Autonomous exoskeleton reduces metabolic cost of human walking during load carriage
© Mooney et al.; licensee BioMed Central Ltd. 2014
Received: 20 February 2014
Accepted: 23 April 2014
Published: 9 May 2014
Many soldiers are expected to carry heavy loads over extended distances, often resulting in physical and mental fatigue. In this study, the design and testing of an autonomous leg exoskeleton is presented. The aim of the device is to reduce the energetic cost of loaded walking. In addition, we present the Augmentation Factor, a general framework of exoskeletal performance that unifies our results with the varying abilities of previously developed exoskeletons.
We developed an autonomous battery powered exoskeleton that is capable of providing substantial levels of positive mechanical power to the ankle during the push-off region of stance phase. We measured the metabolic energy consumption of seven subjects walking on a level treadmill at 1.5 m/s, while wearing a 23 kg vest.
During the push-off portion of the stance phase, the exoskeleton applied positive mechanical power with an average across the gait cycle equal to 23 ± 2 W (11.5 W per ankle). Use of the autonomous leg exoskeleton significantly reduced the metabolic cost of walking by 36 ± 12 W, which was an improvement of 8 ± 3% (p = 0.025) relative to the control condition of not wearing the exoskeleton.
In the design of leg exoskeletons, the results of this study highlight the importance of minimizing exoskeletal power dissipation and added limb mass, while providing substantial positive power during the walking gait cycle.
The ability to carry substantial loads is required by many professions, including many that may experience cognitive deficits associated with the extreme physical demands. For example, soldiers are often expected to carry loads between 20–35 kg at speeds of 1.5-1.75 m/s for over 10 km in a single march [1, 2]. Wheeled vehicles, however, are excellent at reducing the effort of carrying substantial loads, but terrain and space restrictions often limit the practicality of a vehicle and require the versatility of legged locomotion. Exoskeletons have the potential to reduce the energetic cost of carrying such loads while maintaining the flexibility of legged locomotion. To this end, one of the first leg exoskeletons that posited to augment human legged locomotion was patented in the late 19th century . Since that time, interest in developing exoskeletons to augment strength and endurance has increased substantially, driven by the accelerating pace of innovation in several mechanical and computer-related disciplines [4–6]. Reducing the metabolic energy (i.e. energy from food) consumed by the human body during legged locomotion is the goal of many exoskeletal technologies [7, 8]. To our knowledge, no autonomous leg exoskeleton system has been demonstrated to reduce the metabolic demand for either walking, loaded walking or running. In this work, “autonomous” describes a device that is self-contained and has all necessary components on-board (e.g. power supply, controller, and actuators, with no tether to external systems).
Researchers have attempted to reduce the metabolic burden of load carriage by developing both passive and active exoskeletons. Walsh et al. presented a device that used springs in parallel with the ankle and hip joints along with a variable damper at the knee . A preliminary study showed that the device transferred 80% of a 36 kg payload to the ground, but a 10% metabolic increase was observed while wearing the exoskeleton. Kazerooni and Steger developed a powerful lower extremity exoskeleton for load carriage with actuated hip, knee and ankle joints . The device allowed a user to walk at 1.3 m/s while carrying a 34 kg payload along with the 36 kg exoskeleton, but a metabolic improvement was not shown. Both of these devices distributed the payload weight through the structure of the exoskeletons, thus reducing the weight borne by the human user. The device presented by Walsh et al. achieved this by outputting high knee damping during the early stance phase of walking, while Kazerooni and Steger’s device provided active power at the joints to support the load. However, the added mass of these sophisticated exoskeletons may have limited their abilities to improve metabolism.
Exoskeletons have also been developed to assist with unloaded locomotion. To achieve this goal a class of passive exoskeletons have been designed. Donelan et al. developed a device that uses an electromagnetic generator to harvest energy from the knee in a biomimetic fashion [10, 11]. Harvesting energy during periods of negative power at the knee was less metabolically detrimental than continuous harvesting, but a metabolic increase of over 20% was still observed. Recently, van Dijk et al. presented an exoskeleton that has a spring spanning the ankle, knee and hip joints . The average energy expenditure of walking increased by over 30% while wearing the device. Although passive exoskeletons have not reduced the metabolic cost of walking in healthy individuals, they have been shown to augment the energetics of hopping [13, 14]. Adding passive elements in parallel with human joints are able to assist the muscles during periods of spring like behavior. Such work is encouraging, but the extension to exoskeletons designed for walking is unclear.
Many factors have hindered the development of an autonomous performance-enhancing exoskeleton including substantial added mass, limited mechanical power and tethered energy supplies. Autonomous devices capable of providing biologically equivalent levels of joint mechanical power necessary for locomotion have been investigated, but these devices were cumbersome and heavy [7, 15, 16]. Adding mass to the lower limbs requires additional metabolic power, and the effects are amplified as the mass is moved distally or further away from the hip . In an effort to reduce the weight of the worn exoskeleton, researchers have developed passive and quasi-passive exoskeletons. Without an active actuator, these devices are not able to provide levels of positive power that overcome the negative metabolic effects of added device mass [9, 10, 12].
Researchers have reduced weight and provided substantial positive power by tethering exoskeletons to an energy supply not worn by the user [18–22]. The device of Malcolm et al. was able to provide a 6% metabolic improvement during walking using pneumatic artificial muscles. This device required a tether to an air supply and extensive valving control network, thus distancing it from an autonomous solution. Despite the tethered nature of this devices, the study shows that it is possible to reduce the metabolic cost of walking by assisting the ankle with a lightweight device capable of providing positive mechanical power.
The purpose of this study is to present the design and testing of an autonomous leg exoskeleton capable of reducing the metabolic cost of walking with load. The intent of this research is to develop a technology that can assist individuals who must carry loads for extended periods of time, such as soldiers. Our hypothesis is that a leg exoskeleton capable of providing substantial levels of positive mechanical power with minimal added distal mass can provide such a metabolic benefit. In the evaluation of this hypothesis, we augment the ankle joint because it is responsible for over 50% of the average positive mechanical power during loaded walking . We test the metabolic effect of the ankle exoskeleton during walking with load carriage, and present the Augmentation Factor, a general framework of exoskeletal performance that unifies our results with the varying abilities of previously developed exoskeletons.
Exoskeleton component mass distribution
Foot & Shank
A biomechanically-inspired control strategy was implemented to assist the user during the push-off portion of stance phase and become transparent to the user during swing phase. During stance phase, the controller used a linear model of the motor to produce open loop torque profiles. The details of the linear motor model are further discussed in the Actuator Testing Protocol subsection. Upon heel contact, the actuator behaved like a soft virtual spring. The equilibrium position of the soft virtual spring was set to the peak plantar-flexion angle achieved just after heel strike. During the controlled dorsiflexion region of stance phase, the winch actuator applied a slight plantar-flexion torque that linearly increased with the extension of the winch cord. This soft virtual spring maintained tension in the cord and allowed for a gradual increase in applied torque. The step period of each subject was measured while not wearing the exoskeleton. The controller was then set to initiate push-off assistance at 43% of the subject’s personal gait cycle time . During the push-off portion of stance phase, the actuator exerted a large plantar-flexion torque. Over 50 ms, the exoskeleton increased the applied plantar-flexion torque by approximately 120 Nm. Subsequently, the applied plantar-flexion torque linearly decreased with plantar-flexion angle. Once the actuator reached 0.2 radians of ankle plantar flexion, the controller entered a zero applied torque mode (swing phase). This mode did not impede additional plantar flexion by the biological ankle due to the nature of the unidirectional actuator. During swing phase the exoskeleton provided slack in the drive cord to allow the user to freely dorsiflex the biological ankle. To prevent such interference, the motor proceeded to the maximum angle reached during controlled dorsiflexion of the previous cycle. Stance phase was reinitiated when the controller detected heel contact from the insole and any slack in the cord was eliminated with a low applied torque that was imperceptible to the user.
Actuator testing protocol
where I is the motor current, V is the applied voltage, k v is the motor voltage constant, R is the terminal resistance, ω and are the motor’s velocity and acceleration, τ is the estimated motor torque, k t is the torque constant, and J is the rotor inertia. The motor’s angle, as measured by the encoder, was numerically differentiated to get the motor velocity and then differentiated again to get the motor acceleration. The velocity differentiation was calculated by a single finite difference. The acceleration was not calculated for real-time control due to the low rotor inertia. However, the acceleration was calculated by the central-difference method during post-processing to estimate the mean power supplied by the exoskeleton.
where and are the experimentally measured average positive and negative mechanical powers, and p + and p - are the estimated average positive and negative mechanical powers provided by the exoskeleton . The transfer efficiency of the actuator was experimentally determined with an inline force sensor and acquisition equipment (model: LRF350, Futek Advanced Sensor Technology, Inc., Irvine, CA). The force sensor had a max rated force of 890 N, and a sampling rate of 250 Hz with 12 bit resolution. The winch actuator was used to pull the inline force sensor and stiff elastic band attached to the ground. The winch cord linear velocity was derived from the motor rotational velocity, transmission and spool diameter. The measured power, the product of the cord linear velocity and measured force, was compared to the estimated power, the product of the motor velocity and estimated torque.
The metabolic effect of the exoskeleton was tested on seven male subjects (84 ± 6 kg; 181 ± 5 cm; 23 ± 4 years old; mean ± standard deviation) walking on a treadmill at 1.5 m/s with a 23 kg weighted vest. These conditions were chosen because they are consistent with typical loads and speeds experienced by soldiers [1, 2]. All subjects were healthy and exhibited no gait abnormalities. Only subjects with a foot size between 11 and 12.5 were considered to ensure proper boot fit. This study was approved by the MIT Committee on the Use of Humans as Experimental Subjects. Consent was obtained from experimental participants after the nature and possible consequences of the exoskeletal studies were explained. The experimental protocol involved three walking trials and one standing trial, all performed while wearing a portable pulmonary gas exchange measurement instrument (model: K4b2, COSMED, Rome, IT). To account for natural variation in metabolism, the control condition of no exoskeleton was tested before and after the exoskeleton condition. The subjects first walked for 10 minutes with no device. After the subjects donned the exoskeleton, they walked with the active device until they reported being comfortable with the assistance, typically less than 5 minutes. The subjects then walked for 20 minutes with the exoskeleton (Additional file 1), in order to allow for human-machine adaptation . The subjects then walked for another 10 minutes with no device. Finally, after the last no device trial, subjects stood for 5 minutes with the weighted vest and no exoskeleton in order to obtain the resting metabolic rate.
Metabolic rate was calculated from oxygen and carbon dioxide exchange rates measured by the portable pulmonary gas exchange measurement unit. The average flow rates of the last two minutes of each trial were converted into metabolic power using the equation developed by Brockway et al. . The metabolic rate of standing was subtracted from the metabolic rate of walking trials in order to obtain the net metabolic cost of walking. The net metabolic rates measured from the two control trials were averaged and compared to the net metabolic rate of the exoskeleton trial [20, 24]. A paired t-test was used to test for metabolic improvement, with the level of significance set at 0.05.
The mechanical and electrical powers of the exoskeleton were wirelessly recoded via Bluetooth at a sampling rate of 100 Hz. The mechanical power applied by the winch actuators were estimated through the linear motor model and experimentally measured transfer efficiency discussed in the previous section. The electrical power was also recorded on a subset of four subjects by measuring the battery voltage and current during a period of walking with the exoskeleton.
A simple model to estimate the metabolic demand of an exoskeleton design would be a valuable tool for designers, but there are many factors which may affect exoskeletal performance. Sawicki and Ferris presented the performance index as a metric of measuring the relationship between applied positive exoskeleton mechanical power and change in metabolic power . A higher performance index suggests that the exoskeleton is able to more efficiently transfer mechanical power into metabolic power. The efficient transformation of mechanical power into metabolic power is important for autonomous systems that must carry their own energy supply. The generality of the performance index enables the comparison of various exoskeletal designs, but it is limited to developed and experimentally tested devices. The performance index cannot make a prediction about the metabolic performance of an untested exoskeleton.
The calibration tests were performed with a sinusoidal motor position profile, over a range of frequencies (1–4 Hz) with an amplitude of 150 mm. The corresponding force amplitudes ranged from 0 to 350 N. These values were chosen because they are similar to the actuator range of motion and force experienced during walking. The calibration tests demonstrated a positive power transfer efficiency (η + ) of 0.68 ± 0.01 (mean ± standard error) and a negative power transfer efficiency (η - ) of 0.77 ± 0.01, resulting in an average root mean square error of 10 W over the range of tested frequencies and amplitudes. These efficiencies along with (1a), (1b) and (2) were used to estimate the power applied by the exoskeleton during human trials.
Metabolic and mechanical power
Metabolic power, mechanical power and augmentation for seven subjects
Avg. mech. pow.
The measured electrical power suggests that the current exoskeleton can provide assistance for over 10 km of walking. The average electrical power was measured to be 49 ± 5.3 W. If one hundred percent of the battery’s energy was used, or 432 kJ, then the exoskeleton would have a battery life of 2.4 hours, or 13 km at 1.5 m/s.
Augmentation factor comparison
Augmentation factor calculation for six studies
van Dijk et al. 
Walsh et al. 
Donelan et al. 
Malcolm et al. 
The metabolic and mechanical power results support the hypothesis that a metabolic reduction during walking with a load can be achieved by an autonomous leg exoskeleton capable of providing substantial positive mechanical power with minimal added distal mass. The metabolic reduction provided by the exoskeleton is equivalent to reducing the payload by approximately 7 kg or 30% of the original payload of 23 kg .
The lightweight architecture of the exoskeleton allowed it to add positive mechanical power to the user without restricting the natural motions of the ankle joint. In order to apply a large torque about the ankle joint, it must be reacted by both a structure connected to the foot and a structure connected to the shank. Applying large forces to the body must be done carefully, in order to prevent discomfort or pain. One solution is to add a mechanical bearing in parallel with the ankle joint which greatly reduces the shear forces on the foot and shank [4, 18, 36]. However, the mechanical bearing must be closely aligned with the biological joint in order to prevent undesired forces and translations, and a bearing at the ankle joint adds non-trivial distal mass. Other exoskeletons have developed various methods to apply moments about a joint without a parallel bearing, but these devices have been limited in the amount of torque they can apply [37, 38]. Instead, the presented device creates a rigid extension of the foot in only the plantar-flexion direction. Actuating the struts with a cord does not constrain the movement of the ankle and subtalor joints, and also reduces the distal mass, since the boot is only connected to the heel cord and a fiberglass strut. The freedom of the ankle and subtalor joints may have also contributed to the success of this device, but this effect would be difficult to measure and quantify.
The AF suggests the importance of an exoskeleton to provide substantial positive mechanical power to the wearer with minimal added leg mass and net-negative power dissipation. That is, using the fundamental characteristics of device mechanical power and mass, the potential metabolic impact can be estimated using the AF. The metabolic results observed in this study were achieved by a device with an AF of 33 W. Previously, the most successful published exoskeleton (Malcom et al.) had an AF of 10 W. That device was tethered, having an external power supply and yet showed one third the metabolic improvement (12 W) of the device we present in this paper (36 W) . Historically, previously published autonomous exoskeletons have not provided a metabolic improvement, demonstrated by their negative AF values (Figure 4). In accordance with the AF, to design a non-dissipating exoskeleton (p dis = 0) that reduces the metabolic cost of walking, it must apply a mean positive power, p + > η ∑ β i m i (4). Furthermore, a purely dissipative device (p + = 0 and p dis < 0) will have a negative AF (e.g.) and an estimated increase in metabolic cost. Future investigators can use the AF to estimate the metabolic impact of an exoskeletal leg design, reducing the likelihood of the device unintentionally increasing walking metabolic energy once fabricated.
Certain assumptions are made when calculating the AF that must be considered carefully. The AF does not account for different control schemes and only accounts for mechanical power and added distal mass. That is, the AF assumes that power is added in a biomimetic fashion where positive and negative power are added by the exoskeleton during phases of the gait cycle when the joint is also applying positive or negative power, respectively. Current and previous exoskeletal control methodologies apply power in this way. The muscle-tendon efficiency of 0.41 used by the AF is also an estimate based on two studies [20, 22]. The muscle-tendon efficiency may also be specific for each joint and activity [34, 39]. More studies are needed to precisely determine how this apparent muscle-tendon efficiency is affected by joint and activity. Furthermore, the transfer of mechanical energy between joints is not fully considered when calculating the AF. Literature suggests that energy is transferred between joints via bi-articular muscle-tendon action when one joint is performing negative power and another is exhibiting positive power [26, 27]. This may explain why the device presented by Donelan et al. increased the metabolic rate higher than predicted by the AF ; a knee exoskeleton that harvests electrical energy from negative phases of knee mechanical work may reduce the mechanical energy transferred to the hip via bi-articular muscle-tendon units, potentially increasing muscular hip work and adversely affecting metabolism. The possible metabolic advantage of an exoskeleton reducing the negative mechanical power applied by muscle-tendon units is also not considered by the AF. Providing a joint with negative power during phases of eccentric muscle work may reduce the metabolic burden. However, muscles are substantially more efficient at eccentric work than they are at concentric work , thus, aiding the joints during eccentric phases is less effective at reducing the metabolic expenditure during walking, when compared to aiding concentric contraction phases.
The equation found by linear regression of the AF and measured metabolic effect, y = 1.1x-4, (95% C.I. slope: [0.86, 1.33] (p = 0.0002), intercept: [-15, 7] (p = 0.38)), highlights some important features of the AF. When no device is worn the AF should predict no metabolic change; that is, a device that does not supply power and has no mass should have no metabolic effect. The nearly zero y-intercept correctly accounts for this case. The slope of the linear regression is approximately one, indicating the ability of the AF to predict metabolic change caused by a worn exoskeleton. The AF includes the aforementioned assumptions as well as the empirically-estimated muscle-tendon efficiency for positive mechanical work (η). Future work will focus on the validation of these assumptions.
In this work, comparisons are made between exoskeletons that were tested with load carriage and those that were tested during unloaded conditions. The effect of added load on the metabolic improvement of an exoskeleton is unknown, but may be an advantage compared to unloaded studies. Because of the limited number of studies documenting the metabolic impact of exoskeletal walking, the calculation of the AF in this study assumed that the muscle-tendon efficiency was not affected by different loading conditions.
Future improvements of the autonomous exoskeleton should increase the versatility and controllability of the device. Reducing the posterior protrusion of the struts will allow for a greater range of motion. An integrated force sensor will also allow for more precise torque control. While using motor state to apply a torque impulse was successful, more sophisticated control paradigms will require a greater level of force measurement. The maximum applied mechanical power and relative timing varied by subject due to the subtle differences in how the subjects utilized the exoskeleton. The timing of the push-off assistance was statically determined before the exoskeleton trial and did not adapt with changes in step period, due to wearing the exoskeleton. This provided a consistent timing that the subjects could rely on, but it also may have forced the subjects to walk at a non-optimal cadence while wearing the exoskeleton. Future control strategies should be able to adapt to the natural cadence of the user. Finally, a fully autonomous exoskeleton presents the opportunity to develop controls for activities other than walking in a laboratory. Specifically, gait transitions and terrain adaptations will be an exciting area of future investigation.
In this study, a fully autonomous leg exoskeleton was described that reduced the metabolic burden of walking during load carriage. In accordance with the Augmentation Factor framework, the applied mechanical power characteristics of the device coupled with the distal mass were critical factors to its success. The presented exoskeleton could reduce the metabolic burden of individuals expected to carry substantial loads. Instead of reducing the metabolic burden, the device may allow them to carry greater loads at their nominal metabolic cost. A lightweight autonomous powered exoskeleton enables the investigation of real-world applications including the complex controls needed for various terrains and conditions outside of the laboratory.
This work was supported by the National Science Foundation Graduate Research Fellowship award number 1122374, by the NASA award number NNX12AR09G, and by the Department of Defense award number 119–000245.
- Royal marines fitness test [https://pdevportal.co.uk/assets/upload/ckfiles/kayak/files/RM_Fitness_Tests.pdf] 
- Patterson MJ, Roberts WS, Lau W, Prigg SK: Gender and Physical Training Effects on Soldier Physical Competencies and Physiological Strain. Victoria, Australia: Human Protection and Performance Division, Defence Science and Technology Organisation; 2005. [Technical Report]Google Scholar
- Yagn N: Apparatus for facilitating walking, running, and jumping. 1890.Google Scholar
- Kazerooni H, Steger R: The Berkeley lower extremity exoskeleton. J Dyn Syst Meas Control 2006,128(March):14-25.View ArticleGoogle Scholar
- Makinson BJ: Research and Development Prototype for Machine Augmentation of Human Strength and Endurance: Hardiman I Project. Schenectady, New York: General Electric Company; 1971. Tech Rep S-71-1056; [Technical Report]Google Scholar
- Rosheim E: Man-amplifying exoskeleton. Proc SPIE Mob Robot IV 1989, 1195: 402-411.View ArticleGoogle Scholar
- Dollar AM, Herr H: Lower extremity exoskeletons and active orthoses: challenges and state-of-the-art. IEEE Trans Robot 2008, 24: 144-158.View ArticleGoogle Scholar
- Ferris DP, Sawicki GS, Daley MA: A physiologist’s perspective on robotic exoskeletons for human locomotion. Int J HR 2007, 4: 507-528.PubMedPubMed CentralGoogle Scholar
- Walsh CJ, Endo K, Herr H: A quasi-passive leg exoskeleton for load-carrying augmentation. Int J HR 2007, 04: 487-506.Google Scholar
- Donelan JM, Li Q, Naing V, Hoffer JA, Weber DJ, Kuo AD: Biomechanical energy harvesting: generating electricity during walking with minimal user effort. Science 2008, 319: 807-810. 10.1126/science.1149860View ArticlePubMedGoogle Scholar
- Li Q, Naing V, Donelan JM: Development of a biomechanical energy harvester. J Neuroeng Rehabil 2009, 6: 22. 10.1186/1743-0003-6-22View ArticlePubMedPubMed CentralGoogle Scholar
- Van Dijk W, van der Kooij H, Hekman E: A Passive Exoskeleton with Artificial Tendons. Proc IEEE Int Conf Rehabil Robot 2011.Google Scholar
- Grabowski A, Herr H: Leg exoskeleton reduces the metabolic cost of human hopping. J Appl Physiol 2009, 107: 670-678. 10.1152/japplphysiol.91609.2008View ArticlePubMedGoogle Scholar
- Farris DJ, Sawicki GS: Linking the mechanics and energetics of hopping with elastic ankle exoskeletons. J Appl Physiol 2012, 113: 1862-1872. 10.1152/japplphysiol.00802.2012View ArticlePubMedGoogle Scholar
- Zoss A, Kazerooni H: Design of an electrically actuated lower extremity exoskeleton. Adv Robot 2006, 20: 967-988. 10.1163/156855306778394030View ArticleGoogle Scholar
- Zoss A, Kazerooni H, Chu A: Biomechanical design of the Berkeley lower extremity exoskeleton (BLEEX). Mechatronics, IEEE/ASME 2006, 11: 128-138.View ArticleGoogle Scholar
- Browning RC, Modica JR, Kram R, Goswami A: The effects of adding mass to the legs on the energetics and biomechanics of walking. Med Sci Sports Exerc 2007, 39: 515-525. 10.1249/mss.0b013e31802b3562View ArticlePubMedGoogle Scholar
- Ferris DP, Czerniecki JM, Hannaford B: An ankle-foot orthosis powered by artificial pneumatic muscles. J Appl Biomech 2005, 21: 189-197.PubMedPubMed CentralGoogle Scholar
- Sawicki GS, Ferris DP: Mechanics and energetics of level walking with powered ankle exoskeletons. J Exp Biol 2008,211(Pt 9):1402-1413.View ArticlePubMedGoogle Scholar
- Sawicki GS, Ferris DP: Powered ankle exoskeletons reveal the metabolic cost of plantar flexor mechanical work during walking with longer steps at constant step frequency. J Exp Biol 2009,212(Pt 1):21-31.View ArticlePubMedGoogle Scholar
- Ferris DP, Gordon KE, Sawicki GS, Peethambaran A: An improved powered ankle-foot orthosis using proportional myoelectric control. Gait Posture 2006, 23: 425-428. 10.1016/j.gaitpost.2005.05.004View ArticlePubMedGoogle Scholar
- Malcolm P, Derave W, Galle S, De Clercq D: A simple exoskeleton that assists plantarflexion can reduce the metabolic cost of human walking. PLoS One 2013, 8: e56137. 10.1371/journal.pone.0056137View ArticlePubMedPubMed CentralGoogle Scholar
- Huang T-WP, Kuo AD: Mechanics and energetics of load carriage during human walking. J Exp Biol 2014,217(Pt 4):605-613.View ArticlePubMedPubMed CentralGoogle Scholar
- Galle S, Malcolm P, Derave W, De Clercq D: Adaptation to walking with an exoskeleton that assists ankle extension. Gait Posture 2013, 38: 1-5. 10.1016/j.gaitpost.2012.10.007View ArticleGoogle Scholar
- Brockway JM: Derivation of formulae used to calculate energy expenditure in man. Hum Nutr Clin Nutr 1987, 41: 463-471.PubMedGoogle Scholar
- Geyer H, Seyfarth A, Blickhan R: Compliant leg behaviour explains basic dynamics of walking and running. Proc Biol Sci 2006, 273: 2861-2867. 10.1098/rspb.2006.3637View ArticlePubMedPubMed CentralGoogle Scholar
- Endo K, Herr H: A model of muscle-tendon function in human walking at self-selected speed. IEEE Trans Neural Syst Rehabil Eng 2013, 22: 352-362.View ArticleGoogle Scholar
- Whipp BJ, Wasserman K: Efficiency of muscular work. J Appl Physiol 1969, 26: 644-648.PubMedGoogle Scholar
- Gaesser G, Brooks G: Muscular efficiency during steady-rate exercise: effects of speed and work rate. J Appl Physiol 1975, 38: 1132-1139.PubMedGoogle Scholar
- Ryschon TW, Fowler MD, Wysong RE, Anthony A, Balaban RS: Efficiency of human skeletal muscle in vivo: comparison of isometric, concentric, and eccentric muscle action. J Appl Physiol 1997, 83: 867-874.PubMedGoogle Scholar
- Pierrynowski MR, Winter DA, Norman RW: Metabolic measures to ascertain the optimal load to be carried by man. Ergonomics 1981, 24: 393-399. 10.1080/00140138108924861View ArticlePubMedGoogle Scholar
- Bastien GJ, Willems PA, Schepens B, Heglund NC: Effect of load and speed on the energetic cost of human walking. Eur J Appl Physiol 2005, 94: 76-83. 10.1007/s00421-004-1286-zView ArticlePubMedGoogle Scholar
- Winter D: Biomechanical motor patterns in normal walking. J Mot Behav 1983, 15: 303-330.View ArticleGoogle Scholar
- Sawicki GS, Ferris DP: Mechanics and energetics of incline walking with robotic ankle exoskeletons. J Exp Biol 2009,212(Pt 1):32-41.View ArticlePubMedGoogle Scholar
- Valiente A: Design of a Quasi-Passive Parallel Leg Exoskeleton to Augment Load Carrying for Walking: Maters’ thesis. Cambridge, MA: Massachusetts Institute of Technology, Mechanical Engineering Department; 2006.Google Scholar
- Collins SH, Jackson RW: Inducing self-selected human engagement in robotic locomotion training. IEEE Int Conf Rehabil Robot 2013, 2013: 6650488.PubMedGoogle Scholar
- Kao P, Ferris D: Motor adaptation during dorsiflexion-assisted walking with a powered orthosis. Gait Posture 2009, 29: 230-236. 10.1016/j.gaitpost.2008.08.014View ArticlePubMedPubMed CentralGoogle Scholar
- Wehner M, Quinlivan B, Aubin PM, Martinez-villalpando E, Bauman M, Holt K, Wood R, Walsh C: Design and Evaluation of a Lightweight Soft Exosuit for Gait Assistance. 2013.Google Scholar
- Sawicki GS, Lewis CL, Ferris DP: It pays to have a spring in your step. Exerc Sport Sci Rev 2009, 37: 130-138. 10.1097/JES.0b013e31819c2df6View ArticlePubMedPubMed CentralGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.