### Exoskeleton hardware and control parameterization

Participants wore tethered bilateral torque-controlled ankle exoskeletons with a mass of 1.1 kg each. Exoskeletons were actuated by off-board motors connected via a series elastic Bowden cable transmission (Fig. 1) [23]. Insoles with 4 force sensing resistors (Nike, Inc.) were used to detect foot strike and toe-off. Strain gauges assembled in a full Wheatstone bridge were calibrated and mounted to the end effectors to measure applied torque about the ankle joint for feedback control. An identical set of the exoskeleton footwear (Nike, Inc.) was used to evaluate the metabolic cost of running without the exoskeleton (“normal shoes”).

The parameterization of desired torque patterns followed a similar approach to the powered assistance controller in [15], but with only three parameters that defined the timing of assistance: timing of peak torque (peak time), onset of torque (onset time), and return to zero torque (off time), all as percentages of average stance time. The peak torque magnitude, which was defined as the fourth parameter in [23], was fixed. The three timing nodes were connected by cubic spline to form an assistance torque curve.

### Participant demographics

Three recreational runners (*n* = 3; 1 F, 2 M; age: 22–41 years; body mass: 57.5–84 kg; height: 1.68–1.84 m) participated in this study (Additional file 1: Table A1). To be eligible for this extensive study design, each participant had previously run a half marathon, was running at least 20 miles per week, and could run comfortably for at least 1 h at a speed of 3.35 m/s (approximately 8 min/mile pace). These criteria ensured that the participant would be able to complete the experimental protocol in the aerobic respiration range, as the standard equation to calculate average metabolic rate is only valid for aerobic respiration [24]. All participants were consistent mid-to-rearfoot strikers at the study pace of 2.68 m/s. The study protocol was approved by the Stanford University Institutional Review Board, and all participants provided written informed consent before participating in the study. Participants were compensated 15 dollars per hour. Two additional participants were consented and participated but did not complete the study protocol due to circumstances surrounding the COVID-19 pandemic. These participants’ data were discarded.

The sample size of this study was informed by an a priori power analysis and resource tradeoffs. In a previous study, powered ankle exoskeleton assistance led to a metabolic cost reduction of 24.7 ± 6.9% relative to the unpowered condition (*n* = 11) [15]. Using this result, we found that a sample size of three participants gave a statistical power of 0.85 (two-tailed *t*-test, (alpha) = 0.05). Strict study inclusion criteria and lengthy protocol time (10 sessions lasting 4 h per session) favored a smaller sample size of well-trained participants. We performed two data collections per participant and per peak assistance torque level, one following optimization and one final validation session, to improve accuracy of within-participant results.

### Experimental protocol

Participants experienced 9 or 10 total experimental sessions, during which they ran on a treadmill (Woodway USA, Inc.) at a pace of 2.68 m/s (Fig. 2). Participants took at least 1 day of rest between each session. The first session was a short introductory session in which participants were introduced to the exoskeleton controller. Participants ran at least 5 min in the exoskeletons without assistance torque (“zero-torque”) followed by 5 min of generic assistance with timing similar to that from Witte et al. (2020) at a peak torque magnitude of 0.6 Nm/kg, normalized to participant body mass in kilograms [15]. Participants were encouraged to run in the devices (zero-torque or assisted) until they felt comfortable running in the exoskeletons (Additional file 2).

#### Optimization sessions

Following the introductory session, participants experienced 7 or 8 sessions of human-in-the-loop optimization to reduce metabolic rate as described in “Optimization Strategy” below. Participants fasted for 2 h before each session to reduce the thermic effect of food on metabolic rate measurements within each generation of optimization. This fasting requirement ensured that any metabolic rate measurements were taken after the initial steep increase in the thermic effect of food had passed [25]. The slow decline of the thermic effect of food on metabolic rate over the course of the study was assessed to have negligible effect on the reported metabolic results, especially because all validation trials were repeated in reverse. During each optimization, the peak assistance torque was fixed. In each experimental session, the optimization phase lasted approximately 1 h (including a 2-min warm-up with generic assistance). Following the final session of optimization at a fixed peak torque level, a series of 6-min validation trials were performed to evaluate the effects of assistance torque compared to zero-torque and normal shoes. Each experimental session lasted approximately 2.5–4 h with approximately 1–1.5 h of running.

Four peak assistance torque levels were evaluated to provide sufficient resolution across the search space within the constraints of a reasonable protocol length (up to 10 days). The highest level of peak torque that was found comfortable in pilot testing was 0.8 Nm/kg, normalized to participant body mass in kilograms. This value was slightly higher than the average optimized peak torque of 0.75 Nm/kg from a previous study [15]. The other three peak assistance torque levels were evenly spaced between the maximum value and zero torque: 0.6 Nm/kg, 0.4 Nm/kg, and 0.2 Nm/kg.

In the first 3 or 4 experimental sessions of optimization, participants experienced one of the higher assistance levels, beginning with 0.8 Nm/kg for Subject 1 and 0.6 Nm/kg for Subjects 2 and 3. The order of the first and second conditions was altered for two of the participants after the first participant experienced muscle soreness from beginning with the highest assistance level. The multi-session optimization ensured that the participants had adapted to the assistance and that the optimization parameters had fully converged. The optimization parameters were considered to have fully converged once the optimizer step size (sigma) (initially 10) dropped below half of the initial step size. The mean parameters from the end of the first and final session at the same assistance level were also compared to assess convergence.

After the longer optimization period at the first assistance torque level, participants then experienced 2 sessions with optimization at a different high assistance torque level (0.6 Nm/kg for Subject 1, 0.8 Nm/kg for Subjects 2 and 3). Two sessions were completed at this second assistance torque level to ensure participant adaptation translated to a different assistance torque condition, and that the optimizer had fully converged by the same step size criterion. Participants then experienced 1 session of optimization at each of the lower assistance levels (0.4 Nm/kg, then 0.2 Nm/kg). These shorter durations of optimization were a result of minimal shift in the optimized parameters and a clear downward trend in optimizer step size.

The ordering of peak torque conditions was chosen to maximize participant adaptation and facilitate optimization convergence. Poggensee and Collins (2021) found that novice users require over 100 min to learn how to maximally benefit from walking with ankle exoskeleton assistance, and that users adapt most slowly to peak torque magnitude [26]. Although all three participants in the present study had prior experience running with ankle exoskeleton assistance, additional sessions of optimization at the higher peak torque levels mitigated any effects of adaptation on the measured study outcomes. These training effects were expected to translate to lower peak torque levels. In addition, it is possible that beginning with the lowest peak torque magnitude of 0.2 Nm/kg would have resulted in poor optimization convergence. Low magnitude of assistance torque was expected to have less effect on metabolic rate, which could make it more challenging to identify the optimal timing parameters due to the higher noise-to-signal ratio and interaction effects between peak torque and timing of assistance.

During the final experimental session of optimization at a fixed peak torque level, a series of validation trials occurred after the optimization phase (“Day-by-Day Validation”), separated by a minimum break of 10 min. Each validation trial was 6 min in duration, with data collected from the last 3 min. In the first validation trial, participants stood quietly for 6 min to obtain their resting metabolic rate. The participants then ran in three separate validation conditions: assistance (the optimized assistance torque pattern at that peak torque level), zero torque, and normal shoes. These three running conditions were randomized and repeated in reverse (“bidirectional validation”) for a total of 6 running validation trials to reduce any effects of ordering on metabolic cost. Participants took at least 2 min of rest between running trials. These data were used to characterize the relationship between peak torque and metabolic cost reduction (referred to as “Day-by-Day Validation”).

In some interim sessions at the same peak torque level, validation was also performed to track participant adaptation to assistance (Additional file 1: Fig. A2). Due to some participant scheduling constraints, single-direction validation (trials were not repeated in reverse) or no validation was performed in some of these interim testing sessions. Less than 2% variation in metabolic cost reduction across experimental sessions indicated that the participant had become accustomed to running with the prescribed assistance torque level.

#### Final validation session

In the final experimental session (referred to as “Final Validation”), the effect of assistance across all 4 torque levels was compared against running with zero torque and normal shoes in a series of validation trials. No optimization occurred during this experimental session. At the beginning of the experimental session, participants stood quietly for 6 min to obtain their resting metabolic rate. Participants then ran in each of the 6 running conditions for 6 min, with data collected from the last 3 min. For each torque level, the subject-specific optimized assistance pattern was applied. The order of the running conditions was then reversed to improve measurement accuracy and reduce potential effects of ordering. The results of Final Validation were compared with the results of Day-by-Day Validation to ensure that the ordering of optimization sessions did not have an effect on participant adaptation.

### Human-in-the-loop optimization

Participants underwent human-in-the-loop optimization to determine the assistance timing parameters that maximally reduced their metabolic cost at each assistance torque level. A covariance matrix adaptation evolution strategy (CMA-ES) was used [15, 16]. Each generation of 7 candidate assistance strategies-defined by the three timing parameters discussed above-were sampled from a multivariate normal distribution about the current mean parameter set. Each candidate assistance strategy was applied to the participant for 2 min of running, during which an estimate of steady-state metabolic rate was obtained from raw respirometry data [27]. At the end of each generation, the metabolic rate results were used to update the mean parameter set and optimization state variables that defined the multivariate normal distribution. The candidate assistance strategies in the next generation were sampled from the resulting distribution.

During each optimization phase, participants experienced 4 generations of optimization for a total of 28 torque assistance strategies, equating to 56 min of running. The mean parameter set calculated from the final generation was used as the optimal assistance torque pattern at that peak torque magnitude for validation. For each participant, the optimization was initially seeded with the following set of mean timing parameters: onset time of 25% of stance, peak time of 75% of stance, and off time of 95% of stance. The optimization state variables were initialized using the same approach as [16]. The step size ((sigma)) was initialized to 10, and the covariance matrix was initialized to the identity matrix. Peak time and off time were scaled by a factor of two to allow for finer search, as those parameters had smaller comfortable ranges than onset time during pilot testing. During experimental sessions with continued optimization at the same torque level, the optimized mean parameter set and optimization state variables were carried over from the previous experimental session. At each subsequent torque level, the optimization was seeded with the optimized mean parameter set from the previous torque level, but the optimization state variables were reset to the baseline.

During optimization, each of the three timing parameters was restricted to a range that was comfortable in pilot testing: onset time ranged from 5 to 60 percent of average stance time, peak timing ranged from 40 to 80 percent, and off time ranged from 60 to 100 percent. After a new generation of assistance strategies was sampled from the current distribution, values sampled outside of the search region were projected onto the constraint boundary. Furthermore, the onset time and off time of torque were constrained to occur at least 20 percent before and after the peak time, respectively.

### Measured outcomes

#### Metabolic rate

The reported outcomes for each condition from a single experimental session are taken as the average from the two 6-min validation trials to reduce the effects of noise. Metabolic rate, the primary outcome of this study, was measured using a respirometry system (Quark CPET, Cosmed), which was calibrated according to manufacturer instructions. Carbon dioxide and oxygen rates were measured during the last 3 min of a validation trial and substituted into a standard equation [24] to obtain average metabolic rate. The metabolic rate reported for all running validation trials was calculated by subtracting the metabolic rate of the quiet standing validation trial from the metabolic rate for the running condition. Percent reduction in metabolic rate relative to zero torque was evaluated by dividing the change in metabolic rate from zero torque by the net metabolic rate from the zero-torque condition. Percent reduction in metabolic rate relative to normal shoes was evaluated by dividing the change in metabolic rate from normal shoes by the net metabolic rate from the normal shoes condition. All metabolic rate results were normalized to participant body mass.

#### Exoskeleton mechanics

Exoskeleton mechanics were evaluated using the last 3 min of data from each validation trial. Average exoskeleton work was calculated by integrating the exoskeleton torque over ankle angle during the stance period for each stride, then averaging across all strides. Average exoskeleton power was calculated by dividing average exoskeleton work by the average stride time, as no work was performed during swing. Peak exoskeleton power was calculated as the maximum over an average gait cycle of the product of torque and ankle angular velocity. All exoskeleton mechanics were normalized to participant body mass.

#### Step frequency and duty factor

Stride and stance time for a single leg were determined from force-sensing resistors at the heel, hallux (big toe), and first metatarsophalangeal (MTP) joint. Data from the lateral MTP joint sensor was not used because it frequently stayed compressed during swing. Data were collected during the last 3 min of each assistance validation trial. At each assistance torque level, stride time and stance time data were averaged across both legs and validation sessions (Day-by-Day and Final). Step frequency (SF) was calculated from single-leg stride time and reported in steps per minute: (text {SF} = 2 (frac{60}{t_{text {stride}}})). Duty factor (DF) was calculated as the ratio of stance over stride time: (text {DF} = frac{t_{text {stance}}}{t_{text {stride}}}).

### Statistical analyses

We pooled the data from the Day-by-Day Validation and Final Validation sessions for all participants to obtain the mean and standard deviation (SD) of the measured outcomes. To evaluate whether the level of assistance torque had an effect on the measured outcomes, we performed a mixed-effects ANOVA (fixed effect: peak torque; random effect: participant) to account for repeated measures. On measures that showed significant trends, we performed paired, two-sided t-tests comparing each assistance torque condition to the zero-torque condition from the same validation session for that participant with a Šidák-Holm stepdown correction for multiple comparisons ((alpha) = 0.05).

In addition, an exponential model (y = a cdot [1 – exp (bcdot x)]) was fit to the data relating peak assistance torque to percent change in metabolic rate using iterative non-linear least squares. Ninety-five percent confidence intervals (CI) were calculated for the fit parameters. Significance of the model fit was determined by an ANOVA model comparison with the constant model ((y = a)).

An asymptotic exponential model was selected over a linear model ((y = acdot x)) because it gives a theoretical maximum metabolic reduction that can be achieved as peak torque continues to increase. We would not expect percent change in metabolic cost to continue to decrease linearly, as the model would eventually predict an extreme at which there is no metabolic cost to run. Rather, we would expect the benefits of increasing assistance to level off as assistance replaces the contributions of the biological ankle. If the better model was indeed linear, the least squares exponential fit would be nearly linear in the region of interest and have a very large asymptote. Relative likelihood, which provides the likelihood that one model is a better fit to the data than the other, was used to compare the asymptotic exponential fit to a linear fit [28]. Relative likelihood is based on the Akaike information criterion (AIC), which estimates the relative amount of information lost by a given model using the maximum likelihood of the model. AIC also accounts for the number of parameters fit by the model, thus reducing the risk of overfitting. The relative likelihood formula for model comparison is given by (exp left( frac{text {AIC}(H_1) – text {AIC}(H_2)}{2} right)). The resulting value is the likelihood that Model 2 ((H_2)) results in less information loss than Model 1 ((H_1)). The residual sum of squares for each model was also calculated to compare the asymptotic exponential model to the linear model.

The significance level for all model comparisons was (alpha) = 0.05. Data processing was performed using Matlab (Mathworks, Inc.) and statistical analysis was performed in R (R Core Team).

### Effect of timing parameters

To evaluate the relative importance of the three timing parameters on metabolic cost, metabolic rate estimates from human-in-the-loop optimization were recorded for each assistance strategy. Across all three participants, a total of 637 assistance strategies were tested, each of which was associated with a peak torque level, onset time, peak time, off time, and an estimate of steady-state metabolic rate. We performed a mixed-effects ANOVA ((M = t_{text {onset}} + t_{text {onset}}^2 + t_{text {peak}} + t_{text {off}}); fixed effects: onset time ((t_{text {onset}})), peak time ((t_{text {peak}})), off time ((t_{text {off}})); random effects: participant, experimental session) to evaluate the effect of timing parameters on metabolic rate. Here, *M* is the steady-state metabolic rate, normalized to participant body mass (W/kg). In the optimization data, unlike the validation data, quiet standing metabolic rate was not subtracted because a measurement was not taken for every experimental session. Experimental session was treated as a random effect to capture offsets in metabolic rate between experimental days; this included metabolic rate offsets due to torque level and changes in quiet standing metabolic rate. A second-order polynomial was fit to onset time, as we would expect the cost landscape to be bowl-like. Because optimal peak time and off time were near the limit of the allowable range, the relationship between these timing parameters and metabolic rate were assumed to be linear in the region of interest. We assumed no interaction effects between timing parameters.

A single-subject pilot study (Subject 3) was conducted to further examine the effect of onset time on metabolic cost. Peak torque was fixed at 0.8 Nm/kg, and peak time and off time were fixed at the participant’s optimized values (79.7% and 100% of stance, respectively). Six minutes of quiet standing metabolic data were recorded at the beginning of the experimental session to obtain an estimate for resting metabolic rate. The participant then ran in a series of 6-min validation trials under six conditions: four conditions to sweep torque onset time (5%, 15%, 25%, and 35% of stance), zero-torque, and normal shoes. The order of these running trials was randomized. The running trials were repeated in reverse order for a total of 12 trials. The measured outcome of this pilot study was the percent reduction in metabolic rate over the zero-torque condition. A second-order polynomial least squares model was fit to the single-subject pilot study data relating onset time to percent reduction in metabolic rate. The adjusted R-squared value is reported in addition to the model significance.

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