Our data suggest that passive elastic ankle exoskeletons can reduce metabolic cost at multiple, but not all, walking speeds (Fig. 2). The lowest tested exoskeleton rotational stiffness condition (50 Nm rad-1) resulted in a metabolic reduction of -4.2% at slow (1.25 m s-1) and -4.7% at fast (1.75 m s-1) walking speeds when compared to no assistance (i.e. kexo = 0 Nm rad-1 = zero-torque). The results from this study for walking at 1.25 m s-1 (Fig. 2A) support findings from our previous study where rotational stiffness was applied using physical springs rather than the emulated elastic system we present here . At slow and fast walking speeds, we confirm a second order relationship (k2exo) between exoskeleton rotational stiffness and the users’ net metabolic power, indicating a ‘sweet-spot’ such that balancing a trade-off between very high stiffness (not too stiff) and very low stiffness (not too compliant) is necessary to achieve metabolic benefit. Surprisingly, no exoskeleton stiffness condition resulted in an average decrease in metabolic cost at the intermediate speed (1.5 m s-1). Rather, for walking at 1.5 m s-1, we observed a monotonic linear increase in users’ net metabolic rate with increasing exoskeleton stiffness (Fig. 2B).
Using our extensive set of human neuromechanical data across a range of functionally relevant walking speeds, we endeavored to gain a comprehensive understanding of the effect of passive-elastic ankle exoskeleton assistance on lower-limb joint mechanics and muscle activity and establish which factors drive changes in users’ whole body metabolic rate. Traditionally, exoskeleton effects have been analyzed at a single speed where it is assumed that even with the addition of exoskeleton assistance, the stride time remains relatively consistent. The traditional approach calculates an average moment per stride (or period of interest) which is then compared to the metabolic rate (energy per second). For conditions with constant stride times, this approach may be sound. However, to enable the comparison of metabolic rate and other neuromechanical metrics across a wide range of exoskeleton stiffness and multiple speeds, the assumption of constant stride time is no longer sound, and the comparison of average moment per stride (no indication of time) to energy per time did not seem appropriate. Inspired by the field of integrative physiology and research findings from Taylor, Kram, and colleagues [36-42], we calculated the rate of the metric of interest (e.g. ankle moment, muscle activation) computed as the average of the metric per unit time (e.g. average moment per second, or average muscle activation per second). Upon inspection, the changes in rate metrics that were observed across exoskeleton stiffness and walking speed conditions were likely due to both changes in the average magnitude of the metrics and the duration of the stride (Supp. Tables 2-4). We used the rate of the metric of interest (average per second) for a more apt comparison to metabolic rate (J s-1) (See  for a similar approach).
With this approach, we sought to determine which factors drive changes in users’ whole body metabolic rate across speeds. Whole body metabolic rate during walking can in part be attributed to the energetic cost of active muscle contraction (i.e., use of ATP for cycling cross-bridges) across the lower-limbs. Recent work in muscle energetics shows that muscle stretch-shorten cycles requires similar amounts of energy to an isometric contraction over the same duration which suggests that muscle energy use may be more closely tied to costs of force rather than work production . In an exoskeleton hopping study, metabolic cost was reduced when muscle force was reduced but muscle work remained constant . Thus, we anticipated that much of the metabolic improvement from an elastic ankle exoskeleton would be provided by reducing biological ankle joint moment and therefore plantarflexor muscle-tendon force and ultimately active muscle volume of the calf muscles . This would suggest that applying more torque assistance to reducing biological muscle loading as much as possible should be the best way to maximize metabolic benefit of an exoskeleton.
Our results suggest that to some extent the simple solution that exoskeletons reduce biological joint moments, muscle-tendon forces and active muscle volume appears correct. Indeed, the conditions where we achieved a reduction in metabolic cost (kexo=50 Nm rad-1 at 1.25 and 1.75 m s-1) also exhibited measured reductions in biological ankle moment (Figs. 3A and 5A, Supp. Fig. 2B) and reduced soleus muscle activity (Figs. 3C and 5C, Supp. Fig. 2A). However, our data also suggest that across walking speeds, more assistance (i.e., higher exoskeleton stiffness) is not better, and that when a ‘sweet-spot’ where metabolic benefit is achieved is found, it results from balancing appropriate amounts of exoskeleton torque assistance with deleterious side effects that can manifest via altered motor coordination, limb-joint kinetics and muscle-tendon dynamics [47-50]. For example, when further evaluating users’ physiological response to elastic ankle exoskeletons at each speed in isolation, qualitative trends in the effect of increasing device stiffness on ‘non-local’ neuromechanics (i.e., not ankle plantarflexors) were consistent and pointed toward potential metabolic penalties. Increasing exoskeleton assistance consistently resulted in increased MG, LG, and TA muscle activity (Supp. Fig. 2B, C, D). In addition, at the knee, for each of the speeds we studied, we measured a substantial increase in muscle activation from the BFL (Supp. Fig. 2E) that was accompanied by an expected concomitant shift from knee extension to knee flexion moment (Supp. Fig. 3B). Despite these consistent qualitative, if not quantitative, trends in users’ joint an muscle level neuromechanical response to increasing exoskeleton stiffness, it was difficult to find a simple mechanical explanation for the differences in the observed relationships between exoskeleton stiffness and users’ net metabolic rate at both slow and fast speeds (‘bowl-shaped’ at 1.25 and 1.75 m s-1) versus at the intermediate walking speed (monotonically increasing at 1.5 m s-1).
One possibility was that the ankle exoskeleton mechanical performance across stiffness could have been speed dependent, rendering it least effective at 1.5 m s-1. In fact, contrary to the dynamics of the biological ankle, where both the moment and power increase steadily with speed [18, 51], exoskeleton torque actually decreased with increasing walking speed (Supp. Fig. 1B). These results are perhaps not surprising considering passive-elastic exoskeleton torque is driven by the user’s ankle joint kinematics and peak ankle dorsiflexion is known to decreases with increasing walking speed . Indeed, our results indicate that peak ankle dorsiflexion decreased by 11% in unassisted conditions across speed and by as much as 43% in the stiffest exoskeleton within a given speed. As a result, we observed very little increase in exoskeleton positive/negative power with speed and increases in exoskeleton power were small compared to increases in biological power calculated from our unassisted trials (47%) and previous work performed over the same speed range (45%) .
Despite the inability of our passive-elastic ankle device to increase its mechanical output with increasing speed, we found no relationship between exoskeleton positive power (= positive work rate) and users’ net metabolic rate (Fig. 6, Table 1). This is in contrast to previous results from active devices, where exoskeleton mechanical power output seems to drive user benefit [4, 5, 7, 26, 53]. Perhaps this incongruity stems from fundamental differences in the timing of assistance torque, as most active ankle systems are specifically designed to inject positive power to during late stance push-off. Our passive-elastic ankle exoskeletons apply torque to offload biological plantarflexor force with onset much earlier in stance. However, neither changes in users’ biological positive power (i.e. work rate) or biological moment rate could explain the changes in net metabolic rate across all speeds (Fig. 6, Table 1). The lack of relationship between changes in users’ biological moment rate and metabolic rate may seem to contradict the idea that muscle force drives metabolic energy consumption; however, ankle moment is calculated as an externally measured net moment and does not account for co-contraction of antagonists muscles crossing the joint. Thus, an increase in co-contraction of dorsiflexors (e.g., TA) would result in underestimation of plantarflexor muscle force when derived from biological ankle moment. Indeed, we measured a significant increase in TA muscle activity with increasing exoskeleton stiffness which suggests an increase in co-contraction across the ankle. Therefore, in this study, changes in biological ankle moment were likely a poor representation of changes in plantarflexor muscle force and may help explain the poor relationship between changes in biological moment and changes in net metabolic rate.
A closer look at changes in ankle muscle activity reveals a nuanced trade-off between beneficial reductions in plantarflexor activity and costly increases in antagonist dorsiflexor activity across the range of exoskeleton stiffnesses we tested (Figs. 3C, 4C, 5C). In fact, we find that the change in SOL+TA activation rate universally explains the bowl-shape net metabolic rate versus exoskeleton stiffness relationship at 1.25 m s-1 (R2 = 0.56) and 1.75 m s-1 (R2 = 0.69) and also the lack of bowl-shape relationship at 1.5 m s-1 (R2 = 0.64) (Fig. 6, Table 1). Although there was no statistical linear effect of stiffness on SOL+TA activation, the intermediate walking speed (1.50 ms-1) was the only condition in which the data suggest that SOL+ TA activation was not reduced. While the data suggest that SOL activation rate decreased at 50 Nm rad-1 for all three speeds, TA activation rate was substantially increased at the intermediate speed (18%) in comparison to the increase in TA activation rate at slow (1.25 ms-1) and fast (1.75 ms-1) walking speeds (~2%). The changes in activation rate that were observed across exoskeleton stiffness and walking speeds were likely due to both changes in the average magnitude of the activation and the duration of the stride (Supp. Tables 2-4).
As mentioned earlier, and consistent with our previous experimental  and modeling/simulation  results for walking at 1.25 m s-1, our data here show that humans respond to increasing ankle exoskeleton stiffness with deleterious side effects manifesting via altered motor coordination (Supp. Fig. 2), limb kinetics (Supp. Figs, 1,3,4), and muscle-tendon dynamics across the entire range of normal walking speeds (1.25-1.75 m s-1). But why is it that ‘more is not better’? Or more concisely, what physiological mechanisms may be preventing participants from converting larger and larger local reductions in biological plantarflexor muscle loading to metabolic savings? First, we note a trend toward diminishing returns, where between the kexo=150 and 250 Nm rad-1 conditions, although the exoskeleton stiffness is increased by 67%, peak exoskeleton torque increases by only 13% (Fig. 3A). Furthermore, we observe that participants compensated by decreasing the amount of ankle dorsiflexion (Supp. Fig. 1), but the mechanism for this compensation is unclear. One potential explanation is that the user is unable to ‘turn down’ their muscle activation in proportion to the level of assistance provided. Research has shown that joints (and limbs) maintain constant stiffness during a given locomotion condition . It is believed that this is accomplished through a combination of physiological sensors including length (spindle organs) and force (Golgi tendon organs) sensitive transducers that are responsible for maintaining a nearly constant ratio between changes in muscle force and length [54, 55]. We observed a decrease in ankle moment from which we can predict a decrease in plantarflexor muscle force. On the other hand, studies suggest that muscle fascicle lengths become longer with increasing exoskeleton assistance . Thus, a conflict or mismatch in sensory feedback via Golgi tendon and muscle spindle organs could potentially constrain motor adaptation in response to assistive forces. Much of walking is automatic and unconsciously controlled though spinal level central pattern generators, reflexes, cerebellar regulation, and the brainstem . For this reason, users of the exoskeleton may not be able to turn off their plantarflexors as would be required to obtain maximal benefit or coordination with the exoskeleton. Further work in humans and animals into the role of feedforward/feedback mechanisms and how they are modulated during perturbed walking would be insightful and help understand constraints on motor adaptation during walking with exoskeletons.
Another potential side effect of applying exoskeleton assistance was that the normally efficient muscle-tendon dynamics could become ‘detuned’. Muscles dynamics are governed by intrinsic muscle properties where force production and economy are dependent upon the length of a muscle and its contraction velocity [57, 58]. When exoskeleton assistance is applied, biological moment and thus muscle-tendon force decreases, while strain on the tendon decreases. Modeling and experimental studies of hopping [45, 48, 59] and walking [43, 47, 50] with ankle exoskeletons suggest that muscle lengths are in fact longer and undergo increased excursion with increased exoskeleton assistance, and this could limit muscle force capacity and metabolic economy. As well, the biological system may be resistant to increased muscle strain to avoid injury and compensations may arise to limit range of motion [60-62]. A closer look at the effect of elastic ankle assistance on plantarflexor muscle fascicle dynamics may give additional insights into how external forces applied in parallel with biological muscle-tendon units could be controlled to steer individual muscle dynamics [43, 46].
At the joint-level, in early stance, the application of elastic exoskeleton torque did not significantly reduce the biological moment (Figs. 3Aii, 4Aii, 5Aii), but rather enhanced the amount of total ankle moment (i.e., augmentation) (Supp. Fig. 1B). In late stance, on the other hand, the exoskeleton reduced the biological moment while the peak total ankle moment remained fairly constant (i.e., replacement) (Figs. 3Aiii, 4Aiii, 5Aiii). These findings raise the question if, as literature suggests, humans act to maintain a constant total ankle joint moment during walking  then why was the total ankle moment increased during the beginning of stance? One possible explanation is that the biarticular MG and LG muscles become ‘overactive’ to prevent hyperextension of the knee (Supp. Fig. 2 B, C). Due to the kinetic chain within the lower limb, the plantarflexion torque of the exoskeleton also generates an extension moment at the knee through dynamic coupling . Perhaps as a compensation for the increasing knee extension moment with increasing exoskeleton stiffness, MG and LG increased activity that may have served as a countermeasure to push the knee towards flexion (Supp. Fig. 2 B, C; Supp. Fig. 3B). The increased activation of the BFL, which is a knee flexor, also supports the idea that additional muscle activation was required for knee flexion (Supp. Fig. 2E). The effect exists for the entire stride but may be more critical in early stance when the ground reaction force vector briefly passes in front of the knee. The gastrocnemius moment arm is also larger at the knee for more extended postures , giving it more leverage during early stance. It may be possible to avoid costly compensations by using biarticular exoskeleton designs that incorporate a knee component designed to act in a similar manner to the gastrocnemius and compensate for additional load on knee flexors derived from assistive ankle torques . Alternatively, an exoskeleton with a non-linear or piecewise linear stiffness profile where ankle stiffness stayed low until the ground reaction force vector passed behind the knee could also be a potential solution. Unfortunately, delaying the onset angle for the exoskeleton spring or limiting stiffness also has the effect of limiting the amount of energy that can be stored and returned in the device.
Contrary to our expectation, we did not find that optimal exoskeleton stiffness increased substantially with walking speed. Based on the computed exoskeleton stiffness at minimum net metabolic rate from our fitted regressions, we estimate that the optimal stiffness for slow (70 Nm rad-1 at 1.25 m s-1) and fast (79 Nm rad-1 at 1.75 m s-1) walking speeds were similar. The increase in optimal exoskeleton stiffness that we measured (13%) was not proportional to the estimated speed-dependent increase in ankle quasi-stiffness during plantarflexion (21%) or dual-flexion (i.e., late dorsiflexion) (46%) calculated from regression models derived from human walking data . Instead, the 13% increase in optimal exoskeleton stiffness was in closer agreement with the 10% increase in ankle quasi-stiffness during the dorsiflexion phase . This discrepancy can likely be explained by the role of muscle and tendon during stance. During late dorsi-flexion (dual-flexion) and plantarflexion, the contraction of the soleus muscle likely modulates the quasi-stiffness of the joint while the person adapts to walking speed. As walking speed increases, muscle activity increases, plantarflexion begins earlier, and quasi-stiffness in late stance is higher. In early stance during dorsiflexion, the soleus muscle produces force isometrically  and allows the Achilles tendon to stretch against it to store energy . Thus, the Achilles tendon (not concentric muscle contraction) is likely responsible for a large percentage of ankle joint rotational stiffness in early stance, and stiffness during this period is less likely to be actively modulated with speed. Similar to a biological tendon, our passive exoskeleton has no ‘muscle’ and is not capable of modulating stiffness in late stance to adapt to increased walking speeds. Therefore, in hindsight, it may not be that surprising that the optimal exoskeleton stiffness tracks speed-dependent changes in ankle quasi-stiffness during early stance dorsiflexion, when the biological tendon stiffness dominates the quasi-stiffness behavior of the ankle. A positive consequence of the relative invariance in optimal exoskeleton stiffness at slow and fast walking speeds is that even though low-powered clutch-spring systems are being developed that can switch stiffness step by step , designing for variable speed conditions becomes less challenging and may not even be necessary.
The changes in SOL+TA activation explain why metabolic reduction was not obtained at intermediate walking speed (1.5 m s-1); however, the mechanism behind the difference in muscle response at intermediate speed versus the other speeds is less clear. Changes in joint mechanics were similar for all three speeds with differences observed in terms of timing or amplitude that were merely exacerbated at the highest walking speed. This suggests to us that perhaps the differential effect of exoskeleton stiffness on users’ net metabolic rate at 1.5 m s-1 was due to muscle-tendon dynamics that were not evident in joint-level data. Previous literature suggests that preferred walking speed in adults is close to 1.42 m s-1, and this speed aligns closely with that which minimizes the metabolic cost of transport . Humans also select step-frequencies that reduce energetic cost of walking [68, 69]. The structure of the ankle is important for maximizing muscle efficiency [70, 71] (i.e., minimizing metabolic cost) and models of walking have suggested that walking efficiency is maximized when step length and frequency are matched to target ankle stiffness . Therefore, it is possible that, nominally, ankle plantarflexors are preferentially ‘tuned’ to participants’ preferred walking speed. In this study, preferred walking speed collected from participants using a 10m over ground test was 1.39 ± 0.04 m s-1 and the average metabolic cost of transport with no exoskeleton assistance at 1.25, 1.50, and 1.75 m s-1 was 2.5 ± 0.11, 2.67 ± 0.13, and 3.22 ± 0.15 J m-1 respectively. Thus, we suspect that the muscle-level ‘detuning’ associated with the exoskeleton assistance may have been more pronounced at the 1.5 m s-1 walking speed due to its proximity to the preferred (and perhaps most economical) speed.
One difference between these study results and our previous study on passive elastic ankle exoskeletons was that the optimal stiffness reported in this study (50 Nm rad-1) is substantially lower than the reported optimal stiffness from the prior work (180 Nm rad-1) . However, the stiffness values previously reported reflected the stiffness of exoskeleton spring elements rather than the stiffness of the whole exoskeleton system. Conversely, the exoskeleton testbed we used here (Fig. 1) imposes a desired torque/angle relationship rather than relying on physical components to provide stiffness making it less sensitive to structural stiffness and deformation of the exoskeleton frame. When deformation in the previous system is accounted for by measuring stiffness from the exoskeleton’s torque/angle relationship, the optimal stiffness for 1.25 m s-1 walking speed was reduced to ~80 Nm rad. This is close to the optimal value we found here based on the stiffness at minimum net metabolic power from the regression at the same speed (69 Nm rad-1). We note that there may still have been some movement between the human and device that was not accounted for in our system, but we believe that stiffness values reported here give a more accurate portrayal of the applied rotational stiffness than had been previously reported.
We acknowledge that our study has limitations. In terms of the hardware, our exoskeleton emulator behaved more like an ideal spring rather than a physical spring or a biological spring, which would be expected to dissipate energy in each cycle. Achilles tendon hysteresis, for example, could be as much as 15% per cycle , though the true value may be smaller and is still debated . Thus, although our ‘exo-tendon’ did not emulate the exact energy cycle of a biological tendon, our intention was to tightly control stiffness, and vary it systematically, so that we could measure its effect on users’ physiological response. Small amounts of work were generated/dissipated, but we estimate the impact of these amounts of mechanical energy were less than 0.1% of the total net metabolic power. Future work could consider damping in addition to stiffness in the exoskeleton impedance control law to regulate the amount of energy dissipated by the exoskeleton.
Another limitation, in terms of protocol, was that rather than build a streamlined, low-mass and portable version of our device (e.g., as was done in ) we opted to use a high-powered, tethered ankle exoskeleton system to emulate and assess the effect of passive-elastic exoskeleton stiffness on the neuromechanics and energetics of walking across speeds. Our primary goal here was to employ a framework to rapidly and robustly test the specific effects of ankle exoskeleton stiffness independent of the mass and inertia of the device with high repeatability. This choice restricted our ability to definitively claim that the savings we measured with respect to the no assistance baseline condition (i.e., kexo = 0 Nm rad-1 or zero-torque) would transfer to real savings with respect to normal walking in a portable version of the device using similar stiffness. For the tethered exoskeleton emulator we used here (Fig. 1), the increase in metabolic cost due to merely donning the system was on average ~19% (Supp. Table 1). We note, however, that our previous work indicates it is possible to build a passive-elastic system with negligible added mass cost , making the effect of the spring stiffness the primary variable of interest, and perhaps a more useful benchmark for extrapolating our results to expected performance on a portable analogue. Thus, our results suggest it should be possible to reduce metabolic cost of walking at both slow and fast speeds by ~5% using an unpowered, passive- elastic ankle exoskeleton with fixed rotational stiffness ~70-80 Nm rad-1 (Fig. 2).