Mechanics and energetics of walking and running up and downhill: A joint-level perspective to guide design of lower-limb exoskeletons

Lower-limb wearable robotic devices can provide effective assistance to both clinical and healthy populations; however, how assistance should be applied in different gait conditions and environments is still unclear. We suggest a biologically-inspired approach derived from knowledge of human locomotion mechanics and energetics to establish a ‘roadmap’ for wearable robot design. In this study, we characterize the changes in joint mechanics during both walking and running across a range of incline/decline grades and then provide an analysis that informs the development of lower-limb exoskeletons capable of operating across a range of mechanical demands. Eight subjects (6M,2F) completed five walking (1.25 m -1) trials at −15%, −10%, 0%, 10%, and 15% grade and five running (2.25 m s-1) trials at −10%, −5%, 0%, 5%, and 10% grade on a treadmill. We calculated time-varying joint moment and power output for the ankle, knee, and hip. For each gait, we examined how individual limb-joints contributed to total limb positive, negative and net power across grades. For both walking and running, changes in grade caused a redistribution of joint mechanical power generation and absorption. From level to incline walking, the ankle’s contribution to limb positive power decreased from 44% on the level to 28% at 15% uphill grade (p < 0.0001) while the hip’s contribution increased from 27% to 52% (p < 0.0001). In running, regardless of the surface gradient, the ankle was consistently the dominant source of lower-limb positive mechanical power (47-55%). In the context of our results, we outline three distinct use-modes that could be emphasized in future lower-limb exoskeleton designs 1) Energy injection: adding positive work into the gait cycle, 2) Energy extraction: removing negative work from the gait cycle, and 3) Energy transfer: extracting energy in one gait phase and then injecting it in another phase (i.e., regenerative braking).


Introduction
7 145 of the trials. The tracking markers were recorded during each trial and the orientation of the 146 distal segment relative to the proximal segment was used to define the 3D joint angle. Ground 147 reaction force (GRF) data was captured through the force plates embedded in the instrumented 148 treadmill (BERTEC, Columbus, OH, USA). GRF data were filtered with a 2 nd order low pass 149 Butterworth filters with a cut off frequency of 35 Hz. 150 The GRF and the kinematic data from the individual limbs were used to perform an 151 inverse dynamics analysis. We performed inverse dynamics at the joint level using commercially  Whole body metabolic energy expenditure was captured using a portable metabolic 167 system (OXYCON MOBILE, VIASYS Healthcare, Yorba Linda, CA, USA). Rates of oxygen consumption and carbon dioxide production during trials were recorded and converted to 169 metabolic powers using standard equations [42] . Baseline quiet standing metabolic rate was 170 captured prior to gait trials. For each condition, respiratory data from minute 4 to 6 were 171 averaged and used to report the steady state metabolic energy consumptions (watts) for the trial. 172 The metabolic system reported values that were averaged over 30 second intervals so four values 173 were averaged for each trial. In the most extreme case of 10% incline running, subjects could not 174 complete the trial while maintaining a respiratory exchange ratio (RER) below one. Therefore, 175 only data from 3 out of 7 subjects are included for the 10% incline running condition. Task where is mass normalized net metabolic power, and s is speed. Additionally, efficiency was met P 182 calculated as the ratio of average total limb positive mechanical power to net metabolic power: where is efficiency of positive work, is the average total limb positive power (summed to evaluate the effect of gait (walk, run) on the stride average joint power contributions for 193 similar grades (-10%, 0%, and 10%). We did not run statistical analysis on metabolic data.  10% grade (HSD, p = 0.0233) and 52% at 15% grade (HSD, p < 0.0001). For incline grades, the 223 relative contribution of the knee to positive power was the smallest (19%) and did not change as 224 the power was redistributed primarily between ankle and hip. For decline grades, the only 225 significant shift in percent contribution to positive power was a decrease in the ankle 226 contribution from 44% at level to 34% at -15% grade (rANOVA, p < 0.0001; HSD, p = 0.0167).

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There was no significant difference in the contribution to positive power among the joints at -228 15% grade.  Negative limb power was significantly larger in magnitude at -1.60 W kg -1 at -10% grade (HSD, 258 p = 0.0015) and -2.60 W kg -1 at -15% grade (HSD, p < 0.0001). The knee contributed >50% to 259 limb negative power, and the percent contribution was greater than that of the hip in all 260 conditions and that of the ankle in all conditions but the -10% grade (rANOVA, p < 0.0001; 261 HSD, p < 0.05) ( Table 2; Fig. 2B). The percent contribution of the knee to negative limb power 262 increased with incline (rANOVA, p = 0.0038) from 51% at level to 63% at 10% grade (HSD, p = 263 0.0433) and 60% at 15% grade and coincided with a decrease in ankle contribution (rANOVA, p 264 = 0.0007). Ankle negative power contribution was maximized for -10% grade at 41%. Hip 265 contribution to negative power did not change with grade and was 12% on average.  increasing grade (rANOVA, p < 0.0001) ( Table 1; Fig. 3B) from 3.66 W kg -1 at level to 4.12 W 280 kg -1 and 4.53 W kg -1 (HSD, p = 0.0005) at 5% and 10% grades respectively. Limb positive power 281 decreased to 3.14 W kg -1 at -5%, and to 2.64 W kg -1 (HSD, p < 0.0001) at -10% grade. The ankle   Fig. 3B). The limb negative power magnitude increased to -3.25 W kg -1 for 308 -5% and to -3.88W kg -1 for -10% grade (HSD, p = 0.0002). Similar to walking, each joint 309 contributed different amounts to total limb average negative power (rANOVA p < 0.0001) 310 (Table 3; Fig. 3B). The knee was the dominant source of negative power, producing >54% for all 311 conditions and contributed significantly more than the ankle or hip (HSD p < 0.0001). The ankle 312 contributed approximately 35% of the stride average negative power across all grades and the hip 313 contribution was minimal (~7%).

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The average limb positive power was greater in running than walking. Switching from 316 walking to running on level ground resulted in an increase in the ankle's percent contribution 317 from 44% to 55% (paired t-test p = 0.0024) and a decrease in the hip's percent contribution from 318 37% to 28% (paired t-test p = 0.0196). The trend was similar at 10% grade, where switching 319 from walking to running resulted in an increase in the ankle's percent contribution from 34% to 320 46% (paired t-test p = 0.0024) and a decrease in the hip's percent contribution from 47% to 36% 321 (paired t-test p = 0.0196). The transition from walking to running at the 10% grade resulted in 322 the hip being replaced by the ankle as the dominant contributor to positive power. For negative 323 power at the 10% grade, switching from walking to running resulted in an increase in the ankle's 324 percent negative contribution from 27% to 38% (paired t-test p = 0.001) and a decrease in the 325 knee's percent contribution from 62% to 54% (paired t-test p = 0.0338).

Temporal component of power redistribution 327
Time series plots show the redistribution of joint moment and power over the stride cycle 328 for walking (Fig. 4) and running (Fig. 5). Again, the general trend was a shift in positive power 329 generation to the hip with increasing incline, while the knee was the primary site of negative

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of the same leg for running across surface grades from at -10% downhill to +10% uphill.

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For running, the metabolic minimum was also at -10% grade (5.75 W kg -1 ) which was the 345 steepest downhill grade tested in running. Efficiency of positive work was maximized at -10% 346 grade in walking with an efficiency of 0.62. Our aim in this study was to measure and analyze human biomechanical response during . Energy must be injected or extracted to raise or lower the potential energy of the center of 360 mass (COM) for incline/decline walking. [29,30]. Indeed, our data confirm that in both walking 361 and running gait, the stride average total limb (ankle + knee + hip) power changes from net 362 negative on decline grades to net positive on incline grades. Our findings also agree with 363 previous work demonstrating the ankle to be a dominant source of positive mechanical power during both level walking and running gait [47], but that for incline walking the hip becomes an 365 important source of positive mechanical power generation [31,34,35]. In addition, our data 366 confirm that the knee is the dominant source of mechanical energy absorption during both 367 walking and running across grades [38]. In the following sections we first discuss the 368 biomechanical implications of our results and then focus on how these data could be utilized to 369 create lower-limb wearable exoskeletons (or perhaps prostheses) that can respond to and perhaps 370 even take advantage of changing mechanical demands across grades and gaits.  In line with the idea that structure drives function, our walking data demonstrate a shift to 384 power output in more proximal joints with an increase in incline. This finding is similar to prior 385 studies which also show the dominant source of positive mechanical power shifts from the ankle to the hip in uphill walking [22,32]. On the contrary, we found no evidence of a redistribution 387 of positive work to the hip during uphill running. In running, the ankle still produced 46% of the 388 positive power at 10% uphill grade. This finding seems to be in contrast with a previous study 389 which showed that the hip contributed most to the increase in work for incline running [31].  (Table 1, 3, Fig. 3).

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Similar to Margaria et al. [30], we found that the greatest efficiency of positive work at -walking at the extreme uphill (+15%) was ~0.25 reflecting the efficiency of muscle-tendons 430 during tasks exhibiting predominantly positive work [29,[52][53][54][55].  temporarily stores it (e.g., using a battery or a clutch) and then after some delay injects it at the same joint 473 (e.g., using a motor powered by the battery or spring recoil on release of a clutch).
Energy Injection: The first mode of device operation entails adding positive mechanical 475 work at a joint(s) when the joint is producing positive power. This is the most prevalent strategy used in exoskeletons targeting the hip, knee, and ankle with the common desired goal being the 477 reduction of metabolic demand in healthy individuals [3, 6-8, 14, 17, 23, 58]. The common 478 expectation is the outcome where the addition of mechanical power causes a concomitant 479 reduction of biological power while total power mostly remains constant (O1: replacement).

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While it's been demonstrated that users will reduce biological moment such that the total joint 2, 4). Given limited power supply of the device, our data would suggest that assistance should be 500 redirected away from the ankle to the hip when transitioning to incline walking. Conversely, for 501 running (Figs. 3,5), the ankle is the largest contributor to positive average power across all slopes 502 and thus, shifting assistance to the hip may not be as beneficial.

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Energy Extraction: The second mode of device operation involves removing negative 504 mechanical work at a joint(s) when the joint is producing negative power. The extracted 505 mechanical energy could be dissipated as heat (e.g., in a damper) or harvested to generate 506 electricity which can then be stored in a battery or used to power electronic devices (Fig. 6C).

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Additionally, an exoskeleton that effective extracts energy from the gait cycle can potentially 508 reduce the negative power required from muscles which, unlike many mechanical systems, tissues which can no longer be returned, it is possible that additional biological power may need 514 to be generated in the positive phase to make up for lost energy stores (Fig. 6C). However, in the 515 nominal case where the negative biological power is merely dissipated as heat rather than 516 recycled, then the reduction in total power during the latter half of the cycle may not be 517 problematic.

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The knee has been the focus of energy harvesting exoskeletons due to its production of 519 substantial negative power in gait, especially near the end of swing phase of walking (Fig. 4).

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There are several indications that if done correctly it is possible to generate electrical energy 521 while reducing the muscle energetic demands and whole body metabolic cost [18,56,65,66].
With consideration to changing mechanical demands on slopes surfaces, our results suggest 523 enormous potential for harvesting energy using a knee exoskeleton during decline walking due to 524 large increases in knee negative power throughout the gait cycle (Figs. 2, 4). In running, a knee 525 exoskeleton may be widely versatile because the knee generates a large amount of negative 526 power across all slopes including on inclines (Figs. 3, 5).

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Although the ankle produces substantial negative power, harvesting exoskeletons might 528 be ineffective in level gait because much of the joint power is recycled in elastic tissues [28], and 529 thus as mentioned previously, the biological system would need to replace these losses with 530 costly muscle work during a positive power phase at some joint in the limb. However, because 531 ankle negative power increases and positive power decreases on declined surfaces (Fig. 2), 532 energy harvesting may be a viable candidate at the ankle for decline walking.

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Energy Transfer: The third mode of device operation is to transfer energy from one phase to 534 another across the gait cycle either within or across joints (Fig. 6D-F). In this mode, because the 535 exoskeleton extracts energy in the negative phase (e.g., Fig. 6C) and then injects the same energy 536 later (e.g., Fig. 6B) in a positive phase , external power consumption of the device can be 537 minimized (e.g., by using passive elements like springs and clutches) [67]. In addition, intra-joint 538 transfer of energy from a negative power phase to a positive power phase may help mitigate the 539 complication of the reduced biological power in the latter half of the power cycle. As depicted in 540 Figure 5D, it is possible that the total power output of the joint (exo+bio) remains constant 541 despite the reduction of biological power in both the negative and positive power phases. The 542 simplest device applying this mode of operation is an elastic exoskeleton that uses a spring in a 543 parallel with the biological plantarflexors to stores energy (negative biological power) which is 544 returned later in stance (positive biological power) as done by Collins,Wiggins,and Sawicki [5].
According to our data here, while this approach of storing and returning energy at the ankle can 546 be effective for level ground gaits, at other grades the strategy of immediate storage and return of 547 mechanical energy may not be as effective. Adding a spring in parallel on inclines or declines 548 would likely require an additional biological energy source to inject/extract energy elsewhere in 549 the gait. Another option is to transfer power across joints as depicted in Figure 5E (i.e., inter-550 joint transfer). One example is the storage of energy from knee deceleration in late swing and 551 releasing it at the ankle during push-off [2]. From our data, we additionally show that energy 552 storage in the knee during early stance and releasing it at the ankle during push-off becomes 553 increasingly viable with decreasing grade (Figs. 4,5). A final scenario is that the power from the 554 negative phase could be temporarily stored via battery or clutch and returned at a later time -an 555 approach that has been used within a single gait cycle in foot-ankle prosthesis designs [68,69].

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This last approach, extraction, storage, and then delayed release (Fig. 6F) opens up the 557 possibility to store energy over multiple cycle, perhaps accumulating it, and then return it in a 558 single large burst over a shorter time period to achieve power amplification that may be 559 necessary for on-off accelerations or maximum effort jumps [70].

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An important next step is to examine whether using biological patterns of joint power 575 output as a 'road-map' to apply the three exoskeleton operating modes can improve walking and 576 running performance (e.g., reduced metabolic cost) on fixed or time varying uphill and downhill 577 slopes.

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We would like to thank Moran Gad for his help with the calculation of the inverse dynamics and 580 Karl Zelik for multiple discussions that contributed to aspects of the content in Figure 5.