leg length.Aim: Evaluate individual-specific changes in CoM dynamics in unimpaired adults and one individual with post-stroke hemiparesis while walking in shoes-only and with zero-stiffness and high-stiffness passive ankle exoskeletons.

Methods: To identify optimal sets of physically interpretable mechanisms describing CoM dynamics, termed template signatures, we leveraged hybrid sparse identification of nonlinear dynamics (Hybrid-SINDy), an equation-free data-driven method for inferring sparse hybrid dynamics from a library of candidate functional forms.

Results: In unimpaired adults, Hybrid-SINDy automatically identified spring-loaded inverted pendulum-like template signatures, which did not change with exoskeletons (p > 0.16), except for small changes in leg resting length (p < 0.001). Conversely, post-stroke paretic-leg rotary stiffness mechanisms increased by 37–50% with zero-stiffness exoskeletons.

Interpretation: While unimpaired CoM dynamics appear robust to passive ankle exoskeletons, how neurological injuries alter exoskeleton impacts on CoM dynamics merits further investigation. Our findings support Hybrid-SINDy’s potential to discover mechanisms describing individual-specific CoM dynamics with assistive devices.

UW Data Science Seminar with Megan Ebers

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Title slide from the UW eScience Data Science seminar that says "Mobile sensing with shallow recurrent decoder networks. Megan R. Ebers"

Steele lab member and postdoctoral scholar, Megan Ebers, was featured in the Winter 2024 UW Data Science Seminar series. You can watch her full presentation on “Mobile sensing with shallow recurrent decoder networks” linked HERE on UW eScience Institute’s YouTube channel.

Abstract: Sensing is a fundamental task for the monitoring, forecasting, and control of complex systems. In many applications, a limited number of sensors are available and must move with the dynamics, such as with wearable technology or ocean monitoring buoys. In these dynamic systems, the sensors’ time history encodes a significant amount of information that can be extracted for critical tasks. We show that by leveraging the time-history of a sparse set of sensors, we can encode global information of the measured high-dimensional system using shallow recurrent decoder networks. This paradigm has important applications for technical challenges in climate modeling, natural disaster evaluation, and personalized health monitoring; we focus especially on how this paradigm has the potential to transform the way we monitor and manage movement-related health outcomes.

Bio: Megan Ebers is a postdoctoral scholar in applied mathematics with UW’s NSF AI Institute in Dynamic Systems. In her PhD research, she developed and applied machine learning methods for dynamics systems to understand and enable human mobility. Her postdoctoral research focuses on data-driven and reduced-order methods for complex systems, so as to continue her work in human-centered research challenges, as well as to extend her research to a broader set of technical challenges, including turbulent flow modeling, natural disaster monitoring, and acoustic object detection.

Steele Lab presents at CREATE Research Showcase

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A group of Steele Lab members posing for a photo

The Center for Research and Education on Accessible Technology and Experiences (CREATE) hosted a Research Showcase and Holiday party on December 12, 2023. CREATE’s mission is to make technology accessible and to make the world accessible through technology.

Steele Lab members, Kate, Victoria (Tori), and Charlotte presented posters at the CREATE Research Showcase to highlight design, development & research of tech to support individuals with disabilities.

Way to go, team!

Kate is standing in front of her poster "Design of Ability-based Switches"
Mia and Kate are standing next to a table. Mia is wearing glasses to demonstrate a head tilt switch while Kate is explaining the design of the head tilt switch.
Tori (left) and Charlotte (right) are posing in front of their posters

MR Ebers, KM Steele, JN Kutz (2024) “Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects”

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Journal Article in SIAM Journal on Applied Dynamical Systems

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based measurements of the system, revealing the approximate nature of the equations and/or the signal-to-noise ratio of the sensor itself. In modern dynamical systems, such discrepancies between model and measurement can lead to poor quantification, often undermining the ability to produce accurate and precise control algorithms.

Top panel: An approximate dynamical model f(·) provides estimates of system behavior used for both reconstruction and forecasting (shaded region), x(t). However, true behavior x0(t) (without observation noise) deviates from these estimates. The goal of discrepancy modeling is to learn a discrepancy model that recovers the missing physics and augments the approximate dynamics to improve system characterization, ˜x(t). Bottom panel: There are two approaches for building a discrepancy model to estimate missing physics: (i) modeling systematic state-space residual between the approximate state space, x(t), and true state space, x0(t), and (ii) learning the deterministic dynamical error between the true dynamics, x˙ 0(t) = f(x0(t)) + g(x0(t)), and the approximate dynamics, x˙ (t) = f(x(t)). In real-world systems, the true system behavior is noisily observed, yk = x0(tk) + N(μ, σ), model-measurement mismatch contains both deterministic and random effects; measurements yk = y(kΔt) denote a continuous dynamical system’s full state noisily observed at discrete time points.

Aim: Introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error. Regardless of approach, a common suite of data-driven model discovery methods can be used.

Method: Specifically, we use four fundamentally different methods to demonstrate the mathematical implementations of discrepancy modeling: (i) the sparse identification of nonlinear dynamics (SINDy), (ii) dynamic mode decomposition (DMD), (iii) Gaussian process regression (GPR), and (iv) neural networks (NN). The choice of method depends on one’s intent (e.g., mechanistic interpretability) for discrepancy modeling, sensor measurement characteristics (e.g., quantity, quality, resolution), and constraints imposed by practical applications (e.g., state- or dynamical-space operability).

Results: We demonstrate the utility and suitability for both discrepancy modeling approaches using the suite of data-driven modeling methods on three continuous dynamical systems under varying signal-to-noise ratios. Finally, we emphasize structural shortcomings of each discrepancy modeling approach depending on error type.

Interpretation: In summary, if the true dynamics are unknown (i.e., an imperfect model), one should learn a discrepancy model of the missing physics in the dynamical space. Yet, if the true dynamics are known yet model-measurement mismatch still exists, one should learn a discrepancy model in the state space.

AM Spomer, BC Conner, MH Schwartz, ZF Lerner, KM Steele (2023) “Audiovisual biofeedback amplifies plantarflexor adaptation during walking among children with cerebral palsy”

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Journal Article in Journal of NeuroEngineering and Rehabilitation

Biofeedback is a promising noninvasive strategy to enhance gait training among individuals with cerebral palsy (CP). Commonly, biofeedback systems are designed to guide movement correction using audio, visual, or sensorimotor (i.e., tactile or proprioceptive) cues, each of which has demonstrated measurable success in CP.

Figure 1. Experimental Protocol. Audiovisual (AV) biofeedback on soleus activity was provided for the more-affected limb alongside an auto-adjusting target score. Sensorimotor (SM) biofeedback was provided for the more-affected limb using an untethered ankle exoskeleton designed to impart a resistive ankle torque through stance, proportional to baseline values. Participants completed three data collection visits (pre-acclimation, post-acclimation, and follow-up), during which they walked with both biofeedback systems independently and in combination. Trials were pseudo-randomized within and between visits to ensure that feedback modalities were presented to each participant in a different order and control for fatigue and learning effects. Each trial was 10 min long and separated into baseline, feedback, and washout phases. All data analysis was performed for early (strides 1–30), mid (strides 91–110), and late (strides 181–210) feedback phases and washout (strides 1–30). Mean soleus activity for individual strides (purple dots) was normalized to baseline activity. Between the pre-acclimation and post-acclimation visits, participants completed four, 20-min acclimation sessions where they received additional practice with both systems

Aim: The aim of this study is to evaluate how the modality of biofeedback may influence user response which has significant implications if systems are to be consistently adopted into clinical care.

Method: In this study, we evaluated the extent to which adolescents with CP (7M/1F; 14 [12.5,15.5] years) adapted their gait patterns during treadmill walking (6 min/modality) with audiovisual (AV), sensorimotor (SM), and combined AV + SM biofeedback before and after four acclimation sessions (20 min/session) and at a two-week follow-up. Both biofeedback systems were designed to target plantarflexor activity on the more-affected limb, as these muscles are commonly impaired in CP and impact walking function. SM biofeedback was administered using a resistive ankle exoskeleton and AV biofeedback displayed soleus activity from electromyography recordings during gait. At every visit, we measured the time-course response to each biofeedback modality to understand how the rate and magnitude of gait adaptation differed between modalities and following acclimation.

Results: Participants significantly increased soleus activity from baseline using AV + SM (42.8% [15.1, 59.6]), AV (28.5% [19.2, 58.5]), and SM (10.3% [3.2, 15.2]) biofeedback, but the rate of soleus adaptation was faster using AV + SM biofeedback than either modality alone. Further, SM-only biofeedback produced small initial increases in plantarflexor activity, but these responses were transient within and across sessions (p > 0.11). Following multi-session acclimation and at the two-week follow-up, responses to AV and AV + SM biofeedback were maintained.

Interpretation: This study demonstrated that AV biofeedback was critical to increase plantarflexor engagement during walking, but that combining AV and SM modalities further amplified the rate of gait adaptation. Beyond improving our understanding of how individuals may differentially prioritize distinct forms of afferent information, outcomes from this study may inform the design and selection of biofeedback systems for use in clinical care.