Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: A simulation study

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.

1. 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 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)).
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 "total 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 353): 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 365: ...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 184.
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. (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 authors compare the metabolic savings of exoskeletons in literature to the results of simulations presented in the manuscript
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.

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 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)).
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 373 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" twice We 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' referenced
We 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][20][21] and a knee-ankle device [14].

-Line 43-45 the sentence is unclear and contractions should be expanded
We 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.

-Line 46 remove the word still
We 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.
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.
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.

METHODS
Currently, 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 assistance We 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 230: 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 242: 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 : "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  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. 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 discussion paragraph starting on line 323 to reflect the result from our statistical testing.

INTRODUCTION
Line 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.