Graphical Abstract Figure

Machine learning intent recognition system. Depiction of a knee and ankle powered prosthesis (OSL) with embedded mechanical sensors. The prosthesis utilizes six mechanical sensors (two joint encoders, three IMUs, and one 6DOF loadcell). During ambulation, signals are collected and parsed into the ML system which predicts mode and estimates context (walking speed or slope). Based on the ML estimates, impedance parameters that dictate joint torque are scaled as a function of the context and sent back to the user to mediate an appropriate control response to the environment.

Graphical Abstract Figure

Machine learning intent recognition system. Depiction of a knee and ankle powered prosthesis (OSL) with embedded mechanical sensors. The prosthesis utilizes six mechanical sensors (two joint encoders, three IMUs, and one 6DOF loadcell). During ambulation, signals are collected and parsed into the ML system which predicts mode and estimates context (walking speed or slope). Based on the ML estimates, impedance parameters that dictate joint torque are scaled as a function of the context and sent back to the user to mediate an appropriate control response to the environment.

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Abstract

Community ambulation is essential for maintaining a healthy lifestyle, but it poses significant challenges for individuals with limb loss due to complex task demands. In wearable robotics, particularly powered prostheses, there is a critical need to accurately estimate environmental context, such as walking speed and slope, to offer intuitive and seamless assistance during varied ambulation tasks. We developed a user-independent and multicontext, intent recognition system that was deployed in real-time on an Open Source Leg (OSL). We recruited 11 individuals with transfemoral amputation, with seven participants used for real-time validation. Our findings revealed two main conclusions: (1) the user-independent (IND) performance across speed and slope was not statistically different from user-dependent (DEP) models in real-time and did not degrade compared to its offline counterparts, and (2) IND walking speed estimates showed ∼0.09 m/s mean absolute error (MAE) and slope estimates showed ∼0.95 deg MAE across multicontext scenarios. Additionally, we provide an open-source dataset to facilitate further research in accurately estimating speed and slope using an IND approach in real-world walking tasks on a powered prosthesis.

Introduction

The development of smarter prostheses is critical as microprocessor-controlled technology becomes increasingly prescribed for individuals with above-knee amputations [1]. Traditional lower-limb prostheses often lack the necessary functionality to replicate the complex movements of a biological limb, leading to significant mobility challenges for users, such as difficulty with balance and transitioning between different terrains like stairs and ramps [2]. Modern prosthetic technology continues to advance, including powered, semi-active, and pseudo-passive devices to improve user mobility and improve quality of life [316]. However, current control frameworks for powered prostheses are not yet advanced enough for seamless and automatic ambulation assistance in real-world environments.

A primary challenge is transitioning between ambulation modes, which often requires users to slow down, stop, or perform exaggerated movements, making the process cumbersome and mentally taxing [17]. The challenge, specifically in the case of transfemoral amputation, is to ensure that both knee and ankle prosthetic joints can be controlled in a synchronous and stable manner. The most common prosthetic control strategies typically employ a three-tier controller paradigm: high-level, mid-level, and low-level control [18,19].

To address this, machine learning (ML)-based intent recognition algorithms are increasingly employed to classify lower-limb movements; prior studies have deployed user-dependent (DEP) [2022], user-independent (IND) [2026], and semi-independent (SEMI) [2732] systems to classify ambulation modes such as level ground walking, ramps, stairs, sit, and stand. IND models, trained on data from a diverse pool of subjects, have the potential to generalize well to novel users but tend to underperform compared to DEP models that are specifically trained on individual subjects. Recent advancements have also explored SEMI models, which partially adapt IND models to a target user with minimal user-specific data.

Beyond ambulation mode classification, powered prostheses must estimate environmental context—such as walking speed and slope—to appropriately scale assistance. Although context estimation for lower-limb prostheses has been explored using various methods, a gap remains in developing systems that continuously estimate these variables in real-time [3339]. Most approaches rely on stride-by-stride estimation, resulting in delayed responses to dynamic changes during the gait cycle. Stride-to-stride estimation is insufficient because the user may change context at any time during the gait cycle. It should be noted that Medrano et al. achieved context-based control with a powered ankle exoskeleton [40,41]. An extended Kalman filter was paired with a shank and foot inertial measurement units (IMUs) to estimate phase, phase rate, stride length, and slope continuously.

Recent publications have demonstrated that machine learning systems can be implemented in real-time, where embedded controllers continuously receive live signals to predict user intent [27,28]. The first real-time intent recognition system for powered prostheses, developed by Varol et al., used a DEP classifier with mechanical sensors, and this work has since expanded to include mode-specific classifiers with time-history methods using electromyography and mechanical sensors [4244]. Spanias et al. [27] created an adaptive pipeline incorporating user-specific electromyography data into a DEP model, while Woodward et al. [28] enhanced an IND model, achieving similar results with reduced training time.

Terrain navigation is crucial for independent mobility, as studies have shown that individuals with mobility disabilities encounter slopes and uneven surfaces less frequently, likely due to limited access to enabling technologies [4548]. Our goal is to facilitate seamless terrain negotiation for prosthesis users, as this is a natural response for able-bodied individuals. The challenge lies in integrating real-time capabilities, generalization to novel users, and continuous estimation without hindering mobility in different settings.

This study presents a fully IND control system capable of real-time, continuous estimation of walking speed and slope on the Open Source Leg (OSL). We formally compared the performance of DEP, SEMI, and IND systems in real-time across N = 7 individuals with transfemoral amputation. We hypothesized that: (1) across all contexts (slope and speed), offline DEP models would outperform offline IND models based on prior literature results, and (2) across all tasks, the relative change (REL) from offline to real-time would be smaller for IND models compared to DEP models. The rationale here is that IND models have the advantage of being a more generalized system formulated from a larger subject pool which may accommodate for day-to-day subject variation. These comparisons provide insights into the efficacy of real-time IND systems and highlight potential future directions for prosthetic control. Additionally, we contribute an open, multi-subject dataset for further research in prosthetic control and intent recognition. In summary, our contributions in respect to the current state-of-art field are:

  1. We deployed and demonstrated an IND system (Fig. 1), that allows for multispeed and multi-incline continuous estimation in real-time on the OSL.

  2. We provided our data and algorithms to be open-source and accessible (N = 11) to the research community to allow others to build upon our work and continue to make this technology more accessible to all individuals with lower-limb amputation.

  3. We provided a post-hoc analysis of offline IND model performance to compare the benefits of utilizing additional sensors, or lack thereof, in contrast to the base configuration of the OSL for future research considerations.

Fig. 1
Machine learning intent recognition system. Depiction of a knee and ankle powered prosthesis (OSL) with embedded mechanical sensors. The prosthesis utilizes six mechanical sensors (two joint encoders, three IMUs, and one 6DOF loadcell). During ambulation, signals are collected and parsed into the ML system which predicts mode and estimates context (walking speed or slope). Based on the ML estimates, impedance parameters that dictate joint torque are scaled as a function of the context and sent back to the user to mediate an appropriate control response to the environment.
Fig. 1
Machine learning intent recognition system. Depiction of a knee and ankle powered prosthesis (OSL) with embedded mechanical sensors. The prosthesis utilizes six mechanical sensors (two joint encoders, three IMUs, and one 6DOF loadcell). During ambulation, signals are collected and parsed into the ML system which predicts mode and estimates context (walking speed or slope). Based on the ML estimates, impedance parameters that dictate joint torque are scaled as a function of the context and sent back to the user to mediate an appropriate control response to the environment.
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Material and Methods

Participant Demographics.

Eleven participants (mean ± SD; nine male/two female, age = 50.36 ± 12.09 yr; mass = 80.13 ± 15.64 kg; height = 1.77 ± 0.10 m; mobility level = 4 K3/7 K4) participated in this study. This study was approved by the Georgia Institute of Technology Institutional Review Board. All participants provided written informed consent before they participated in the study. The prosthetic device was configured for each user by a certified prosthetist for appropriate alignment and comfort. Additional information and video footage can be found in the Supplemental Materials on the ASME Digital Collection.

Prosthetic Device.

The prosthetic device used in this study is known as the OSL. The OSL is a knee–ankle powered prosthesis that is actuated by two DEPHY ActPack actuators [12]. Our device was equipped with one six degree-of-freedom (DOF) loadcell (Sunrise Instruments M3564F, Nanning, China), two joint encoders (AS5047P and AK7452—DEPHY ActPack, Maynard, MA), and a single shank IMU (MPU-9250 InvenSense, San Jose, CA). In addition, we incorporated two 6DOF IMUs and attached them at the thigh and foot (3DMCX5-25 IMU (LORD Microstrain, Williston, VT)) (Fig. 2). A Raspberry Pi 4 (RPi 4) Model B (8 GB) located on the knee housing served as the primary computing platform of the system for running the real-time machine learning intent recognition system. An external laptop was used to communicate with the RPi 4 for signal visualization and impedance parameter tuning. All sensors were sampled at 100 Hz. Both offline and real-time ML models were generated using python 3.9+ and saved/embedded using the xgboostpythonapi (1.3.0+) which generated Json files that could be loaded onto the Raspberry Pi 4 Model B (8 GB).

Fig. 2
Participant walking with OSL. (a) One participant with a transfemoral amputation ambulating on a Bertec split-belt treadmill with the OSL. (b) Users were asked to complete two training tracking profiles for the offline walking speed session (session 1) and to test the real-time walking speed estimation models for two different tracking profiles (session 3). (c) One participant walking with the OSL on our custom-made terrain park that allows for easy modulation of slope angles (sessions 2 and 4).
Fig. 2
Participant walking with OSL. (a) One participant with a transfemoral amputation ambulating on a Bertec split-belt treadmill with the OSL. (b) Users were asked to complete two training tracking profiles for the offline walking speed session (session 1) and to test the real-time walking speed estimation models for two different tracking profiles (session 3). (c) One participant walking with the OSL on our custom-made terrain park that allows for easy modulation of slope angles (sessions 2 and 4).
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Prosthetic Control Paradigm.

Prosthetic control was structured hierarchically, with high-, mid-, and low-level controllers (Fig. 1). The high-level controller detected and interpreted the user's intent, such as transitions between ambulation modes or environmental contexts. During offline sessions, the experimenter manually triggered mode transitions using a custom graphical user interface (GUI). The prosthesis was programed to execute the transition at the next gait event (e.g., heel contact) after receiving the command. The specific timing of the button press within the gait cycle was flexible, as long as it occurred during the correct step, ensuring that transitions were always accurate. If an error occurred, the trial was restarted to maintain 100% accuracy in the training data. In real-time sessions, pretrained mode classifiers automatically predicted and triggered transitions at gait events, while the experimenter simultaneously triggered transitions for labeling purposes, which did not influence the prosthetic control.

Context estimation was performed mode-specifically, with walking speed estimated during level walking (LW), positive slope estimated during ramp ascent (RA), and negative slope estimated during ramp descent (RD). Separate estimators were trained for each ambulation mode. At the mid-level, a finite state machine managed transitions between ambulation modes based on the high-level controller's decisions, while gait phase transitions were handled by a state machine with mechanical sensor thresholds [21,23,49,50]. Within each state, the controller regulated the torque provided at the joint level by using a torque law that is a function of the current joint state and the stiffness and damping parameters that define the impedance law (Eq. (1))
(1)

The impedance parameters were either kept constant or dynamically adjusted based on environmental conditions and sensor readings [49]. At the low level, DEPHY ActPack actuators used a built-in proportional, integral, and derivative controller to deliver the desired assistance with proper scaling.

Training Data Collection Protocols.

This study was comprised of a control parameter tuning session (session 0), an offline collection of speed data (session 1), an offline collection of slope and transition data for level ground and ramps (session 2), a real-time evaluation of speed estimators (session 3), and a real-time evaluation of slope estimators and mode classifiers (session 4). A total of 11 individuals with transfemoral amputation participated in the study. Participants were instructed to minimize handrail use during walking trials, though some used them for added assurance. Handrail use was not explicitly controlled or labeled in data collection, and trials involving handrail contact were included in both training and testing datasets across all sessions. This approach reflected real-world variability, as prosthesis users at times may or may not use handrails, making it reasonable to incorporate this variability in the training data for machine learning purposes.

Session 0: Tuning.

In the tuning session, every participant (N = 11) walked on a Bertec instrumented treadmill at a low (0.3 m/s), medium (0.6 m/s), and high (0.9 m/s) speed while we tuned a set of baseline level walking impedance parameters to the preference of the user. Similarly, we had participants walk up and down a ramp (10.5 deg) while we tuned a set of baseline ramp ascent and descent impedance parameters to the preference of the user [49]. These speeds and slopes were selected for practical time constraints. The tuning session was considered complete as soon as the user felt comfortable, and the prosthetist was satisfied with their gait mechanics (at least ∼30 min).

Session 1: Offline Walking Speed Data Collection.

We collected data from 10 of the 11 participants; seven static trials in which participants walked on a Bertec treadmill at the following walking speeds for 60 s each: 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 m/s. Two training dynamic trials were collected for varying walking speed profiles (Fig. 2).

Session 2: Offline Mode and Slope Data Collection.

All 11 participants completed three ramp circuits per slope setting and three level walking circuits. A ramp circuit consisted of LW → RA → LW → RD → LW. We collected data at the following slope settings: 7.3 deg, 8.7 deg, 10.5 deg, and 12.3 deg. Level walking circuits included walking back and forth (5x) between two cones spaced 3 m apart, counterclockwise (5x) around two cones spaced 1 m apart, and clockwise (5x) around two cones spaced 1 m apart. During the offline session, ambulation mode transitions were controlled by a trained research scientist by selecting modes in a GUI that displayed the prosthetic leg's finite state. Mode transitions were governed by preprogramed rules, ensuring that specific sensor thresholds or gait conditions were met before moving to the next mode. This system ensured transitions happened within one stride of selection, minimizing reliance on the exact timing of the researcher.

Machine Learning Models and Optimization.

From previous research studies, our group validated machine learning algorithm (xgboost) for both offline mode classification and walking speed estimation [22,51]. In this study, we explore the use of xgboost for offline and real-time speed estimation, slope estimation, and mode classification. xgboost is an optimized gradient tree boosting library that can learn problems that are nonlinear and complex in an efficient and parallelized structure [52,53]. The advantages of utilizing this model include: clever penalization of trees to overcome overfitting, the use of weighted functions to create additional trees with respect to a bias-variance tradeoff, and also the use of a differentiable loss function to minimize the loss gradient, which in turn makes this algorithm easy to use and flexible to different problems [53]. Window size, increment size, hyperparameter tuning, and phase-specific models were selected using a standard optimization procedure outlined in our previous studies [22,51]. Note, we only optimized parameters via a directed search on the training and validation data for each model type (sessions 1 and 2). Additionally, it is important to mention that our hyperparameter optimization yielded similar values compared to our previous studies, minimizing the need for extensive tuning on the current dataset. This approach further reduces the risk of overfitting, as the withheld subjects were not involved in the hyperparameter optimization process, ensuring that the test data remained independent for evaluation purposes. Simon et al. in 2017 showed that delaying the transition decision by 90 ms between modes did not affect the user but also allowed for richer information for a mode classifier to detect a mode change (i.e., transition) which vastly improved the overall classification accuracy [23]. In mode classification tasks, discrete feature extraction windows of 500 ms were taken with a 150 ms delayed transition post heel contact [23]. The delay of 150 ms was verified to not perturb the user while allowing for smooth ambulation mode transitions. In both slope and speed estimation tasks, continuous windows of 500 ms were taken with an increment size of 20 ms (∼50 Hz). The following features were extracted from each window of data and served as inputs to the respective xgboost model: mean, standard deviation, maximum, minimum, and last value. From a previous study, a four-phase configuration was shown to be optimal for regression tasks (early stance/late stance/swing flexion/swing extension) [54]. For each phase of walking, a separate regressor was trained on data from that specific phase to capture phase dependent signal information. In this method, speed and slope determinations were generated continuously throughout the gait cycle, switching between models during the appropriate phase based on the state machine.

In real-time, speed and slope estimates were paired with a Kalman filter to further enhance results [55]. We implemented continuous measurement noise estimators that estimated the uncertainty associated with every context estimate. Kalman filters fuse a predefined model of the environment with uncertainties of context estimates to produce filtered context estimates. The Kalman filter state extrapolation equation used here modeled the environment as a static system in which context did not change during 20 ms (50 Hz) intervals. Modeling the environment as a static system is useful for smoothing noisy estimates and ideal for estimating static speeds. We included a process noise term in the Kalman filter covariance extrapolation equation to correct for uncertainty associated with our static system model. In walking speed estimation, a process noise of 0.00001 was utilized across all models, while in slope estimation, a process noise of 0.0001 was used across all models.

We describe below the data splits used for offline and online model training, validation, and evaluation. During training, 20% of the data was allocated as validation data. Offline DEP mode classifiers and slope estimators were evaluated using a leave-one-trial-out cross-validation approach, where models were trained on all but one trial from a given subject and evaluated on the left-out trial (one trial per incline) from the same subject. For walking speed estimators in the DEP system, models were trained on static walking speed data and evaluated on dynamic speed data.

Offline IND mode classifiers, slope estimators, and walking speed estimators were evaluated using a subject-wise cross-validation approach. Specifically, models were trained on all static walking speed data from nontest subjects and then evaluated on the dynamic walking speed data of the test subject. Offline SEMI walking speed estimators were also evaluated using subject-wise cross-validation. Specifically, during training, we mixed static walking speed data from nontest subjects with 90 s of static walking speed data from the test subject (30 s each at walking speeds of 0.4, 0.6, and 0.8 m/s). This means that both data sources were used together to train the model. The inclusion of the test subject's data allows the model to personalize its estimations based on the individual's specific gait characteristics. After training on this combined dataset, the model was then evaluated on the test subject's dynamic speed data to assess its performance under real-world conditions.

For real-time experiments, DEP models were trained on all offline test data from the same subject and evaluated on that subject during real-time tests. IND models were trained on all offline data from nontest subjects and evaluated on the test subject in real-time. SEMI models were trained on all offline nontest-subject data, plus 90 s of offline test-subject data, and then evaluated on the test subject during real-time experiments.

In each case, context estimators were paired with measurement noise estimators, which provided uncertainty measures for the context estimates. These noise estimators were trained using the same data as the context estimators, but with different labels. Absolute error values, obtained from evaluating context estimators on the validation data, were used as measurement noise labels. This approach allowed for dynamically estimating measurement noise and enabled the application of a Kalman filter to smooth machine learning-generated context estimates.

Model Assessment Protocols

Session 3: Real-Time Speed Estimation.

Based on a power analysis of the offline data, we determined that N = 7 subjects would need to return for real-time testing to compare DEP and IND conditions. Seven of the session 1 participants were involved in session 3. During the real-time session, DEP, IND, and SEMI speed estimators were evaluated on two dynamic trials in real-time for a total of six conditions. These models were only evaluated for speeds between 0.3 m/s and 0.9 m/s. Furthermore, no meaningful estimates were conducted below 0.3 m/s as the prosthesis was effectively in standing mode during those times. We assumed that the treadmill speed closely approximated the participant's walking speed, as treadmill walking generally constrains the user to move at the set speed of the treadmill. This approach simplifies the comparison and provides a controlled baseline for speed estimation.

Session 4: Real-Time Mode Classification and Slope Estimation.

Seven of the session 2 participants were involved in session 4. During the real-time session, DEP and IND ambulation mode classifiers and slope estimators were evaluated for two ramp circuits per slope setting and one level-walking circuit for a total of 11 trials at a self-selected speed. Five slope settings were included: 8.0 deg, 8.7 deg, 9.6 deg, 10.5 deg, and 11.4 deg. We wanted to include slopes that were not used in the training of the models to ensure that the model could still predict in a novel setting. The level-walking-only circuit involved participants walking back and forth for three iterations. In real-time, ambulation mode transitions were controlled by the output of pretrained locomotion xgboost mode classifiers deployed on the Raspberry Pi 4. Transitions were correctly labeled in real-time by a trained research scientist with a custom GUI for comparison.

Sensor Selection Analysis.

An analysis of all the embedded sensors on the OSL versus machine learning performance (only in offline IND models) was conducted to understand the importance of utilizing certain mechanical sensors to predict mode and estimate context. The “baseline” set of sensors (two joint encoders, one shank IMU, and one single-axis loadcell) was used as a reference point since the most basic build of the OSL contains only those sensors. Additional IMUs and 6DOF loadcell comparisons were added until all sensors were utilized in the “all” case as these sensors represent optional add-ons from the base state of the device.

Fig. 3
Walking speed estimation results. (a) Three machine learning models were evaluated in the offline case. The error metric calculated for each model was the MAE with 95% confidence interval bars. None of the models were statistically different from each other (DEP|IND: p = 0.16; DEP|SEMI: p = 1.0; IND|SEMI: p = 0.1). DEP models were trained with user-specific data. IND models were trained on a pool of subjects and evaluated on the novel subject. SEMI models were trained with a % of user-specific data added to the baseline IND condition. (b) In real-time, none of the models were found to be statistically different (p = 1 for all comparisons). (c)The average REL between offline and real-time was calculated for all models (% change). A significant difference was found between the IND and SEMI models (p < 0.05). (d) Two real-time tracking profiles were evaluated for all three models (DEP, IND, and SEMI); shown is the cross-subject average±SEM tracking performance across both profiles.
Fig. 3
Walking speed estimation results. (a) Three machine learning models were evaluated in the offline case. The error metric calculated for each model was the MAE with 95% confidence interval bars. None of the models were statistically different from each other (DEP|IND: p = 0.16; DEP|SEMI: p = 1.0; IND|SEMI: p = 0.1). DEP models were trained with user-specific data. IND models were trained on a pool of subjects and evaluated on the novel subject. SEMI models were trained with a % of user-specific data added to the baseline IND condition. (b) In real-time, none of the models were found to be statistically different (p = 1 for all comparisons). (c)The average REL between offline and real-time was calculated for all models (% change). A significant difference was found between the IND and SEMI models (p < 0.05). (d) Two real-time tracking profiles were evaluated for all three models (DEP, IND, and SEMI); shown is the cross-subject average±SEM tracking performance across both profiles.
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Statistical Analysis.

A power analysis was conducted using offline accuracy metrics, specifically average error across subjects in speed estimation, slope estimation, and mode classification. This allowed us to determine that a sample size of N = 7 subjects would be sufficient to detect significant differences between DEP, IND, and SEMI conditions in real-time testing. A Shapiro–Wilk test and Levene's test on accuracy metrics was performed to verify normality and variance assumptions. Then, we conducted three one-way repeated measures analysis of variance to compare the performance for speed estimation, where the independent variables were the models (DEP/IND/SEMI), and the dependent variable was the error (offline; real-time; relative % change). Across all tasks, the dependent variable was average error across subjects (mode: % error, slope: root-mean-square error (RMSE) (deg), and speed: RMSE (m/s)). For slope estimation, paired t-tests were conducted since there were only two independent groups to compare between (DEP and IND). In each analysis, the type 1 error was set to 0.05 for significance. In the case of the one-way repeated measures analysis of variance analysis, Bonferroni post-hoc corrections were used to make pairwise comparisons to understand if there were statistical differences between each individual condition (spss 28.0). Furthermore, we reported the effect size (Cohen's d) to evaluate the practical significance of each comparison (Table 1).

Table 1

Summarized statistics

Comparison pairsp-valueEffect size (Cohen's d)
SpeedOFF DEPOFF IND0.1600.945
OFF DEPOFF SEMI1.000
OFF INDOFF SEMI0.100
RT DEPRT IND1.0000.221
RT DEPRT SEMI1.000
RT INDRT SEMI1.000
REL DEPREL IND0.4371.488
REL DEPREL SEMI1.000
REL INDREL SEMI0.024a
ModeOFF DEPOFF IND0.012a1.339
RT DEPRT IND0.5260.254
REL DEPREL IND0.009a1.439
SlopeOFF DEPOFF IND0.010a1.414
RT DEPRT IND0.0850.778
REL DEPREL IND0.029a1.077
Sensor analysisSpeed baselineSpeed all0.0550.897
Mode baselineMode all0.016a1.259
Slope baselineSlope all<0.001a3.437
Comparison pairsp-valueEffect size (Cohen's d)
SpeedOFF DEPOFF IND0.1600.945
OFF DEPOFF SEMI1.000
OFF INDOFF SEMI0.100
RT DEPRT IND1.0000.221
RT DEPRT SEMI1.000
RT INDRT SEMI1.000
REL DEPREL IND0.4371.488
REL DEPREL SEMI1.000
REL INDREL SEMI0.024a
ModeOFF DEPOFF IND0.012a1.339
RT DEPRT IND0.5260.254
REL DEPREL IND0.009a1.439
SlopeOFF DEPOFF IND0.010a1.414
RT DEPRT IND0.0850.778
REL DEPREL IND0.029a1.077
Sensor analysisSpeed baselineSpeed all0.0550.897
Mode baselineMode all0.016a1.259
Slope baselineSlope all<0.001a3.437
a

Just means statistical significance.

Results

Both offline and real-time ML models were evaluated under three different conditions. DEP models were trained with user-specific data, and IND models were trained with all users' data except for the subject being evaluated. SEMI models were trained with a percentage of user-specific data added to the baseline IND condition (see Methods for additional details). Each subsection presents the results for each machine learning task, starting with the context estimation of walking speed, followed by the mode classification, and slope estimation. All mechanical sensors (two joint encoders, three IMUs, and one 6DOF loadcell) were used in real-time experiments. While the absolute errors of the DEP, IND, and SEMI models are similar, the REL calculations show how well each model maintains its performance from offline to real-time conditions.

Walking Speed Estimation.

The offline IND model error was 0.09 ± 0.03 m/s (mean absolute error (MAE) ± 95% confidence intervals (CI)) which was, on average, worse, but not significantly different than the offline DEP model (0.06 ± 0.02 m/s) and offline SEMI model (0.06 ± 0.01 m/s) (Fig. 3(a)). The real-time model performance across all three systems was statistically similar (p = 1 for all comparisons) with real-time IND error of 0.09 ± 0.03 m/s, real-time DEP model error of 0.08 ± 0.01 m/s, and the real-time SEMI model error of 0.08 ± 0.02 m/s (Fig. 3(b)). In addition, the REL of going from offline to real-time was calculated using Eq. (2). It was found that the average REL for the DEP models was 55.83 ± 50.55%, IND models was 5.20 ± 13.93%, and for SEMI models 50.46 ± 19.38% (Fig. 3(c)). The only statistical difference found was between the REL of the IND model and SEMI model (p < 0.05) due to the large standard deviation observed in the DEP condition. Figure 3(d) shows an example of the real-time tracking performance of all subjects across all models for both dynamic profiles that were tested. We found that for user-detectable changes in walking speeds (∼1 Hz) the time delay of our filter can range from 157 ms to 180 ms for measurement noises within one standard deviation of the mean. Individual subject errors are shown in the Supplemental Materials on the ASME Digital Collection.
(2)
Fig. 4
(a) Two machine learning models were evaluated for slope estimation in the offline case, in which a statistical difference was found (p < 0.05). The error metric calculated for each model was the MAE with 95% confidence interval bars. (b) In real-time, no significant differences were found (p = 0.085). (c) The average REL between offline and real-time was calculated (% change), and a significant difference was found between the DEP and IND slope models (p < 0.05).
Fig. 4
(a) Two machine learning models were evaluated for slope estimation in the offline case, in which a statistical difference was found (p < 0.05). The error metric calculated for each model was the MAE with 95% confidence interval bars. (b) In real-time, no significant differences were found (p = 0.085). (c) The average REL between offline and real-time was calculated (% change), and a significant difference was found between the DEP and IND slope models (p < 0.05).
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Slope Estimation.

The offline slope estimation DEP model error was 0.81 ± 0.11 deg (mean absolute error ± 95% CI) which was significantly better (p < 0.05) than the offline IND model error which was 1.11 ± 0.08 deg (Fig. 4(a)). The real-time DEP error was 1.12 ± 0.15 deg which was worse but not significantly different than the real-time error of the IND model which was 0.95 ± 0.08 deg (Fig. 4(b)). The average REL (Eq. (2)) between offline and real-time for the IND model was −13.07 ± 10.50%, which was significantly better (p < 0.05) than the REL for the DEP model which was 43.42 ± 32.95% (Fig. 4(c)).

Fig. 5
Offline IND sensor selection results. The baseline set of sensors (two joint encoders, one shank IMU, and one single-axis loadcell—typical OSL setup using DEPHY ActPacks) was used as a reference point. Additional IMUs (Lord Microstrain 3DMCX5-25) and 6DOF loadcell (Sunrise Instruments M3564F) comparisons were added until all sensors were utilized in the all case as these sensors represent optional add-ons from the baseline state of the device. Other combinations of sensors were added for comparison. (a) There was no significant difference found between the baseline and all cases for the speed models (p = 0.055). In both slope models (b), a 19.96% reduction, and mode models (c), a 30.28% reduction, a statistical difference was found indicating that additional sensors are beneficial in these tasks (p < 0.05) (Table 1).
Fig. 5
Offline IND sensor selection results. The baseline set of sensors (two joint encoders, one shank IMU, and one single-axis loadcell—typical OSL setup using DEPHY ActPacks) was used as a reference point. Additional IMUs (Lord Microstrain 3DMCX5-25) and 6DOF loadcell (Sunrise Instruments M3564F) comparisons were added until all sensors were utilized in the all case as these sensors represent optional add-ons from the baseline state of the device. Other combinations of sensors were added for comparison. (a) There was no significant difference found between the baseline and all cases for the speed models (p = 0.055). In both slope models (b), a 19.96% reduction, and mode models (c), a 30.28% reduction, a statistical difference was found indicating that additional sensors are beneficial in these tasks (p < 0.05) (Table 1).
Close modal

Mode Classification.

Mode classification error was computed by taking the total number of misclassified steps across both steady-state steps and transitional steps over the total number of strides taken. The offline DEP model error was 5.37 ± 0.92% (mean percent error ± 95% CI) which was significantly better (p < 0.05) than the offline IND model error which was 12.61 ± 4.42%. The real-time DEP error was 19.04 ± 6.14% which was not significantly different than the real-time error of the IND model which was 17.39 ± 7.35%. The average relative change (Eq. (2)) between offline and real-time for the IND model was 39.77 ± 43.97% which was significantly better (p < 0.05) than the change for the DEP model which was 292.26 ± 171.10%. The confusion matrices were generated to show where the misclassifications occurred (see Supplemental Materials). Specifically, in the DEP case, the LW to RA transition had the highest error; in the IND case, the LW to RD transition had the highest error.

Offline User-Independent Sensor Selection.

Speed results indicated that there was no difference between the baseline and all conditions indicating good performance without additional sensing capability added to the OSL (Fig. 5). However, in mode classification and slope estimation, the error was significantly lower (p < 0.05) when utilizing all additional sensing modalities. For mode classification, the improved result required the combination of all additional sensors to achieve the highest level of performance. However, for slope estimation, the improved result from additional sensing was achieved with the addition of a foot or thigh IMU. Individual subject errors are shown in the Supplemental Materials.

Discussion

This study introduced a fully user-independent control system capable of estimating user walking speed and ground slope in real-time. Our findings demonstrated that the IND system maintained its performance in real-time without degradation, unlike the DEP system, highlighting the generalizability of IND models, which are less sensitive to inter- and intrasubject variation (supporting hypothesis 2). In alignment with previous studies, our classification results confirmed that offline DEP models outperformed IND models (supporting hypothesis 1) [21,23].

We successfully developed an IND system that continuously estimated walking speed on level ground, achieving a MAE of 0.08 ± 0.02 m/s, comparable to recent studies on powered knee and ankle devices, which reported a speed estimator RMSE of 0.11 m/s [39]. While lower error is desirable, we provided context by comparing our results to the minimally clinically important difference of ∼0.1 m/s. Although this minimally clinically important difference was not explicitly intended as a benchmark for speed tracking in powered prostheses, it aligns with clinical measures commonly used in practice, linking our quantitative findings to functional assessments of prosthetic technology [56]. In the offline setting, SEMI models demonstrated benefits, but these trends did not carry over to real-time performance, indicating that IND systems warrant further improvement. It is worth noting that alternative approaches to incorporating individual user data exist, such as training models on nontarget subjects and fine-tuning them with varying amounts of target subject data. Though we did not evaluate this approach, it is important to consider how our data structure and training processes may have influenced the outcomes.

To our knowledge, this is the first real-time IND ML system to continuously estimate slope on a lower-limb powered knee and ankle prosthesis, with an average error of 0.95 ± 0.08 deg. These results are comparable to similar lower-limb exoskeleton studies using extended Kalman filters, though our method outperformed previous efforts, which reported errors as high as 2.4 ± 1.3 deg RMSE due to high intersubject variability [40,57]. Furthermore, our system estimated slope achieving similar error values (1.03–1.81 deg) but at 50 Hz, a significant improvement over the more common approach of estimating once per gait cycle (∼1 Hz) [39].

We utilized the OSL, a compact system with embedded mechanical sensors, frequently used by researchers. Our analysis revealed that additional sensors, particularly the foot IMU, significantly improved slope estimation. The inclusion of the foot and thigh IMUs, along with a 6DOF loadcell, enhanced mode classification accuracy compared to the baseline sensor set (Fig. 5).

Despite these advancements, the primary limitation is that a fully “out-of-the-box” IND solution for novel users remains elusive. The number of subjects needed to achieve true generalizability is still unknown, and further validation on a larger, more diverse participant pool is required to make broader claims. While data augmentation techniques have been explored, more research is necessary to ensure these ML algorithms are robust to the variations and perturbations encountered in everyday walking. Although IND models outperform DEP models in handling day-to-day subject variation, our intent recognition system is still limited to specific ambulation modes. Future research should focus on expanding these systems to handle more dynamic and unstructured environments (e.g., side-stepping, backward walking, and shuffling).

Another limitation lies in mode classification performance. Our real-time IND classification system, which was commonly used method in previous studies, did not fare well, with 17.39% error, which achieved similar accuracy as the only previous real-time DEP study (14.10%) that classified ramps as separate classes that used only mechanical sensors [27,28,44]. This is consistent with other user-independent systems. Although many studies, including those using DEP systems, report better results in offline settings, we found that IND systems tend to have higher error when evaluated in real-time. We postulate that these errors were largely due to signal similarities between level walking and ramp transitions during the first step, where most misclassifications occurred [44,54,58]. We suggest that future studies should explore replacing hard mode classification with continuous regression approaches (e.g., speed and slope estimation) for high-level control [38,39]. Additionally, we acknowledge the imbalance in available training data between IND and DEP models, with IND models benefiting from a larger dataset drawn from multiple subjects. This imbalance, coupled with our relatively small sample size, particularly for DEP models, may limit the robustness of our conclusions. To bridge this gap, we included a SEMI model that looks to improve upon just a purely DEP system. Future work should explore methods such as data augmentation or alternative training strategies to ensure a more balanced and equitable comparison between IND and DEP systems.

In continuous estimation tasks, we must also consider delays introduced by the Kalman filter. With constant measurement noise, our model revealed time delays of 157–180 ms for user-detectable speed changes (∼1 Hz). These delays, combined with variable noise and static environmental modeling, could result in observable tracking delays during dynamic speed changes. Although continuous systems might address this, we argue that discrete mode classifiers remain valuable due to their ability to anticipate mode changes before environmental shifts occur.

Future work should explore how tuning parameters, such as stiffness and damping, influence the accuracy of slope and speed estimations, which are essential for real-time prosthesis adjustments to match dynamic user needs. Accurate estimations would ensure that the system is neither overly rigid nor overly responsive to environmental noise, thereby supporting stable, responsive control of the prosthesis. Implementing adaptive control strategies—beginning with offline tuning in controlled settings, followed by iterative adjustments in real-world scenarios—could refine both control parameters and estimators over time. This progressive approach, along with complex scaling functions for improved biomimicry to healthy biological limbs, will ultimately enhance the prosthesis's autonomous, task-specific functionality and responsiveness.

Our final contribution was to make our methods open-source (see Supplemental Materials on the ASME Digital Collection) and accessible to the research community. Azocar et al. previously released an N = 3 dataset of individuals with transfemoral amputations walking on the OSL across level ground, stairs, and ramps [12]. Expanding upon that work, the dataset presented in this paper contains a wide range of speed and slope data for level ground and ramp ambulation including additional data from IMUs located on the foot and thigh on 11 participants. This dataset offers a benchmark for future models and provides immediate access to deployable intent recognition systems. We believe that these advancements will contribute to the development of smarter prosthetic devices, which will soon become the gold standard in clinical practice, helping restore normal gait mechanics and improving the quality of life for individuals with limb loss [59].

Acknowledgment

We thank all of our participants who took part in this study. We also thank Dr. Elliott Rouse and the Neurobionics Lab from the University of Michigan for all their assistance and expertise with the OSL. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the Department of Defense.

Funding Data

  • Fulbright Fellowship (JC) Office of the Assistant Secretary of Defense for Health Affairs—Orthotics and Prosthetics Outcomes Research Program—Prosthetics Outcomes Research (Award No. W81XWH-21-1-0686 (AY); Funder ID: 10.13039/100005713).

Data Availability Statement

The data and information that support the findings of this article are freely available at this link.2

Nomenclature

DEP =

user-dependent

IMU =

inertial measurement unit

IND =

user-independent

MAE =

mean absolute error

ML =

machine learning

OFF =

offline

OSL =

Open Source Leg

REL =

relative change

RMSE =

root-mean-square error

RT =

real-time

SEMI =

semi-independent

Footnotes

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Supplementary data