Nicholas A Bianco1, Patrick W Franks1, Jennifer L Hicks2, Scott L Delp1,2,3. 1. Department of Mechanical Engineering, Stanford University, Stanford, California, United States of America. 2. Department of Bioengineering, Stanford University, Stanford, California, United States of America. 3. Department of Orthopaedic Surgery, Stanford University, Stanford, California, United States of America.
Abstract
Assistive exoskeletons can reduce the metabolic cost of walking, and recent advances in exoskeleton device design and control have resulted in large metabolic savings. Most exoskeleton devices provide assistance at either the ankle or hip. Exoskeletons that assist multiple joints have the potential to provide greater metabolic savings, but can require many actuators and complicated controllers, making it difficult to design effective assistance. Coupled assistance, when two or more joints are assisted using one actuator or control signal, could reduce control dimensionality while retaining metabolic benefits. However, it is unknown which combinations of assisted joints are most promising and if there are negative consequences associated with coupled assistance. Since designing assistance with human experiments is expensive and time-consuming, we used musculoskeletal simulation to evaluate metabolic savings from multi-joint assistance and identify promising joint combinations. We generated 2D muscle-driven simulations of walking while simultaneously optimizing control strategies for simulated lower-limb exoskeleton assistive devices to minimize metabolic cost. Each device provided assistance either at a single joint or at multiple joints using massless, ideal actuators. To assess if control could be simplified for multi-joint exoskeletons, we simulated different control strategies in which the torque provided at each joint was either controlled independently or coupled between joints. We compared the predicted optimal torque profiles and changes in muscle and total metabolic power consumption across the single joint and multi-joint assistance strategies. We found multi-joint devices-whether independent or coupled-provided 50% greater metabolic savings than single joint devices. The coupled multi-joint devices were able to achieve most of the metabolic savings produced by independently-controlled multi-joint devices. Our results indicate that device designers could simplify multi-joint exoskeleton designs by reducing the number of torque control parameters through coupling, while still maintaining large reductions in metabolic cost.
Assistive exoskeletons can reduce the metabolic cost of walking, and recent advances in exoskeleton device design and control have resulted in large metabolic savings. Most exoskeleton devices provide assistance at either the ankle or hip. Exoskeletons that assist multiple joints have the potential to provide greater metabolic savings, but can require many actuators and complicated controllers, making it difficult to design effective assistance. Coupled assistance, when two or more joints are assisted using one actuator or control signal, could reduce control dimensionality while retaining metabolic benefits. However, it is unknown which combinations of assisted joints are most promising and if there are negative consequences associated with coupled assistance. Since designing assistance with human experiments is expensive and time-consuming, we used musculoskeletal simulation to evaluate metabolic savings from multi-joint assistance and identify promising joint combinations. We generated 2D muscle-driven simulations of walking while simultaneously optimizing control strategies for simulated lower-limb exoskeleton assistive devices to minimize metabolic cost. Each device provided assistance either at a single joint or at multiple joints using massless, ideal actuators. To assess if control could be simplified for multi-joint exoskeletons, we simulated different control strategies in which the torque provided at each joint was either controlled independently or coupled between joints. We compared the predicted optimal torque profiles and changes in muscle and total metabolic power consumption across the single joint and multi-joint assistance strategies. We found multi-joint devices-whether independent or coupled-provided 50% greater metabolic savings than single joint devices. The coupled multi-joint devices were able to achieve most of the metabolic savings produced by independently-controlled multi-joint devices. Our results indicate that device designers could simplify multi-joint exoskeleton designs by reducing the number of torque control parameters through coupling, while still maintaining large reductions in metabolic cost.
Wearable robotic exoskeletons that reduce the metabolic cost of walking could improve mobility for many individuals including those with musculoskeletal or neurological impairments and assist soldiers and firefighters carrying heavy loads. Assistance strategies that reduce metabolic cost have only recently been discovered using both powered [1-4] and unpowered [5] devices. Despite these successes, designing controllers for exoskeletons can be counterintuitive and time-consuming. Some exoskeleton designs focused on biomimicry, where assistive devices attempt to emulate biological joint kinematics, kinetics, and power, but these seemingly intuitive approaches have had limited success in reducing metabolic cost [6, 7]. To better understand what aspects of exoskeleton assistance affect metabolic cost, many recent studies have designed assistance by varying the timing and magnitude of assistive torques and powers [8-12]. For example, a recent study showed that optimizing both assistance torque onset timing and average power together produces larger metabolic reductions than when considering each quantity alone [11]. More recent approaches, such as human-in-the-loop optimization experiments, which continuously optimize assistance for a subject based on real-time estimates of metabolic energy, have produced large reductions in metabolic cost [8, 10]. However, since each human-in-the-loop optimization evaluation requires several minutes of human metabolic data from indirect calorimetry, it is time-consuming and expensive to test a large number of devices. For example, a human-in-the-loop optimization may take several days of experimentation to complete.Simulations and experiments suggest that assisting multiple joints at once could deliver larger metabolic savings than assisting a single joint [12-15]. However, designing assistance for these “multi-joint” exoskeletons can magnify the challenges of optimizing the control, since such devices can include multiple actuators with independent control laws, which increases the number of parameters that must be tested in experiments. For example, the convergence time for human-in-the-loop optimization experiments scales poorly with increasing optimization variables, and therefore may be prohibitively long for multi-joint exoskeletons due to the large number of control variables needed for several assistive torques. As a result, most exoskeleton studies focus on assisting only one degree of freedom to simplify parameter design, usually preferring the hip or the ankle since they produce most of the positive power during walking and running [4, 16–18].Coupled assistance could greatly simplify the mechanical and control design of exoskeleton devices by reducing control complexity (i.e., the number of parameters personalized to a subject) and thus reducing the time needed to perform human-in-the-loop optimizations to achieve desired reductions in metabolic cost. Coupled assistance could also simplify the mechanical design of exoskeletons which could make the device lighter and less restrictive for the sure. Assisting two joints at once using one actuator, or “coupling” assistance, produced significant reductions in metabolic cost in recent exoskeleton studies with an ankle-hip soft exosuit [12, 19–21] and a knee-ankle device [14]. These studies exploit the similar timings of joint moments (e.g., the hip flexion moment and ankle plantarflexion moment reach a maximum at approximately the same point in the gait cycle). Other exoskeletons that assist multiple joints may be effective, but they have not been tested in experiments. Simulations could help us identify which combinations of joints to assist and how control could be coupled across joints, while achieving significant decreases in metabolic cost.Musculoskeletal simulation has become a valuable tool for examining the complex muscle-level and whole-body metabolic changes produced by exoskeleton devices [22]. Researchers have used simulation to analyze an existing exoskeleton and optimize its mechanical design [23] and to better understand human-device interaction [24]. Other studies have used simulation to help interpret experimental results, for example, to understand how muscle mechanics drive metabolic changes for an ankle exoskeleton [25]. Researchers have also used simulation to model exoskeleton devices as ideal actuators to discover guidelines for designing walking [26] and running [13] exoskeletons. A recent study [27] applied results from assisted running simulations [13] to design assistance for a soft running exoskeleton. The simulation-derived controls provided greater metabolic cost reductions compared to assistance designed based on biological joint moments, demonstrating the ability of simulations to improve exoskeleton design. Another recent study conducted by our group used simulation to design assistance for an experimental hip-knee-ankle exoskeleton, resulting in a large metabolic reduction [28]. While this study and the running simulation study examined multi-joint assistance [13], no study has used simulation to systematically compare different multi-joint assistance strategies for walking.In this study, we examined how simulated multi-joint assistance affects the metabolic cost of walking. We added ideal, massless assistive devices to a lower-extremity musculoskeletal model and simultaneously optimized muscle activity and device controls to match the net joint moments of normal walking and minimize metabolic cost. Each device assisted a single joint or assisted multiple joints simultaneously. Multi-joint devices could control assistance at joints independently or couple assistance for multiple joints, using the same control with independent peak torque magnitudes. We used the simulations to achieve two goals. First, we sought to estimate the metabolic savings provided by multi-joint exoskeletons during walking as compared to exoskeletons that assist only a single joint. Second, we sought to determine if coupled assistance could achieve similar metabolic savings compared to independent assistance. To address our second aim, we compared total and muscle metabolic cost savings and optimal device torques between coupled and independent multi-joint assistance.
Materials and methods
Experimental data
We used a previously-collected dataset from 5 healthy individuals walking on a treadmill (mean ± s.d.: age: 29.2 ± 6.3 years, height: 1.80 ± 0.03 m, mass: 72.4 ± 5.7 kg) [29]. Subjects in this previous study provided informed consent to a protocol approved by the Stanford Institutional Review Board. The data included marker trajectories, ground reaction forces, and electromyography (EMG) signals. For each subject, we simulated three gait cycles of walking at 1.25 m/s. One gait cycle was used in a model calibration step, and the other two were used for simulations of exoskeleton devices. For validating muscle activation patterns predicted from simulation, we used the processed EMG signals as described in the previous study [29], where signals were normalized by the highest value recorded across all walking speeds (see section “Comparison of simulations with experimental results”).
Musculoskeletal model
A generic 29 degree-of-freedom skeletal model was scaled to each subject’s data based on static marker trials [30]. Nine Hill-type muscle-tendon units, as modeled in a previous simulation study from our group [31], were included on each leg of the model: gluteus maximus, biarticular hamstrings, iliopsoas, rectus femoris, vasti, biceps femoris short head, gastrocnemius, soleus, and tibialis anterior. We used this reduced muscle set since we only simulated sagittal-plane exoskeleton devices and since fewer muscles kept the optimizations tractable. To create the set of nine muscles, we combined muscles (from the model of [30]) that had similar sagittal-plane functions into one muscle with a combined maximum isometric force value. Joint and muscle kinematics and net joint moments were computed through inverse kinematics and inverse dynamics tools using OpenSim 3.3 [32].
Simulation framework
We used a simulation framework [33] based on the GPOPS-II direct collocation optimal control software (Version 2.3) [34] to solve the muscle redundancy problem for unassisted walking. In each simulation, we solved for muscle activity while enforcing muscle activation and tendon compliance dynamics. Muscle kinematics were constrained to match muscle-tendon lengths and velocities obtained from inverse kinematics, and muscle-generated moments were constrained to match net joint moments computed from inverse dynamics. Since we only included sagittal-plane muscles in our model, only sagittal-plane joint moments (hip flexion-extension, knee flexion-extension, and ankle plantarflexion-dorsiflexion) were matched in each optimization. We assumed left-right symmetry of walking and therefore only solved for muscle activity in the right leg. Each problem included reserve torque actuators in addition to muscle-generated moments to help ensure dynamic consistency; these actuators were penalized in the objective function such that the muscles were the primary actuators enforcing the joint moment constraints. Each optimal control problem was solved with the Legendre-Gauss-Radau quadrature collocation method provided by GPOPS-II using an initial mesh of 100 mesh intervals per second. The initial mesh was updated using mesh refinement with a tolerance of 10−3 to reduce muscle activation and tendon compliance dynamic errors in the solution trajectories. The resulting nonlinear programs produced from the collocation method were solved with a convergence tolerance of 10−3 using IPOPT, the non-linear optimization solver [35].
Muscle parameter calibration
We calibrated the model’s muscle parameters so that estimated muscle activations would better match EMG measurements. Our model calibration approach consisted of three main steps. In the first step, we scaled maximum isometric force values based on a previously reported relationship between muscle volume and total body mass [36]. In the second step, we optimized optimal fiber lengths, tendon slack lengths, and passive muscle strain parameters while minimizing the error between model and reported experimental passive muscle moments [37]. We used MATLAB’s fmincon to minimize passive moment errors across a range of static joint positions with a rigid-tendon assumption for computing passive muscle force. In addition to the cost term penalizing deviations from experimental passive muscle moments, secondary cost terms were included to minimize total muscle passive force and prevent deviations from default parameter values which would lead to undesirable solutions with large passive forces in individual muscles.The third step of our model calibration used EMG data to further adjust the model’s muscle parameters. Passive muscle strain parameters were fixed to the values obtained from the first calibration step, and tendon slack length and optimal fiber lengths were again optimized within 25% of their original values, using the first-step calibration values as an initial guess. The error between EMG data and muscle excitations was the primary term minimized in the objective function. Passive muscle forces were also minimized to prevent undesired increases in passive forces due to the readjusted parameters. The muscle activations were also included as a lower-weighted, secondary objective term to aid convergence. The resulting muscle parameters were used in all subsequent simulations.
Exoskeleton device simulations
After calibrating the model for a given subject, we simulated unassisted and assisted gait using the subject’s remaining two gait cycles. In both unassisted and assisted gait, the primary objective was to minimize metabolic cost computed from a version of the metabolic energy model developed by Umberger et al. (2003) that was modified to have a continuous first derivative for gradient-based optimization [38, 39]. We included additional secondary objective terms to minimize muscle excitation, muscle activation, and the derivative of tendon force, all of which aided problem convergence. Since our simulation method relied on kinematics obtained from an inverse kinematics solution, the unassisted and assisted simulations used the same healthy walking kinematics (i.e., the simulation did not change the model’s kinematics in response to the assistive device). In the unassisted simulations, the muscles and the heavily-penalized reserve torque actuators were the only actuators available to reproduce the net joint moments.In the assisted simulations, exoskeleton devices were modeled as massless torque actuators and could apply torques to reduce muscle effort, while still matching the net joint moment constraints from inverse dynamics. The actuators had no power limits, but had peak torque limits for hip flexion-extension (1.0 N-m/kg), knee flexion-extension (1.0 N-m/kg), and ankle plantarflexion (2.0 N-m/kg); these peak torque limits were included to speed convergence and were chosen such that optimized device controls never exceeded the optimization bounds. Torques were applied in the following five joint directions: hip flexion, hip extension, knee flexion, knee extension, and ankle plantarflexion. Single-joint exoskeleton devices provided assistive torques in one of the five joint directions. Multi-joint exoskeleton devices provided assistance to the following combinations of joint directions: (1) hip-extension knee-extension, (2) hip-flexion knee-flexion, (3) knee-flexion ankle-plantarflexion, (4) hip-flexion ankle-plantarflexion, and (5) hip-flexion knee-flexion ankle-plantarflexion. The multi-joint exoskeleton devices were actuated by individual control signals (i.e., “independent” control) or with only one control signal applied to all joint directions (i.e., “coupled” control). When using coupled control, additional “gain” variables scaled the applied exoskeleton torques to allow different applied torque magnitudes since net joint moment magnitudes differed between the hip, knee, and ankle.For all unassisted and assisted conditions, we computed both total and muscle-level metrics of metabolic cost to assess device performance. The gross average total metabolic rate was computed by integrating the sum of individual muscle metabolic rates, multiplying by two (since we only solved for the right leg and assumed medio-lateral symmetry), dividing by the motion duration and total body mass, and adding a constant basal rate of 1.2 W/kg [38]. The average muscle metabolic rate was computed by integrating the metabolic rate of a muscle, multiplying by two, and dividing by the duration of the motion and body mass. Changes in both gross average total metabolic rate and average muscle metabolic rate due to assistance were computed as a percent of unassisted gross average total metabolic rate.
Validation approach
To validate our simulations, we compared musculoskeletal model outputs to experimental data. We compared the value and timing of peak joint moments and joint angles computed with OpenSim to values previously reported in the literature. Simulated muscle activations were compared to normalized EMG based on onset and offset timings as suggested by Hicks et al. (2015) [40]. For these comparisons, we defined muscles, both simulated and experimental, when their activation was above 5% of peak activation. Errors in muscle timing were defined when the simulated muscle activations were above the 5% threshold and the EMG was not above the threshold, and vice versa. We accounted for electromechanical delay in muscles by shifting the simulated muscle activations in time by 75 ms [41]. Timing errors were computed across the gait cycle, where 0% error indicated a perfect match at all time points and 100% error indicated no match across all time points.In addition to comparisons to experimental data, we computed a set of error metrics also based on suggestions by Hicks et al. (2015). We computed the RMS errors between experimental and model marker trajectories from inverse kinematics. To estimate the dynamic consistency of our simulations, we computed pelvis residual forces and moments from inverse dynamics across simulation gait cycles. Finally, we computed the RMS magnitude of the reserve torques to ensure that the constraints imposed to match experimental net joint moments was achieved primarily by muscle-generated torques.
Sensitivity analysis
We performed a sensitivity analysis to ensure that the convergence tolerance used in our walking optimizations did not affect our results. We varied the convergence tolerance between 1 and 10−4 and solved the unassisted walking problem for all subjects with the same gait cycles used to generate our results. We normalized objective values using the solution generated with the 10−4 tolerance and computed the mean and standard deviation across subjects and gait cycles (S4 Fig). The objective values for the 10−3 convergence tolerance, were close to a normalized objective value of 1 in our sensitivity analysis, meaning that tightening the tolerance to 10−4 would yield no improvement in objective values. Therefore, we used a 10−3 convergence tolerance for each walking optimization in this study.
Statistical testing
To compare the effect of devices on percent changes in metabolic cost, we employed a linear mixed model (fixed effect: device; random effect: subject) with analysis of variance (ANOVA) tests and Tukey post-hoc pairwise tests [42]. We used a significance level of α = 0.05. The data for the statistical analyses consisted of 75 observations (5 subjects and 15 devices); we averaged over the 2 walking trials used to simulate each single and multi-joint device to remove hierarchical structure from our data [43]. The statistical tests were performed with R [44-46].
Results
Device performance
All 15 ideal assistance devices–single joint, multi-joint coupled, and multi-joint independent–significantly decreased average total metabolic rate compared to unassisted walking (Fig 1, S2 and S3 Tables; p < 0.05). The largest reduction in metabolic cost among multi-joint devices was produced by the hip-flexion knee-flexion ankle-plantarflexion devices (34% coupled, 39% independent). Other multi-joint devices produced large metabolic savings: hip-flexion ankle-plantarflexion (29% coupled, 34% independent), knee-flexion ankle-plantarflexion assistance (30% coupled, 32% independent), and hip-extension knee-extension assistance (12% coupled, 14% independent). While independent assistance outperformed coupled assistance, the differences between coupled and independent were small (the percent change in cost for coupled assistance was 3.5% lower on average across multi-joint devices). The single-joint hip-flexion device provided the largest savings of the single joint devices (22% reduction), closely followed by knee-flexion assistance (21%). Multi-joint devices provided greater savings compared to single joint devices for all conditions (Tukey post-hoc test, p < 0.05) except for two conditions. First, coupled and independent multi-joint hip-extension knee-extension assistance was not significantly different from single-joint hip-flexion and knee-flexion assistance. Second, coupled hip-flexion knee-flexion assistance was not significantly different from single-joint knee-flexion assistance.
Fig 1
Reduction in metabolic rate for single and multi-joint assistance devices.
The percent change in gross total metabolic rate, averaged over the gait cycle, for the single joint (gray), multi-joint coupled (orange), and multi-joint independent (blue) assistance devices. Negative values indicate decreases in metabolic cost. Each bar value and corresponding error bar provides the mean reduction and standard deviation across subjects. Asterisks indicate devices that produced significantly larger metabolic reductions compared to single-joint devices.
Reduction in metabolic rate for single and multi-joint assistance devices.
The percent change in gross total metabolic rate, averaged over the gait cycle, for the single joint (gray), multi-joint coupled (orange), and multi-joint independent (blue) assistance devices. Negative values indicate decreases in metabolic cost. Each bar value and corresponding error bar provides the mean reduction and standard deviation across subjects. Asterisks indicate devices that produced significantly larger metabolic reductions compared to single-joint devices.
Muscle metabolic changes
The change in average muscle metabolic rates for a given multi-joint device were similar between the coupled and independent control devices. Both coupled and independent multi-joint hip-extension knee-extension assistance produced metabolic reductions in the gluteus maximus (5% coupled, 6% independent) and vastus intermedius (6% coupled and independent) muscles (Fig 2). Multi-joint hip-flexion knee-flexion assistance primarily reduced the iliopsoas average metabolic rate (19% coupled, 20% independent), and produced smaller reductions in the gastrocnemius (4% coupled and independent) and semimembranosus (2% coupled and independent) (Fig 3). Multi-joint knee-flexion ankle-plantarflexion assistance reduced the average metabolic rates of the soleus (11% coupled, 14% independent) and gastrocnemius (4% coupled and independent), but also produced a large reduction in the iliopsoas (15% coupled and independent), which was not directly assisted (Fig 4). Iliopsoas effort was reduced since rectus femoris activity increased to counteract knee-flexion assistive torque, as seen by the small increase in rectus femoris average metabolic rate (4% coupled and independent). Multi-joint hip-flexion ankle-plantarflexion assistance produced large metabolic reductions in the iliopsoas (19% coupled and independent) and soleus (12% coupled, 14% independent) (Fig 5). Multi-joint hip-flexion knee-flexion ankle-plantarflexion assistance similarly produced large iliopsoas (18% coupled, 19% independent) and soleus (11% coupled, 13% independent) metabolic reductions, and the added knee-flexion torque produced a reduction (rather than increase) in the semimembranosus (2% coupled and independent) and a larger reduction in the gastrocnemius (4% coupled and independent) (Fig 6).
Fig 2
Summary of multi-joint hip-extension knee-extension assistance.
Top: the device torques for multi-joint hip-extension knee-extension assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-extension knee-extension multi-joint devices reported in Fig 1.
Fig 3
Summary of multi-joint hip-flexion knee-flexion assistance.
Top: the device torques for multi-joint hip-flexion knee-flexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-flexion knee-flexion multi-joint devices reported in Fig 1.
Fig 4
Summary of multi-joint knee-flexion ankle-plantarflexion assistance.
Top: the device torques for multi-joint knee-flexion ankle-plantarflexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the knee-flexion ankle-plantarflexion multi-joint devices reported in Fig 1.
Fig 5
Summary of multi-joint hip-flexion ankle-plantarflexion assistance.
Top: the device torques for multi-joint hip-flexion ankle-plantarflexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-flexion ankle-plantarflexion multi-joint devices reported in Fig 1.
Fig 6
Summary of multi-joint hip-flexion knee-flexion ankle-plantarflexion assistance.
Top: the device torques for multi-joint hip-flexion knee-flexion ankle-plantarflexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-flexion knee-flexion ankle-plantarflexion multi-joint devices reported in Fig 1.
Summary of multi-joint hip-extension knee-extension assistance.
Top: the device torques for multi-joint hip-extension knee-extension assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-extension knee-extension multi-joint devices reported in Fig 1.
Summary of multi-joint hip-flexion knee-flexion assistance.
Top: the device torques for multi-joint hip-flexion knee-flexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-flexion knee-flexion multi-joint devices reported in Fig 1.
Summary of multi-joint knee-flexion ankle-plantarflexion assistance.
Top: the device torques for multi-joint knee-flexion ankle-plantarflexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the knee-flexion ankle-plantarflexion multi-joint devices reported in Fig 1.
Summary of multi-joint hip-flexion ankle-plantarflexion assistance.
Top: the device torques for multi-joint hip-flexion ankle-plantarflexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-flexion ankle-plantarflexion multi-joint devices reported in Fig 1.
Summary of multi-joint hip-flexion knee-flexion ankle-plantarflexion assistance.
Top: the device torques for multi-joint hip-flexion knee-flexion ankle-plantarflexion assistance with coupled (orange) and independent (blue) control compared to net joint moments (gray). Bottom: changes in average muscle metabolic rates as a percent of unassisted gross average total metabolic rate for the multi-joint assistive devices. Negative values indicate decreases in metabolic cost. Solid bars and error bars indicate the mean and standard deviation across subjects, respectively. Summing the individual muscle percent changes yields the total percent changes for the hip-flexion knee-flexion ankle-plantarflexion multi-joint devices reported in Fig 1.
Device torques and powers
Average peak device torques and powers were similar between coupled and independent multi-joint assistance for many of the devices (S2 Table), but there were some notable differences between peak torques and powers at individual degrees-of-freedom (S4 Table). For multi-joint hip-flexion knee-flexion assistance, a lower average peak knee-flexion torque was observed with coupled control (0.4 N-m/kg) compared to independent control (0.7 N-m/kg). However, despite this peak moment decrease, coupled control provided larger knee-flexion average peak power (1.7 W/kg) compared to independent control (1.0 W/kg). The largest differences in peak device torques were seen in ankle-plantarflexion assistance for multi-joint devices, but this did not necessarily result in similarly large metabolic changes. For example, the average peak ankle plantarflexion torque for independent knee-flexion ankle-plantarflexion assistance (1.6 N-m/kg) was larger than the average peak torque for coupled assistance (1.0 N-m/kg), but these devices produced similar metabolic savings (S2 Table, Fig 4). This could be partially explained by the relatively small difference in average peak powers at the ankle for knee-flexion ankle-plantarflexion multi-joint assistance between independent (3.4 W/kg) and coupled control (3.2 W/kg) (S4 Table). These results suggest that multi-joint assistance can exploit the timing of torque assistance to provide device powers necessary for large metabolic savings, even when coupled torque timing limits assistance torque magnitudes at individual joints.
Validation results
Joint moments (S1 Fig) and joint angles (S2 Fig) computed with OpenSim had similar peak values and timings compared to previously reported joint moments and joint angles for normal treadmill walking at a similar walking speed [47]. The onset-offset timing errors between simulated muscle activations and normalized EMG recordings, averaged across gait cycles and subjects, were as follows: gluteus maximus (28.4%), rectus femoris (31.4%), semimembranosus (32.1%), vastus intermedius (11.1%), gastrocnemius (17.0%), soleus (7.9%), and tibialis anterior (25.1%) (S3 Fig).Estimates of gross total metabolic rate (3.2 ± 0.2 W/kg, S1 Table) were lower than typical experimental values for normal unassisted walking (4.0–4.3 W/kg, [48]). This metabolic underestimation is likely because we did not include frontal-plane muscles (e.g., hip adductors-abductors) or upper-extremity muscles in our musculoskeletal model. However, since we were evaluating trends in percent metabolic changes between sagittal-plane single-joint and multi-joint devices and between coupled and independent multi-joint devices rather than absolute values of metabolic cost, we deemed this underestimation acceptable for the purposes of this study.The RMS errors between experimental and model marker trajectories from inverse kinematics had a mean value of 2.2 cm across lower-limb markers and simulation gait cycles. The mean RMS error in the pelvis residual forces, expressed as a percent of the peak ground reaction force (GRF) magnitude, was 4.8%, which is within the 5% guideline suggested by Hicks et al. (2015). The mean RMS error in the pelvis residual moments, expressed as a percentage of the product of average mass center height and peak GRF magnitude, was 2.8%, which exceeds the 1% guideline suggested by Hicks et al. (2015). However, given the good agreement between net joint moments and previously reported walking data and between muscle activity and EMG measurements, we deemed this error to be acceptable. Finally, the RMS magnitude of the reserve torques had a mean value of 0.06 N-m across degrees of freedom and simulations; the maximum error across time, degrees of freedom, and simulations was 2.01 N-m. The ratio of the RMS reserve magnitude to the maximum absolute net joint moment had mean and peak values of 0.1% and 3.7%, respectively, which meet the guideline of 5% provided by Hicks et al. (2015).
Discussion
We found that most multi-joint devices, both coupled and independent, could provide significantly larger metabolic savings compared to single-joint torque assistance in simulated lower-limb exoskeleton devices for walking. This is noteworthy considering that most current exoskeleton devices only assist one degree-of-freedom [3, 5, 8, 11, 49–51]. This is also promising for the recent development of multi-joint exoskeletons [12, 14, 15]. Our results suggests that designers should consider coupled multi-joint assistance when building multi-joint exoskeletons since coupled devices could reduce device weight and simplify device architecture by requiring fewer actuators. In addition, the largest metabolic reduction with coupled assistance occurred with hip-flexion knee-flexion ankle-plantarflexion assistance, suggesting that assisting more than two joints with one actuator can be beneficial. In many cases, peak assistive moments and powers were similar between coupled and independent multi-joint assistive devices, in spite of the reduced control complexity when coupling assistance between joints.We did not model device masses in our simulations, which would increase metabolic cost estimates, especially when adding mass to distal body segments [52]. We chose to assess the benefit from torque assistance separately from the exoskeleton designs, since devices that apply the same assistance can have varying metabolic penalties depending on actuator torque and power densities. This approach is similar to that of exoskeleton emulator systems, which use off-board motors to deliver torque assistance to the user and eliminate the cost of worn masses from actuators. In addition, when implementing our simulated assistance strategies in experiments, designers can account for the metabolic cost for wearing a particular exoskeleton design using the mass distribution of the device (e.g., by using the relationships in Browning et al. (2007) [52]).Other limitations of our simulation approach should be considered when interpreting our results. As previously mentioned, we excluded frontal plane muscles (e.g., hip adductors-abductors) from our simulations, but these muscles have important functions in walking, and this could partially explain why our simulation underestimates whole-body metabolic cost relative to ranges reported in the literature (S1 Table). Since muscles that act in the sagittal plane often also have moment arms in the frontal plane (e.g., adductor longus), our simulations may exclude muscle interactions between sagittal and frontal plane degrees of freedom [26]. We also did not include upper-extremity muscles in our simulations, which would have contributed to our total metabolic cost estimates. Since we used a minimal muscle set in our musculoskeletal model, absolute predictions of metabolic cost would be less reliable than comparisons between simulated assistance conditions. Therefore, for this study, we focused on the metabolic trends between single-joint and multi-joint devices and between coupled and independent multi-joint devices. As previously mentioned, there were quantitative differences between simulated and measured muscle activity (S3 Fig), so uncertainty in muscle model model parameters obtained from our calibration step may have also contributed to metabolic cost underestimates. In addition, while we optimized for metabolic cost in our simulations, users in exoskeleton experiments would likely also consider comfort, balance, or joint injury risk in response to assistance, and these factors may affect metabolic cost measurements. Absolute metabolic cost predictions from simulation could be made more accurate by including a full whole-body muscle set, including upper-extremity muscles, and optimizing for user comfort and safety (e.g., minimizing joint contact forces and ligament strains). Finally, we created simulations using experimental gait data from only five subjects, which may partially explain why some of the multi-joint devices we tested did not produce significantly different metabolic cost changes compared to single-joint devices.It is important to address how the noted limitations of the study are relevant to designers aiming to test coupled control strategies in experiments. First, we excluded frontal plane muscles in our simulations since we only tested exoskeleton devices acting in the sagittal plane. Some hip abductor-adductor muscles produce moments in the sagittal plane; thus, we would likely see differences in some of the metabolic changes we observed had we included these muscles. However, these frontal plane muscles would likely also benefit from device assistance, potentially leading to overall greater reductions. We also did not model upper extremity muscles, but including these muscles in our simulation approach would shift metabolic reductions for all devices by the same amount and not change the trends we observed. Lastly, we did not model device masses, which could influence percent metabolic changes as device masses increase. However, as noted previously, we chose to separate the effect of assistance from device mechanical design. Therefore, we would expect the trends we observed to hold in experiments where worn masses are consistent across tested assistance strategies. In summary, we believe that the metabolic trends observed between single-joint and multi-joint devices and between coupled and independent assistance will be replicable in experiments, even if differences in absolute metabolic cost measurements are observed.Future studies should build upon the simulation methods used in this study to further improve metabolic predictions. Users in experiments often adapt their kinematics in response to assistance (e.g., [5, 11, 12, 20, 27, 53–55]), but our simulations utilized an approach where kinematics were prescribed exactly based on normal walking data. Devices may cause different changes in walking kinematics depending on which joints were assisted and the torque or power applied to the user. Therefore, the metabolic cost trends we observed in our simulations could differ depending on the magnitude of kinematic adaptations between single and multi-joint devices. Predictive simulation methods that can optimize kinematic changes in addition to muscle adaptations could provide a better understanding of why exoskeleton users often change their gait with assistance. The inclusion of muscle synergies to constrain muscle activation predictions has been shown to improve predictions of subject-specific walking motions [56] and could potentially improve predictions of user adaptations to exoskeleton assistance. In addition, it has been shown that personalizing joint axes, electromechanical delays, activation dynamics time constants, and other musculoskeletal parameters can affect metabolic cost estimates and should be considered for future calibration methods [57]. Finally, muscle kinematic states estimated from ultrasound measurements for both assisted and unassisted walking could be used to calibrate metabolic models and improve predictions [58].Future work should include experimental testing of assistance strategies designed through simulation to help reveal where simulation methods fall short. For example, our group recently successfully reduced the metabolic cost of walking for a hip-knee-ankle exoskeleton using simulation-designed assistance [28], but percent changes in metabolic cost and estimated muscle activity changes from the simulation did not match well with experimental measurements. Therefore, combining simulations and experiments in an iterative loop could be particularly effective for designing assistive devices to reduce metabolic cost. Experiments should test the multi-joint strategies we simulated in this study to verify the metabolic relationships between coupled and independent control strategies and should especially consider coupled hip-flexion knee-flexion ankle-plantarflexion assistance, since this device outperformed all the two-joint devices in our simulations. Simulations could pair with experiments in other novel ways aside from this “predict-test-validate” framework. With the advent of human-in-the-loop optimization methods, simulation may not need to predict metabolic cost changes with high accuracy to have utility, but only to generate good initial guesses or help optimizers prioritize promising assistance control strategies.
Conclusion
We used musculoskeletal modeling and optimal control methods to simulate 15 single-joint and multi-joint ideal assistance devices. This work helps provide an understanding of the musculoskeletal factors driving the metabolic benefits of multi-joint assistance. Our results, showing that the greatest reduction in metabolic cost using a single actuator to assist multiple joints (39% reduction) was significantly larger than the reduction produced by the best single-joint device (22% reduction), suggest that exoskeleton designers should consider coupled assistance when designing multi-joint devices. Coupled assistance approaches could simplify wearable devices, increase metabolic reductions when actuation is limited, and help keep experiment times tractable. Designers can use these results as a guide for generating new hypotheses to test in exoskeleton experiments or when prototyping new exoskeleton designs. We invite researchers to use our freely available data (https://simtk.org/projects/coupled-exo-sim) and code (https://github.com/stanfordnmbl/coupled-exo-sim) to build upon our work.
Net joint moments.
Left: net joint moments from inverse dynamics for individual subjects. Right: joint moment means (black) and standard deviations (gray bands) across subjects.(TIF)Click here for additional data file.
Joint angles.
Left: joint angles from inverse kinematics for individual subjects. Right: joint angle means (black) and standard deviations (gray bands) across subjects.(TIF)Click here for additional data file.
Experimental electromyography data compared to unassisted simulation activations.
This figure shows electromyography data (gray bands) recorded from walking experiments compared to optimized activations generated from unassisted simulations (black). Both electromyography data and simulated activations are averaged across gait cycles not included in the muscle parameter calibration procedure.(TIF)Click here for additional data file.
Sensitivity of objective value to convergence tolerance.
The mean (bars) and standard deviation (whiskers) of normalized objective values for unassisted walking solutions across subjects and gait cycles. Objective values at each convergence tolerance are normalized by objective values using a convergence tolerance of 10−4. We used a convergence tolerance of 10−3 to generate our results, since tightening the tolerance to 10−4 had little effect on the objective (i.e., the normalized objective values were close to one for the 10−3 tolerance).(TIF)Click here for additional data file.
Muscle activations for unassisted and assisted simulations.
This figure shows muscle activations averaged across subjects for unassisted walking (black), single-joint assisted walking (gray), and multi-joint coupled (orange) and independent (blue) assisted walking.(TIF)Click here for additional data file.
Simulation-predicted unassisted metabolic rates.
This table shows the predicted gross average total metabolic rates for each subject. The columns represent the gait cycles used when testing single and multi-joint devices. These values underestimate experimental values typical of normal unassisted walking (4.0–4.3 W/kg, [48]).(TIF)Click here for additional data file.
Total metabolic reductions and device powers.
This table shows (a) relative and (b) absolute reductions in gross average total metabolic rate and the (c) peak positive, (d) average positive, and (e) average negative power for each single and multi-joint device. Quantities in columns (b)-(e) are normalized by subject mass. All columns are reported as mean ± standard deviation across 5 subjects.(TIF)Click here for additional data file.
Subject-specific relative metabolic reductions.
This table shows subject-specific relative reductions in gross average total metabolic rate for each single and multi-joint device. All quantities are percent reductions in metabolic cost relative to unassisted walking.(TIF)Click here for additional data file.
Peak device moments and powers at each degree-of-freedom.
This table shows the peak device moments and powers for individual degrees-of-freedom for each single and multi-joint device. All quantities are normalized by subject mass and are reported as mean ± standard deviation across 5 subjects. Peak moment values are peak magnitudes of device moments applied at each degree-of-freedom.(TIF)Click here for additional data file.5 Aug 2021PONE-D-21-10817Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: a simulation studyPLOS ONEDear Dr. Bianco,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.Thank you for this submission. The reviewers acknowledged the importance of the proposed research and pointed to the clarity of this manuscript. They brought up a couple of major questions. The questions related to the assumptions and limitations in this study (reviewer 1) and the methodological questions related to the statistical support of claims (reviewer 2) should be adequately addressed.Please submit your revised manuscript by Sep 19 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.Please include the following items when submitting your revised manuscript:A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.We look forward to receiving your revised manuscript.Kind regards,Sergiy YakovenkoAcademic EditorPLOS ONEJournal Requirements:When submitting your revision, we need you to address these additional requirements.1.Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found athttps://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf andhttps://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdfAdditional Editor Comments (if provided):Thank you for this submission. The reviewers acknowledged the importance of the proposed research and pointed to the clarity of this manuscript. They brought up a couple of major questions. The questions related to the assumptions and limitations in this study (reviewer 1) and the methodological questions related to the statistical support of claims (reviewer 2) should be adequately addressed.[Note: HTML markup is below. Please do not edit.]Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.Reviewer #1: PartlyReviewer #2: Partly**********2. Has the statistical analysis been performed appropriately and rigorously?Reviewer #1: N/AReviewer #2: No**********3. Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.Reviewer #1: YesReviewer #2: Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)Reviewer #1: Summary:This paper aims at investigating the relative benefits of exoskeleton assistance applied at lower limb joint(s). Musculoskeletal simulations are well employed to explore the design space possibilities of a coupled control algorithm. The results demonstrate the potential of coupled control of multi-joint exoskeletons to yield a metabolic benefit. The manuscript is well-written and the results of the manuscript may guide future development of assistive devices in this field. There are several issues to address.Major Comments1. While I understand the rationale behind using ideal massless actuators for simulation in this research, it is possible this assumption could affect the generalization of these results toward real world implementation of exoskeletons. Specifically, adding the mass of an assistive device to more distal joints would result in larger increases in lower limb moment of inertia and may have a larger metabolic penalty than adding the same mass to proximal joints. In this way, it’s possible that the added mass at a joint or multiple joints could affect the relative metabolic benefit of applied assistance as simulated here.2. The term ' whole-body metabolic rate' is misleading in reference to simulated metabolic rate because the authors are using a metabolic probe that incorporates muscle activity on a model with limited muscles in the lower limb, and no upper limb simulated muscle activity. The lack of the upper limb activity is not mentioned as a limitation, nor its potential effect on relative metabolic performance across simulated conditions. On Line 184 a reference should also be provided for the 1.2 W/kg basal rate.3. The author includes language in the methods/results section that would more appropriately be in the discussion. This is especially true in the "Comparison of simulations with experimental results" section, which may be more appropriate as a subsection of results rather than methods. Specifically, any comparison of the presented results to existing literature (lines 209-210), or interpretation of results (e.g. lines 211-212, 296-299) should be relocated to the discussion.4. The authors compare the metabolic savings of exoskeletons in literature to the results of simulations presented in the manuscript (lines 315-336) and offer many reasons why the simulated metabolic benefits are larger than measured metabolic rate. We agree with the authors’ assertion in lines 212-216 that the metabolic quantity calculated for this work is sufficient for comparing percent metabolic changes between assisted/unassisted simulations; however, there are several limitations to comparing the simulated metabolic rate to metabolic rates reported in literature which should be addressed: (1) The authors did not record any experimental metabolic measurements, and are using the minimization of simulated metabolic rate in the optimization, so there is no verification of the accuracy of simulated metabolic rate with experimental data (2) the calculation of simulated metabolic cost here excludes upper limb muscles and several lower limb muscles (3) the referenced previously collected data was limited to lower limb kinematics, and therefore the metabolic impacts of upper limb kinematics including trunk swing and arm motion were excluded.5. The authors are correct that the use of massless idealized actuators may impact the comparison of metabolic rates with experimental studies compared to the study by Quinlivan et al. (2017) (line 322). However, rather than only acknowledging the impacts of added mass on an individual comparison of simulated vs experimental metabolic outcomes, a statement at the beginning or end of this paragraph that references the metabolic impact of added mass effects on the simulations themselves and their relative performance should be added.6. The authors acknowledge that no kinematic changes were permitted between simulated conditions. However, additional discussion of whether different combinations of assistance are more of less likely to elicit altered kinematics, and how that may impact results.Minor- Lines 22-23 remove the word "from"-Lines 34-38 this statement is a bit difficult/unclear to read, especially with the use of "either" twice- Line 39 define the metric of 'success' referenced- Line 43-45 the sentence is unclear and contractions should be expanded- Line 46 remove the word still- Line 74-75 missing the word "compared" before "to"- Line 263 Muscle metabolic changes section could use quantitative values in the text to contextualize the stated reductions.Reviewer #2: The proposed manuscript is a computational study of the potential benefits of multi- and coupled-joint actuated exoskeletons. The study design is well conceived and straight-forward with reasonable modeling assumptions and could provide useful insight into the design of exoskeletons. However, there are several significant issues that must be addressed. Specifically, the manuscript lacks appropriate statistical analyses and does not provide sufficient subject-specific data. These limitations, combined with a relatively small sample size (5 participants, 3 gait cycles per participant), make it difficult to evaluate the study’s conclusions and could undermine the findings. These issues are described in more depth below.MAJOR REVISIONSMETHODSCurrently, the study lacks any inferential statistics or hypothesis testing. Although the paper makes two specific claims, 1) that multi-joint assistance increases metabolic savings compared to single-joint assistance and 2) that coupled multi-joint assistance achieves similar metabolic savings to single-joint assistance, neither of these hypotheses are specifically tested. This is particularly worrisome with the modest sample size used. For example, Figure 1 shows changes in gross average whole-body metabolic rate. The manuscript claims:Lines 259-261: “Multi-joint devices provided greater savings compared to single joint devices for all conditions except for multi-joint hip-extension knee-extension assistance, which was outperformed by single-joint hip-flexion and knee-flexion assistance.”While it is true that the average savings were greater for multi-joint devices, the error bars in Figure 1 are nontrivial. Appropriate hypothesis tests should be performed, especially with such a limited sampling size. Furthermore, the data would be more transparent for the reader if individual subject values and/or variances were provided in the main text and figures. While many of these raw data values are provided in the supplementary data, their omission from the primary manuscript could facilitate misinterpretation. The combination of 1) small sample size, 2) insufficient statistical methods, 3) frequent reliance on averaged values, and 4) unforthcoming individual values make the conclusions difficult to evaluate and could undermine readers’ confidence in the study findings. Therefore, it is critical that these issues be addressed across all the results and figures.Another specific example can be found in the section titled ‘Comparison of simulations with experimental results’:Lines 194-195: “The simulated muscle activations were similar to normalized EMG with a few exceptions (S3 Fig).”This language is very obtuse and subjective. Supplementary Figure 3 shows average recorded and simulated EMG profiles, but no quantification of their similarity. Some examples of error are sparsely listed:Lines 202-207: “The average peak values of simulated soleus and gastrocnemius activity were within 7% and 5%, respectively of the EMG measurements, but peaks occurred 13% and 9% later in the gait cycle, respectively, compared to the EMG measurements. Average peak simulated tibialis anterior activity was similar to the peak timing of EMG measurements (within 6% of the gait cycle), but had differences in activity magnitudes for some subjects”However, it is not clear how these errors are calculated, e.g. RMSE. Nor does it provide an indication of the variability of these errors across muscles or participants. Cross correlation, regression, or normalized RMSE would all provide better clarity and transparency of the model accuracy and one of these metrics, or an appropriate alternative, should be performed for each muscle.DISCUSSIONOverall, the discussion is well written and clear. The authors give reasonable speculation about why their simulations may have overestimated metabolic changes and, importantly, acknowledge several limitations of their work. They also appropriately relate their findings to other studies in the field of exoskeletons.There are, however, several claims which can not yet be made until the aforementioned issues are addressed and appropriate hypothesis tests are performed. They include:Lines 301-303: “We found that multi-joint torque assistance could provide larger metabolic savings compared to single-joint torque assistance in simulated lower-limb exoskeleton devices for walking.”Lines 306-309: “We found that the simulated multi-joint exoskeletons using coupled torque assistance could provide similar metabolic savings to those using independently-controlled torque assistance. This result suggests that exoskeleton designers should consider coupling torque actuators when building multi-joint exoskeletons.”MINOR REVISIONSINTRODUCTIONLine 1: “Wearable robotic exoskeletons that reduce the metabolic cost of walking could improve mobility for individuals with musculoskeletal or neurological impairments and assist soldiers and firefighters carrying heavy loads.”The current phrasing of this sentence insinuates that exoskeletons ONLY help soldiers and firefighters but their applications in the general population are much broader.Line 34: “Coupled assistance could greatly simplify the mechanical and control design of exoskeleton devices either by reducing either the number of actuators needed for a device or by simplifying control complexity (i.e., the number of parameters personalized to a subject) and thus reducing the time needed to perform human-in-the-loop optimizations to achieve good reductions in metabolic cost.”I believe there is a typo here: “…either by reducing either…”. There should be only one ‘either’.**********6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #1: NoReviewer #2: No[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.21 Sep 2021Reviewer #1SummaryThis paper aims at investigating the relative benefits of exoskeleton assistance applied at lower limb joint(s). Musculoskeletal simulations are well employed to explore the design space possibilities of a coupled control algorithm. The results demonstrate the potential of coupled control of multi-joint exoskeletons to yield a metabolic benefit. The manuscript is well-written and the results of the manuscript may guide future development of assistive devices in this field. There are several issues to address.We are glad the reviewer finds that our manuscript has the potential to positively impact future exoskeleton development via our coupled control approach. We are grateful for the reviewer’s thoughtful comments, which have improved the manuscript. We have revised the manuscript to address the reviewers comments, as described below.Major Comments1. While I understand the rationale behind using ideal massless actuators for simulation in this research, it is possible this assumption could affect the generalization of these results toward real world implementation of exoskeletons. Specifically, adding the mass of an assistive device to more distal joints would result in larger increases in lower limb moment of inertia and may have a larger metabolic penalty than adding the same mass to proximal joints. In this way, it’s possible that the added mass at a joint or multiple joints could affect the relative metabolic benefit of applied assistance as simulated here.We agree that the mass added to a body segment can influence the net metabolic change produced by an assistive device, especially when mass is added to distal body segments (Browning et al. 2007). We chose to exclude the masses of actuators from our devices to directly evaluate how the choice of control strategy affects changes in metabolic cost. This is because there could be multiple exoskeleton devices capable of applying a particular type of assistance, but the metabolic penalty of the device would depend on the device's design, mass-efficiency, and actuator torque and power densities. These designers could then estimate the expected mass penalty for their particular design using the mass distribution of the device. This approach is also often used experimentally by exoskeleton researchers. Exoskeleton experiments sometimes use emulator systems to reduce the mass added to the user by using off-board motors when designing device control strategies (e.g., Zhang et al. 2017, Quinlivan et al. 2017). With emulator systems, the expected benefit of assistance can be assessed independent of device architecture so that exoskeleton designers could know what benefit to expect. In this way, our approach mimics the approach of emulator experiments. We also excluded the constant mass of the emulator, since the metabolic cost of wearing this mass is also constant across control conditions. Adding this constant cost to our simulations would change percent differences in metabolic cost, but would not change the trends in metabolic cost changes we observed in our simulations.We have added the following paragraph to the Discussion section to clarify how excluding device masses may affect the performance of each simulated device and how this may impact our results:We did not model device masses in our simulations, which would increase metabolic cost estimates, especially when adding mass to distal body segments (Browning et al. 2007). We chose to assess the benefit from torque assistance separately from the exoskeleton designs, since devices that apply the same assistance can have varying metabolic penalties depending on mass-efficiency and actuator torque and power densities. This approach is similar to that of exoskeleton emulator systems, which use off-board motors to deliver torque assistance to the user and eliminate the cost of worn masses from actuators. While emulator systems add mass to the user, this mass, and the resulting metabolic cost, is constant across conditions. Therefore, while including the mass from an emulator system in our simulations would increase absolute metabolic cost predictions, it would likely not affect the trends in metabolic cost changes we observed in our experiments. In addition, when implementing our simulated assistance strategies in experiments, designers can account for the metabolic cost for wearing a particular exoskeleton design using the mass distribution of the device (e.g., by using the relationships in Browning et al. (2007)).2. The term ' whole-body metabolic rate' is misleading in reference to simulated metabolic rate because the authors are using a metabolic probe that incorporates muscle activity on a model with limited muscles in the lower limb, and no upper limb simulated muscle activity. The lack of the upper limb activity is not mentioned as a limitation, nor its potential effect on relative metabolic performance across simulated conditions. On Line 184 a reference should also be provided for the 1.2 W/kg basal rate.We agree that the term “whole-body metabolic rate” is misleading due to the lack of upper extremity muscles. We’ve renamed this term to “lower-limb metabolic rate” in the text and in the figures to better reflect the metabolic quantity we computed. We have added the following text to the Discussion section to explain this limitation (line 370):We also did not include upper extremity muscles in our simulations, which would have contributed to our total metabolic cost estimates.We have also revised the sentence starting on line 382:...could be made more accurate by including a whole-body muscle set, including upper-extremity muscles, and optimizing for user comfort...We have also added the reference for the 1.2 W/kg basal metabolic rate (Umberger et al. 2003) on line 190.3. The author includes language in the methods/results section that would more appropriately be in the discussion. This is especially true in the "Comparison of simulations with experimental results" section, which may be more appropriate as a subsection of results rather than methods. Specifically, any comparison of the presented results to existing literature (lines 209-210), or interpretation of results (e.g. lines 211-212, 296-299) should be relocated to the discussion.We agree that much of the content in the subsection “Comparison of simulations with experimental results” is appropriate within the Results. We have moved the appropriate text from this subsection to the Results and added a paragraph to the Methods summarizing our validation approach. While the lines comparing the validation results to existing literature (original manuscript lines 209-210, 211-212, and 296-299) could potentially be moved to the Discussion, we have left them in the Results section for clarity.4. The authors compare the metabolic savings of exoskeletons in literature to the results of simulations presented in the manuscript (lines 315-336) and offer many reasons why the simulated metabolic benefits are larger than measured metabolic rate. We agree with the authors’ assertion in lines 212-216 that the metabolic quantity calculated for this work is sufficient for comparing percent metabolic changes between assisted/unassisted simulations; however, there are several limitations to comparing the simulated metabolic rate to metabolic rates reported in literature which should be addressed: (1) The authors did not record any experimental metabolic measurements, and are using the minimization of simulated metabolic rate in the optimization, so there is no verification of the accuracy of simulated metabolic rate with experimental data (2) the calculation of simulated metabolic cost here excludes upper limb muscles and several lower limb muscles (3) the referenced previously collected data was limited to lower limb kinematics, and therefore the metabolic impacts of upper limb kinematics including trunk swing and arm motion were excluded.The reviewer raises many good questions about our comparisons between experimental metabolic cost reductions and the metabolic changes we observed from our simulation study. After considering these points, we agree that these comparisons are not as useful as the comparisons between simulation conditions due to the assumptions made for our study. We have decided to remove this paragraph and instead expand the Discussion to address the other comments made by the reviewer.5. The authors are correct that the use of massless idealized actuators may impact the comparison of metabolic rates with experimental studies compared to the study by Quinlivan et al. (2017) (line 322). However, rather than only acknowledging the impacts of added mass on an individual comparison of simulated vs experimental metabolic outcomes, a statement at the beginning or end of this paragraph that references the metabolic impact of added mass effects on the simulations themselves and their relative performance should be added.We agree that we should acknowledge if excluding device masses on our comparisons between simulated devices would affect predicted metabolic savings. We excluded device masses to isolate the effect of each assistance strategy independently from the variable device architectures that could deliver this torque assistance. If we were to include device masses in our simulations, we would assume a constant device architecture, similar to exoskeleton emulator experiments. A constant device architecture would add a constant mass to the exoskeleton user, which would incur a constant metabolic cost across simulation conditions. Adding this constant cost to our simulations would change percent differences in metabolic cost, but would not change the trends in metabolic cost changes we observed in our simulations. We have added the following paragraph to the discussion to summarize our modeling choices regarding device masses:We did not model device masses in our simulations, which would increase metabolic cost estimates, especially when adding mass to distal body segments (Browning et al. 2007). We chose to assess the benefit from torque assistance separately from the exoskeleton designs, since devices that apply the same assistance can have varying metabolic penalties depending on mass-efficiency and actuator torque and power densities. This approach is similar to that of exoskeleton emulator systems, which use off-board motors to deliver torque assistance to the user and eliminate the cost of worn masses from actuators. While emulator systems add mass to the user, this mass, and the resulting metabolic cost, is constant across conditions. Therefore, while including the mass from an emulator system in our simulations would increase absolute metabolic cost predictions, it would likely not affect the trends in metabolic cost changes we observed in our experiments. In addition, when implementing our simulated assistance strategies in experiments, designers can account for the metabolic cost for wearing a particular exoskeleton design using the mass distribution of the device (e.g., by using the relationships in Browning et al. (2007)).6. The authors acknowledge that no kinematic changes were permitted between simulated conditions. However, additional discussion of whether different combinations of assistance are more of less likely to elicit altered kinematics, and how that may impact results.The reviewer raises an important point that the fixed kinematics assumption may affect simulated devices differently depending which joints are assisted and the number of joints assisted. We have added the following to the Discussion paragraph starting on line 390 to provide more details about this modeling assumption and how it may have impacted our results:Devices may cause different changes in walking kinematics depending on which joints were assisted and the torque or power applied to the user. Therefore, the metabolic cost trends we observed in our simulations could differ depending on the magnitude of kinematic adaptations between single and multi-joint devices.Minor Comments- Lines 22-23 remove the word "from"We have made this change.- Lines 34-38 this statement is a bit difficult/unclear to read, especially with the use of "either" twiceWe have improved the clarity of the sentence on these lines by rephrasing to the following:Coupled assistance could simplify the control design of exoskeleton devices by reducing control complexity (i.e., the number of parameters personalized to a subject) and thus reducing the time needed to perform human-in-the-loop optimizations to achieve desired reductions in metabolic cost. Coupled assistance could also simplify the mechanical design of exoskeletons by reducing the number of actuators needed for a device which could be lighter and impose less restriction on the user.- Line 39 define the metric of 'success' referencedWe have clarified that “success” in this sentence refers to metabolic cost reductions:Assisting two joints at once using one actuator, or “coupling" assistance, produced significant reductions in metabolic cost in recent exoskeleton studies with an ankle-hip soft exosuit [12, 19-21] and a knee-ankle device [14].- Line 43-45 the sentence is unclear and contractions should be expandedWe have rephrased the sentence on these lines to be clearer:Other exoskeletons that assist multiple joints may be effective, but they have not yet been tested in experiments, since optimizing controls for multiple joints is often resource-intensive.- Line 46 remove the word stillWe have made this change.- Line 74-75 missing the word "compared" before "to"We have made this change.- Line 263 Muscle metabolic changes section could use quantitative values in the text to contextualize the stated reductions.We have added quantitative values for the muscle metabolic changes in the results subsection. We have also added error bars in the bar charts for Figures 2 through 6 representing standard deviations in muscle metabolic reductions across subjects.Reviewer #2The proposed manuscript is a computational study of the potential benefits of multi- and coupled-joint actuated exoskeletons. The study design is well conceived and straight-forward with reasonable modeling assumptions and could provide useful insight into the design of exoskeletons. However, there are several significant issues that must be addressed. Specifically, the manuscript lacks appropriate statistical analyses and does not provide sufficient subject-specific data. These limitations, combined with a relatively small sample size (5 participants, 3 gait cycles per participant), make it difficult to evaluate the study’s conclusions and could undermine the findings. These issues are described in more depth below.We are thankful for the reviewer’s thoughtful comments and are glad that our study shows promise for providing insight into device design. We have added statistical tests, which have strengthened our results and study conclusions, and provided better quantitative comparisons between simulated and experimental data. The revised manuscript addresses the reviewer’s comments as described below.Major CommentsMETHODSCurrently, the study lacks any inferential statistics or hypothesis testing. Although the paper makes two specific claims, 1) that multi-joint assistance increases metabolic savings compared to single-joint assistance and 2) that coupled multi-joint assistance achieves similar metabolic savings to single-joint assistance, neither of these hypotheses are specifically tested. This is particularly worrisome with the modest sample size used. For example, Figure 1 shows changes in gross average whole-body metabolic rate. The manuscript claims:Lines 259-261: “Multi-joint devices provided greater savings compared to single joint devices for all conditions except for multi-joint hip-extension knee-extension assistance, which was outperformed by single-joint hip-flexion and knee-flexion assistance.”While it is true that the average savings were greater for multi-joint devices, the error bars in Figure 1 are nontrivial. Appropriate hypothesis tests should be performed, especially with such a limited sampling size. Furthermore, the data would be more transparent for the reader if individual subject values and/or variances were provided in the main text and figures. While many of these raw data values are provided in the supplementary data, their omission from the primary manuscript could facilitate misinterpretation. The combination of 1) small sample size, 2) insufficient statistical methods, 3) frequent reliance on averaged values, and 4) unforthcoming individual values make the conclusions difficult to evaluate and could undermine readers’ confidence in the study findings. Therefore, it is critical that these issues be addressed across all the results and figures.We agree with the reviewer that statistical analyses would provide more confidence in our results. We performed statistical tests and found that the metabolic changes from multi-joint devices were significantly different from those from single joint devices (Tukey post-hoc test, p < 0.05), with the following exceptions:Coupled hip-flexion, knee-flexion assistance was not significantly different from knee-flexion only assistance.Coupled hip-extension, knee-extension assistance was not significantly different from hip-extension only and knee-extension only assistance.Independent hip-extension, knee-extension assistance was not significantly different from hip-extension only assistanceWe have added the following paragraph to the Methods section to describe our statistical testing:To compare the effect of devices on percent changes in metabolic cost, we employed a linear mixed model (fixed effect: device; random effect: subject) with analysis of variance (ANOVA) tests and Tukey post-hoc pairwise tests (Bretz et al., 2011). We used a significance level of α = 0.05. The data for the statistical analyses consisted of 75 observations (5 subjects and 15 devices); we averaged over the 2 walking trials used to simulate each single and multi-joint device to remove hierarchical structure from our data (Samuels et al., 1999). The statistical tests were performed with R (Core Team R, 2021; Bates et al., 2015; Hothorn et al., 2008).We have revised the Results section to include our findings from our statistical testing. Starting on line 237:All 15 ideal assistance devices–single joint, multi-joint coupled, and multi-joint independent–significantly decreased average whole-body metabolic rate compared to unassisted walking (Fig 1, S6 Table, S7 Table; p < 0.05).Starting on line 249:Multi-joint devices provided greater savings compared to single joint devices for all conditions (Tukey post-hoc test, p < 0.05) except for two conditions. First, coupled and independent multi-joint hip-extension knee-extension assistance was not significantly different from single-joint hip-flexion and knee-flexion assistance. Second, coupled hip-flexion knee-flexion assistance was not significantly different from single-joint knee-flexion assistance.Finally, we have added a new table in the supplementary material (S7 Table) that includes subject-specific metabolic reductions across all devices, and we have cited this table in the main text.Another specific example can be found in the section titled ‘Comparison of simulations with experimental results’:Lines 194-195: “The simulated muscle activations were similar to normalized EMG with a few exceptions (S3 Fig).”This language is very obtuse and subjective. Supplementary Figure 3 shows average recorded and simulated EMG profiles, but no quantification of their similarity. Some examples of error are sparsely listed:Lines 202-207: “The average peak values of simulated soleus and gastrocnemius activity were within 7% and 5%, respectively of the EMG measurements, but peaks occurred 13% and 9% later in the gait cycle, respectively, compared to the EMG measurements. Average peak simulated tibialis anterior activity was similar to the peak timing of EMG measurements (within 6% of the gait cycle), but had differences in activity magnitudes for some subjects”However, it is not clear how these errors are calculated, e.g. RMSE. Nor does it provide an indication of the variability of these errors across muscles or participants. Cross correlation, regression, or normalized RMSE would all provide better clarity and transparency of the model accuracy and one of these metrics, or an appropriate alternative, should be performed for each muscle.We agree that the comparisons between predicted muscle activations and experimental EMG signals could be improved. We computed a new metric to quantify the error in the onset and offset timings between simulated muscles and the EMG signals based on the suggestion provided by Hicks et al. (2015). We defined muscles, both simulated and experimental, as activated when above 5% of peak activation; this activation threshold was chosen to only compare regions of significant muscle activity. Errors in muscle timing were defined when the simulated muscle activations were above the 5% threshold and the EMG was not above the threshold, and vice versa. We accounted for electromechanical delay in muscles by shifting the simulated muscle activations in time by 75 ms (Seth and Pandy, 2007). Timing errors were computed across the gait cycle, where 0% error indicated a perfect match at all time points and 100% error indicated no match across all time points. The timing errors, averaged across gait cycles and subjects, were as follows: gluteus maximus (28.4%), rectus femoris (31.4%), semimembranosus (32.1%), vastus intermedius (11.1%), gastrocnemius (17.0%), soleus (7.9%), and tibialis anterior (25.1%).We’ve updated the sections in the Methods and Results to describe these new quantitative comparisons between muscle activations and EMG signals.DISCUSSIONOverall, the discussion is well written and clear. The authors give reasonable speculation about why their simulations may have overestimated metabolic changes and, importantly, acknowledge several limitations of their work. They also appropriately relate their findings to other studies in the field of exoskeletons.There are, however, several claims which can not yet be made until the aforementioned issues are addressed and appropriate hypothesis tests are performed. They include:Lines 301-303: “We found that multi-joint torque assistance could provide larger metabolic savings compared to single-joint torque assistance in simulated lower-limb exoskeleton devices for walking.”Lines 306-309: “We found that the simulated multi-joint exoskeletons using coupled torque assistance could provide similar metabolic savings to those using independently-controlled torque assistance. This result suggests that exoskeleton designers should consider coupling torque actuators when building multi-joint exoskeletons.”We are glad that the Discussion section is clear, and we agree that the conclusions could be strengthened by the suggested hypothesis testing. By addressing the comments related to statistical testing above, we believe we have sufficiently supported these conclusions by showing that most multi-joint devices (both using independent and coupled control) produced significantly greater metabolic cost savings compared to single-joint devices. We have rephrased the conclusion on lines 336-340 to reflect the result from our statistical testing:We found that for most multi-joint devices, the metabolic savings achieved with both coupled and independent torque control were significantly greater compared to single-joint devices. This result suggests that designers should consider coupled multi-joint assistance when building multi-joint exoskeletons, especially when reducing the number of actuators in an exoskeleton can optimize device weight and architecture.Minor CommentsINTRODUCTIONLine 1: “Wearable robotic exoskeletons that reduce the metabolic cost of walking could improve mobility for individuals with musculoskeletal or neurological impairments and assist soldiers and firefighters carrying heavy loads.”The current phrasing of this sentence insinuates that exoskeletons ONLY help soldiers and firefighters but their applications in the general population are much broader.We have rephrased this line to imply that exoskeletons could have a positive impact on populations outside of the examples we provide:Wearable robotic exoskeletons that reduce the metabolic cost of walking could improve mobility for many individuals including those with musculoskeletal or neurological impairments and soldiers and firefighters who frequently carry heavy loads.Line 34: “Coupled assistance could greatly simplify the mechanical and control design of exoskeleton devices either by reducing either the number of actuators needed for a device or by simplifying control complexity (i.e., the number of parameters personalized to a subject) and thus reducing the time needed to perform human-in-the-loop optimizations to achieve good reductions in metabolic cost.”I believe there is a typo here: “…either by reducing either…”. There should be only one ‘either’.We have fixed this typo and improved the clarity of this sentence on by rephrasing it to the following:Coupled assistance could greatly simplify the control design of exoskeleton devices by reducing control complexity (i.e., the number of parameters personalized to a subject) and thus reducing the time needed to perform human-in-the-loop optimizations to achieve reductions in metabolic cost. Coupled assistance could also simplify the mechanical design of exoskeletons by reducing the number of actuators needed for a device.Submitted filename: RebuttalLetterRev1.pdfClick here for additional data file.20 Oct 2021PONE-D-21-10817R1Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: a simulation studyPLOS ONEDear Dr. Bianco,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.Thank you for the revision that addressed all the major questions, as indicated by the enthusiastic review by both reviewers. There are a couple of minor points leftover that would improve the quality of this publication. The discussion could potentially have a brief interpretation of the null results and the requested discussion expansion of limitations. It would also be useful to identify the significant differences in the plotted comparisons. Otherwise, this submission is ready for publication.Please submit your revised manuscript by Dec 04 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.Please include the following items when submitting your revised manuscript:If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.We look forward to receiving your revised manuscript.Kind regards,Sergiy YakovenkoAcademic EditorPLOS ONEJournal Requirements:Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.Additional Editor Comments (if provided):Thank you for the revision that addressed all the major questions. There are a couple of minor points leftover that would improve the quality of this publication. The discussion could potentially have a brief interpretation of the null results and the requested discussion expansion of limitations. It would also be useful to identify the significant differences in the plotted comparisons. Otherwise, this submission is ready for publication.[Note: HTML markup is below. Please do not edit.]Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.Reviewer #1: All comments have been addressedReviewer #2: All comments have been addressed**********2. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.Reviewer #1: YesReviewer #2: Yes**********3. Has the statistical analysis been performed appropriately and rigorously?Reviewer #1: YesReviewer #2: Yes**********4. Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.Reviewer #1: YesReviewer #2: Yes**********5. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes**********6. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)Reviewer #1: (No Response)Reviewer #2: The authors have appropriately addressed my previous comments regarding the manuscript titled ”Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: a simulation study”. While I am satisfied with the edits, there are some minor points that I think could be expanded upon which would increase the overall quality of the publication. These points are described below.MethodsAfter performing the requested statistical testing, there are several comparisons in which the null hypothesis could not be rejected. It would be worthwhile for the authors to speculate why these specific instances did not provide metabolic savings compared to the other coupled assistance systems. Could insufficient sampling be excluded as a possibility? Or is 5 participants and only 3 steps of locomotion imply insufficient to detect the metabolic savings? If the sampling is appropriate, why do only some of the coupled systems show metabolic savings?DiscussionThe authors have, very appropriately, acknowledged several limitations, e.g. massless actuators, of their simulation study and have emphasized the necessity of experimental data to validate their findings. It may be worthwhile for the authors to expand on why they think these findings will be validated or why the assumptions they made are reasonable.Minor IssuesIt would be very helpful to the readers to indicate on the figures which comparisons were statistically significant (with * or some other visual).**********7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #1: NoReviewer #2: No[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.15 Nov 2021Reviewer #2The authors have appropriately addressed my previous comments regarding the manuscript titled ”Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: a simulation study”. While I am satisfied with the edits, there are some minor points that I think could be expanded upon which would increase the overall quality of the publication. These points are described below.We are glad that our edits have addressed the reviewer’s major concerns. We have further revised the manuscript to address the reviewer’s remaining comments related to statistical testing and the value of this study in light of the limitations, as described in detail below.MethodsAfter performing the requested statistical testing, there are several comparisons in which the null hypothesis could not be rejected. It would be worthwhile for the authors to speculate why these specific instances did not provide metabolic savings compared to the other coupled assistance systems. Could insufficient sampling be excluded as a possibility? Or is 5 participants and only 3 steps of locomotion imply insufficient to detect the metabolic savings? If the sampling is appropriate, why do only some of the coupled systems show metabolic savings?We agree that insufficient sampling could explain why the null hypothesis could not be rejected for these devices. Accordingly, we have added a sentence on lines 368-371:Finally, we created simulations using experimental gait data from only five subjects, which may partially explain why some of the multi-joint devices we tested did not produce significantly different metabolic cost changes compared to single-joint devices.We chose not to speculate broadly on why certain multi-joint devices did not produce significantly different metabolic cost changes compared to single-joint devices.DiscussionThe authors have, very appropriately, acknowledged several limitations, e.g. massless actuators, of their simulation study and have emphasized the necessity of experimental data to validate their findings. It may be worthwhile for the authors to expand on why they think these findings will be validated or why the assumptions they made are reasonable.We are glad that the previous revisions adequately address the reviewer’s comments about the limitations of our study. As suggested, we updated the discussion to note why our findings are valid and assumptions are reasonable. These updates are included in the revised manuscript (line 372-388).Minor IssuesIt would be very helpful to the readers to indicate on the figures which comparisons were statistically significant (with * or some other visual).As suggested, we have updated Figure 1 to include asterisks to visualize which multi-joint devices produced significantly different metabolic cost changes compared to their respective single-joint devices. We have also updated the Figure 1 caption to reflect the change.Submitted filename: RebuttalLetterRev2.pdfClick here for additional data file.1 Dec 2021Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: a simulation studyPONE-D-21-10817R2Dear Dr. Bianco,We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.Kind regards,Sergiy YakovenkoAcademic EditorPLOS ONEAdditional Editor Comments (optional):Thank you for the thorough revision. All reviewers are in agreement that this work is ready for publication.Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.Reviewer #2: All comments have been addressed**********2. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.Reviewer #2: Yes**********3. Has the statistical analysis been performed appropriately and rigorously?Reviewer #2: Yes**********4. Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.Reviewer #2: Yes**********5. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #2: Yes**********6. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)Reviewer #2: The authors have addressed all of my previous concerns. They have added an appropriate statistical analysis, acknowledged the study's limitations, and provided reasonable rationale for their modeling assumptions. Although the sample size could still be a reason for pause, this limitation has been acknowledge more explicitly.**********7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #2: No14 Dec 2021PONE-D-21-10817R2Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: a simulation studyDear Dr. Bianco:I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.If we can help with anything else, please email us at plosone@plos.org.Thank you for submitting your work to PLOS ONE and supporting open access.Kind regards,PLOS ONE Editorial Office Staffon behalf ofDr. Sergiy YakovenkoAcademic EditorPLOS ONE
Authors: Apoorva Rajagopal; Christopher L Dembia; Matthew S DeMers; Denny D Delp; Jennifer L Hicks; Scott L Delp Journal: IEEE Trans Biomed Eng Date: 2016-07-07 Impact factor: 4.538
Authors: Brandon N Fournier; Edward D Lemaire; Andrew J J Smith; Marc Doumit Journal: IEEE Trans Neural Syst Rehabil Eng Date: 2018-07-09 Impact factor: 3.802
Fig 1
Fig 2
Fig 3
Fig 4
Fig 5
Fig 6