Exotendons for assistance of human locomotion
© van den Bogert; licensee BioMed Central Ltd. 2003
Received: 24 April 2003
Accepted: 14 October 2003
Published: 14 October 2003
Powered robotic exoskeletons for assistance of human locomotion are currently under development for military and medical applications. The energy requirements for such devices are excessive, and this has become a major obstacle for practical applications. Legged locomotion in many animals, however, is very energy efficient. We propose that poly-articular elastic mechanisms are a major contributor to the economy of locomotion in such specialized animals. Consequently, it should be possible to design unpowered assistive devices that make effective use of similar mechanisms.
A passive assistive technology is presented, based on long elastic cords attached to an exoskeleton and guided by pulleys placed at the joints. A general optimization procedure is described for finding the best geometrical arrangement of such "exotendons" for assisting a specific movement. Optimality is defined either as minimal residual joint moment or as minimal residual joint power. Four specific exotendon systems with increasing complexity are considered. Representative human gait data were used to optimize each of these four systems to achieve maximal assistance for normal walking.
The most complex exotendon system, with twelve pulleys per limb, was able to reduce the joint moments required for normal walking by 71% and joint power by 74%. A simpler system, with only three pulleys per limb, could reduce joint moments by 46% and joint power by 47%.
It is concluded that unpowered passive elastic devices can substantially reduce the muscle forces and the metabolic energy needed for walking, without requiring a change in movement. When optimally designed, such devices may allow independent locomotion in patients with large deficits in muscle function.
Powered robotic exoskeletons are currently under development for enhancement of human locomotor performance in the military , in industry , and for patients with mobility impairments . When compared to wheeled vehicles and wheelchairs, exoskeleton-based assistive devices have several advantages. They allow the user to go outside of paved surfaces, and there is the possibility of an intuitive haptic user interface, which senses the user's intended movement and assists it automatically . Energy efficiency is, however, a major problem for such technology. Wheeled vehicles, once at constant speed, only require power to overcome small amounts of energy lost due to rolling friction and air resistance. Legged systems, on the other hand, require considerable additional energy to accelerate and decelerate the limbs and to dynamically support the body mass against gravity . Inverse dynamic analysis of human movement has shown that, when driven by hypothetical motors at each joint, walking would require about 60 W of steady state power . Powered exoskeletons for military applications are estimated to require 600 W of steady state power at running speeds when carrying a maximum payload . Supplying power to such devices for several hours is well beyond the capabilities of current battery technology. Only an internal combustion engine can provide sufficient energy while still being small enough to be carried, with sufficient fuel, in a backpack .
In this paper we explore the potential utility of passive elastic devices for assisting human movement, attached external and in parallel to the body. Such "exotendons" would span multiple joints as in the design of equine limbs. Artificial exotendons offer some additional possibilities that are not found in natural systems. For example, they can cross over from the posterior side to the anterior side of a limb, and can even originate in one limb and insert into another limb. We will first present a general procedure to find an optimal geometrical arrangement of exotendons for assistance of any given movement. Subsequently, we will show an application of this method, resulting in specific assistive devices for normal human walking.
We consider exotendons guided by one to six pulleys, each attached at one of the joints in the lower extremities: left and right hip, knee, and ankle. The analysis considers motion in the sagittal plane only, i.e. flexion and extension. In such a system, exotendon length L is a linear function of six joint angles φ (in radians):
where L 0 is exotendon length when all joint angles are zero and r i is the moment arm at joint i. We use the convention that joint angles increase during an anterior swing of the distal segment of the joint . Hence, a positive moment arm r i in equation (1) indicates that the exotendon runs anterior to the joint i. Conversely, a negative sign indicates that the exotendon runs posteriorly.
The exotendon is assumed to be made of a rubber-like material, with zero force below slack length and a constant stiffness k at larger length. Exotendon force F is thus given by:
This exotendon force F generates a moment F·r i at joint i. Assuming that the total joint moments, M i , required for the movement are known from an inverse dynamic analysis, e.g. , the residual joint moment R i required from the muscles crossing joint i, after accounting for contributions from N exotendons, can be calculated as:
For design optimization, we may assume without loss of generality that L 0 is zero, since only the difference between L 0 and slack length is of importance. Similarly, it can be seen that stiffness k is not an independent design parameter, since only products of the type kr i r j will affect performance. An exotendon system with N exotendons, each crossing J joints, therefore has N p = N(J + 1) design parameters, J moment arms (pulley radii) and one slack length for each exotendon. Stiffness was given an arbitrary value (k = 100 kN m-1), which can be realized using rubber material, and was found to result in pulley radii of a convenient size.
Two optimization criteria are proposed to find optimal design parameters. The first criterion is based on minimization of the residual joint moments, averaged over all joints and over the duration of the gait cycle:
where T is the duration of the gait cycle. This cost function is proportional to the muscle forces that contribute to the joint moments. Minimization of C mom would be suitable for patients with deficits in muscle strength. For military applications, the objective would be to reduce the metabolic energy required for movement, or to reduce muscle fatigue. C mom is qualitatively related both of these objectives . In order to explore alternative energy-based objectives, we also minimized a cost function that represents the average mechanical power generated by the residual joint moments:
Application to human walking
Time histories of sagittal plane joint angles and joint moments for the hip, knee, and ankle joints during normal walking were obtained from the literature  and scaled to obtain representative data for a hypothetical 70 kg subject with 0.9 m leg length at a walking speed of 1.2 m s-1 . Data for the contralateral limb were obtained by a half-cycle phase shift. Joint angular velocities were obtained from the joint angle data by numerical differentiation with a 3-point central difference method. The complete set of gait data is included in Sheet 1 of the additional data file exotendons.xls, which also evaluates cost functions (4) and (5).
Global optimization of the design parameters for each of the four systems was performed using simulated annealing , using the moment-based criterion (4) as well as the power-based optimization criterion (5). Exotendon moment arms were optimized within the range -0.1 to 0.1 m, and slack lengths were allowed to vary between -0.3 and 0.3 m. The temperature reduction rate for the annealing algorithm was set to 1% for each 1000 N p cost function evaluations, and optimizations were terminated after 30 million function evaluations. To verify that a global optimum was found, each optimization was performed five times, with different random number sequences used in the annealing process. The simulated annealing procedure consistently found the same optimal design parameters in all five optimization runs, except for the design D where multiple solutions were found that had almost identical cost function values. For design D, the cost function was then augmented with 10-5 times the peak exotendon force, in order to find the solution with lowest exotendon force. This resulted in a unique global optimum that was consistently found by the simulated annealing algorithm.
Design parameters for all optimized exotendon systems. Designs A, B, and C consist of a single exotendon and a symmetric twin, each spanning one, three, or six joints respectively. Design D consists of two exotendons, each spanning six joints, plus their symmetric twins. Each exotendon has up to six moment arms r and a slack length (L slack). The cost function values are shown in the two rightmost columns. The cost function values without exotendon assistance were C mom = 14.09 N m and C pow = 20.14 W.
r hip (mm)
r knee (mm)
r ankle (mm)
r hip (mm)
r knee (mm)
r ankle (mm)
L slack (mm)
C mom (N m)
C pow (W)
r hip (mm)
r knee (mm)
r ankle (mm)
r hip (mm)
r knee (mm)
r ankle (mm)
L slack (mm)
C mom (N m)
C pow (W)
The complete results, including all gait data, are included in the additional file exotendons.xls.
It was found that exotendons could significantly reduce the muscle forces required for locomotion. For practical relevance, it is important to show that these results are robust and not dependent on particular details of the model and data that were used in the present analysis.
The gait data that were used for the analysis were obtained from a gait analysis laboratory  which uses a well-established and validated methodology (C.G. Kirtley, personal communication). These data, included in the additional data file, are consistent with other commonly cited sources, e.g. . However, these data are an average of many subjects and therefore lack subject-specific details that may be important. Therefore, the analyses were repeated with gait data collected in our own laboratory from an adult female subject. The optimized designs and cost function values were virtually the same as those obtained with the normative gait data, suggesting that the design optimization only needs to consider the movement task that is to be assisted (e.g., walking), and not the detailed differences in movement execution between individuals.
All analyses were also repeated with a nonlinear (quadratic) force-length relationship for the exotendons, which is closer to the properties of biological soft tissue. Again the results were identical for all practical purposes, indicating that nonlinear material properties are probably unimportant for energetics. However, nonlinear exotendon material would have the advantage that the user would not feel a sudden change in stiffness when the exotendon goes from slack to taut.
It should be noted that we used two simple cost functions that are related to muscle forces and the metabolic cost of locomotion. Other expressions could have been used to better represent muscle energetics, such as a reduced weighting of negative joint power to account for the lower energy cost of eccentric muscle contractions. Although we have not explored this, the fact that both cost functions (residual moment and residual power) were reduced simultaneously (Figure 5) suggests that these results are robust with respect to the choice of cost function for optimization.
Most of the benefit of exotendons derived from the fact that the ankle plantarflexor and hip flexor moments in walking both reach their peak at the end of the stance phase (Figure 3). The rotational movements in the ankle and hip joints during normal walking happen to be such that a properly placed exotendon can produce both joint moments passively and automatically at the right time. However, none of the exotendon systems were able to assist the knee extensors significantly during the first part of the stance phase. Further analysis showed that, within the class of systems examined, no exotendon with an extensor moment arm at the knee could be designed to switch automatically from slack (during swing) to stiff (during stance) through length changes caused by movements at other joints. An active control system may be required to provide this function. Surprisingly, solutions that resemble the action of the bi-articular human Gastrocnemius muscle were not found. Optimization of the three-joint system (B) resulted in a design that exploits the ankle-hip synergy rather than the ankle-knee synergy. Optimization of an additional two-joint (ankle-knee) exotendon system was also done, and was found to reduce joint moments and power by 23% and 11% respectively, only marginally better than the one-joint system (A). It is possible that the ankle-knee synergy is more useful in movements such as running and jumping (7). Overall, a good compromise between performance and design complexity seems to be the three-joint exotendon design (B), which requires only one pulley on each joint and reduces joint moments and powers by about 50%.
This analysis has been entirely theoretical, based on the assumption that human muscles can produce the residual joint moments that are required to maintain a normal gait in the presence of exotendons. Because the residual moments are low, this is certainly within the force generating capacity of even very weak muscles. A more challenging concern is that of controllability. When more than half of the muscle force is replaced by passive elastic mechanisms, neural feedback mechanisms that operate during locomotion may become less effective and this could make the user less stable. However, exotendons have force-length properties, which contribute to short-term (within the gait cycle) gait stability , probably enough so that the residual neuromuscular function can actively maintain long-term stability over multiple gait cycles. This is supported by the observation that bipedal animals with passive elastic mechanisms, such as kangaroos and ostriches, are stable even at low levels of muscle recruitment. Furthermore, the human motor control system has a remarkable ability to adapt to unusual force fields such as those presented by exotendons . In fact, it is likely that humans will benefit more from exotendons than the present analysis has predicted, because they could self-optimize their movements to gain additional advantages. The potential benefits of exoskeletons can therefore only be fully determined with human experiments, including metabolic measurements. Theoretical design optimization of exotendon systems will still be required, since it is impossible to sufficiently explore the space of possible designs in human subject experiments. Such optimizations will necessarily involve forward dynamic simulations to optimize muscle activation patterns and device design parameters simultaneously [22, 24].
The design optimization procedure presented here will result in optimal performance for one specific movement task: walking on level ground at a single speed. Tasks other than that for which the system has been optimized will benefit less, or could even become energetically costly. This issue becomes important when considering exotendons as an alternative for wheelchairs, with the advantage of access to uneven terrain where limb movements necessarily will deviate from the nomimal patterns used in the present analysis. Further analysis with experimental data is needed to quantify these effects. We do expect, however, that an exotendon system will have sufficient elasticity to accomodate moderate changes in limb movements without affecting its assistive function. When considering a range of speeds, from walking to running, larger changes in movement will be needed. It is straightforward to include other movements in the design optimization process, and arrive at design that is best for the total of all movement patterns under consideration. However, such designs would always be a compromise and therefore suboptimal. A better approach may be to find a set of new movement patterns, analogous to the gaits of horses, that can all make effective use of the same passive exotendon system. This would, again, require forward dynamic modeling to find those new movements.
Exotendons are attached in parallel to the human body, and therefore are essentially different from series elastic mechanisms such as compliant running surfaces , pogo-stick-like devices  and energy-storing prosthetic feet . Series devices do not directly assist muscles, but rather alter the human movement such that muscles can operate under more favorable conditions. The energy savings from such devices are much smaller than what is possible with exotendons, especially if drastic alterations in movement must be avoided. Parallel elastic devices have only been described previously for single joints, such as an elastic shoe to assist flexors of the metatarso-phalangeal joint  and a spring with controlled release to assist knee extension in the swing phase of gait . We have shown here that elastic devices can be much more effective if they span multiple joints.
Control complexity and energy requirements are two major obstacles for the design of robotic devices for locomotion assistance for military applications and for persons with disabilities. We have shown here that a properly designed passive exotendon system can replace most of the muscle forces in human walking without requiring a control system or an energy supply. Such a reduction in muscle forces will significantly increase endurance time and reduce fatigue in healthy individuals. More importantly, this may allow independent locomotion in individuals with large deficits in muscle function. These benefits are obtained without altering the normal gait pattern. Anthropomorphic legged robots could benefit similarly from these mechanisms, resulting in a dramatic increase in battery life.
The author thanks Dr. Chris Kirtley (Catholic University of America, Washington DC) for providing the gait data and scaling algorithms.
- Lemley B: Future Tech: Really Special Forces. Discover 2002, 23, February [http://www.discover.com/issues/feb_02/departments/featteach]
- Kazerooni H: The human power amplifier technology at the University of California, Berkeley. Rob Autonom Syst 1996, 19: 179–187. 10.1016/S0921-8890(96)00045-0View ArticleGoogle Scholar
- Belforte G, Gastaldi L, Sorli M: Pneumatic active gait orthosis. Mechatronics 2001, 11: 301–323. 10.1016/S0957-4158(00)00017-9View ArticleGoogle Scholar
- Kram R, Taylor CR: Energetics of running: a new perspective. Nature 1990, 346: 265–267. 10.1038/346265a0View ArticleGoogle Scholar
- Winter DA: Energy generation and absorption at the ankle and knee during fast, natural, and slow cadences. Clin Orthop 1983, 175: 147–154.Google Scholar
- Jansen J, Richardson B, Pin F, Lind R, Birdwell J: Exoskeleton for soldier enhancement systems feasibility study. Technical Report TM-2000/256 Oak Ridge National Laboratory 2000. [http://www.ornl.gov/~webworks/cpr/rpt/108469_.pdf]Google Scholar
- van Ingen Schenau GJ, Bobbert MF, Rozendal RH: The unique action of bi-articular muscles in complex movements. J Anat 1987, 155: 1–5.Google Scholar
- Alexander RM, Bennet-Clark HC: Storage of elastic strain energy in muscle and other tissues. Nature 1977, 265: 114–117.View ArticleGoogle Scholar
- Dickinson MH, Farley CT, Full RJ, Koehl MA, Kram R: How animals move: an integrative view. Science 2000, 288: 100–106. 10.1126/science.288.5463.100View ArticleGoogle Scholar
- Biewener AA: Muscle-tendon stresses and elastic energy storage during locomotion in the horse. Comp Biochem Physiol B Biochem Mol Biol 1998, 120: 73–87. 10.1016/S0305-0491(98)00024-8View ArticleGoogle Scholar
- Minetti AE, Ardigo LP, Reinach E, Saibene F: The relationship between mechanical work and energy expenditure of locomotion in horses. J Exp Biol 1999, 202: 2329–2338.Google Scholar
- Biewener AA, Roberts TJ: Muscle and tendon contributions to force, work, and elastic energy savings: a comparative perspective. Exerc Sport Sci Rev 2000, 28: 99–107.Google Scholar
- Riemersma DJ, van den Bogert AJ, Schamhardt HC, Hartman W: Kinetics and kinematics of the equine hind limb: in vivo tendon strain and joint kinematics. Am J Vet Res 1988, 49: 1353–1359.Google Scholar
- van den Bogert AJ, Hartman W, Schamhardt HC, Sauren AAHJ: In vivo relationship between force, EMG, and length change in the deep digital flexor muscle in the horse. In Biomechanics XI-A (Edited by: de Groot G, Hollander AP, Huijing PA, van Ingen Schenau GJ). Champaign, Illinois: Human Kinetics Publishers 1989, 68–74.Google Scholar
- van Weeren PR, Jansen MO, van den Bogert AJ, Barneveld A: A kinematic and strain gauge study of the reciprocal apparatus in the equine hind limb. J Biomech 1992, 25: 1291–1301.View ArticleGoogle Scholar
- Wilson AM, McGuigan MP, Su A, van den Bogert AJ: Horses damp the spring in their step. Nature 2001, 414: 895–899. 10.1038/414895aView ArticleGoogle Scholar
- Wilson AM, Watson JC, Lichtwark GA: A catapult action for rapid limb protraction. Nature 2003, 421: 35–36. 10.1038/421035aView ArticleGoogle Scholar
- Pratt GA, Williamson MW, Dillworth P, Pratt J, Ulland K, Wright A: Stiffness isn't everything. In Proceedings of the Fourth International Symposium on Experimental Robotics (ISER '95): Stanford, California June 30–July 2 1995
- Stansfield BW, Hillman SJ, Hazlewood ME, Lawson AM, Mann AM, Loudon IR, Robb JE: Normalisation of gait data in children. Gait Posture 2003, 17: 81–87. 10.1016/S0966-6362(02)00062-0View ArticleGoogle Scholar
- Kirtley C, Cisper J, Sukal T, Wall A: Normalization for autointerpretation of gait analysis data. In Proceedings of the Gait and Clinical Movement Analysis Society (GCMAS): Chattanooga, Tennessee 2002.Google Scholar
- Goffe WL, Ferrier GD, Rogers J: Global optimization of statistical functions with simulated annealing. J Econometrics 1994, 60: 65–99. 10.1016/0304-4076(94)90038-8View ArticleGoogle Scholar
- Gerritsen KG, van den Bogert AJ, Hulliger M, Zernicke RF: Intrinsic muscle properties facilitate locomotor control – a computer simulation study. Motor Control 1998, 2: 206–220.Google Scholar
- Bhushan N, Shadmehr R: Computational nature of human adaptive control during learning of reaching movements in force fields. Biol Cybern 1999, 81: 39–60. 10.1007/s004220050543View ArticleGoogle Scholar
- van den Bogert AJ: Optimization of the human engine. In Proceedings of the 8th Conference of the Canadian Society for Biomechanics: 1994; Calgary, Canada 1994, 160–161.Google Scholar
- McMahon TA, Greene PR: The influence of track compliance on running. J Biomech 1979, 12: 893–904.View ArticleGoogle Scholar
- Dick GJ, Edwards EA: Human bipedal locomotion device. U.S. Patent 5,016,869 1990.Google Scholar
- Prince F, Winter DA, Sjonnensen G, Powell C, Wheeldon RK: Mechanical efficiency during gait of adults with transtibial amputation: a pilot study comparing the SACH, Seattle, and Golden-Ankle prosthetic feet. J Rehabil Res Dev 1998, 35: 177–185.Google Scholar
- Stefanyshyn DJ, Nigg BM: Influence of midsole bending stiffness on joint energy and jump height performance. Med Sci Sports Exerc 2000, 32: 471–476. 10.1097/00005768-200002000-00032View ArticleGoogle Scholar
- Gharooni S, Heller B, Tokhi MO: A new hybrid spring brake orthosis for controlling hip and knee flexion in the swing phase. IEEE Trans Neural Syst Rehabil Eng 2001, 9: 106–107. 10.1109/7333.918283View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL.