Dr H. Witte, Technische Universität Ilmenau, Institut für Mikrosystemtechnik, Mechatronik und Mechanik, Fachgebiet Biomechatronik. T: +49 3677692456; E: Hartmut.Witte@tu-ilmenau.de
Due to technological improvements made during the last decade, bipedal robots today present a surprisingly high level of humanoid skill. Autonomy, with respect to the processing of information, is realized to a relatively high degree. What is mainly lacking in robotics, moving from purely anthropomorphic robots to ‘anthropofunctional’ machines, is energetic autonomy. In a previously published analysis, we showed that closer attention to the functional morphology of human walking could give robotic engineers the experiences of an at least 6 Myr beta test period on minimization of power requirements for biped locomotion. From our point of view, there are two main features that facilitate sustained walking in modern humans. The first main feature is the existence of ‘energetically optimal velocities’ provided by the systematic use of various resonance mechanisms: (a) suspended pendula (involving arms as well as legs in the swing phase of the gait cycle) and matching of the pendular length of the upper and lower limbs; (b) inverted pendula (involving the legs in the stance phase), driven by torsional springs around the ankle joints; and (c) torsional springs in the trunk. The second main feature is compensation for undesirable torques induced by the inertial properties of the swinging extremities: (a) mass distribution in the trunk characterized by maximized mass moments of inertia; (b) lever arms of joint forces at the hip and shoulder, which are inversely proportional to their amplitude; and (c) twisting of the trunk, especially torsion. Our qualitative conclusions are three-fold. (1) Human walking is an interplay between masses, gravity and elasticity, which is modulated by musculature. Rigid body mechanics is insufficient to describe human walking. Thus anthropomorphic robots completely following the rules of rigid body mechanics cannot be functionally humanoid. (2) Humans are vertebrates. Thus, anthropomorphic robots that do not use the trunk for purposes of motion are not truly humanoid. (3) The occurrence of a waist, especially characteristic of humans, implies the existence of rotations between the upper trunk (head, neck, pectoral girdle and thorax) and the lower trunk (pelvic girdle) via an elastic joint (spine, paravertebral and abdominal musculature). A torsional twist around longitudinal axes seems to be the most important.
Some introductory remarks for a robotics community readership: the common mammalian heritage
Humans are placental mammals, tetrapods, and vertebrates. These zoological classifications might only seem to be of interest in the context of drug tests, in which animals are effectively used as measuring devices. However, humans have not come into being completely de novo. Our species incorporates the developmental possibilities and constraints of our ancestors, and hence in former times evolutionary selection may have acted on our precursors under quite different ecological circumstances to those prevailing today. Evolution has not flowed purposefully towards humans as the ‘Lords of Creation’. Thus, human form and function are the result of a zigzag course through adaptations towards circumstances that have themselves changed over the course of time. No species is ‘optimal’: all are adapted to fulfil survival needs, and as long as they perform this function there will be no driving force towards an optimum.
So as not to present our arguments in a manner that may be too discouraging to engineers, even if we are not able to derive optimal conformations from ‘natural paragons’, it is worthwhile to follow bionic approaches, because nature has developed many functions for which no solution is offered by the technical sciences. In our present special context, before aiming at optimal bipedal walking machines, we should at first develop some that actually do walk and run in a humanoid manner. The bipedal specialization of humans, with its unique morphofunctional adaptations, has stimulated anthropocentric approaches in robotics as well as in medicine. But for locomotion, humans use more or less the same principles as do most other mammals.
The stem line of mammals is characterized by limbs with three long segments: a forelimb consisting of the scapula, humerus and lower arm, and a hindlimb consisting of thigh, shank and elongated metatarsus (Fischer, 1999). The human lower limb still retains an ancestral three-segmented construction, with proportions adapted to the needs of self-stabilization (Seyfarth et al. 2001). The human upper limb appears to be reduced to two long segments (the locomotor meaning of the scapula is usually ignored due to the fact that in humans this bone adopts an orientation at right angles to the plane of motion). As a consequence of the absence in bipedalism of a kinematic coupling between forelimbs and ground, dysfunction of the scapular pivot leads only to dynamic disturbance, which generally may be compensated for by input of additional energy into the system (resulting in turn in disturbance of other parts of the locomotor system).
For both the trunk and the limbs, neural control of locomotion is achieved by excitatory waves running cranio-caudally down the spinal cord (Cheng et al. 1998; Ryan et al. 1998). Spatiotemporal redistribution of these excitations from the spinal cord into the musculature is realized by nerve plexus. Hence, different locomotor schemes in the limbs may be accompanied by different conformations of plexus (cf. Fischer, 2001).
In locomotion, energy is periodically transferred between its two states, kinematic and potential energy. Potential energy may be stored in the gravitational field, which leads to the concept of the extremities forming pendula (Weber & Weber, 1836). Or, it may be stored in elastic springs (cf. Dawson & Taylor, 1973; Cavagna et al. 1977). In large ‘master’ cursors such as the horse and camel, such springs may be realized by collagen and elastin in tendons and ligaments (cf. Alexander, 1988) or by giant elastic proteins such as titin or nebuline in the muscle bellies of all mammals, including humans (Wang et al. 1991; cf. discussion in Witte et al. 1995).
To summarize, for limbed animals, the mechanics of terrestrial locomotion follow surprisingly simple common rules. Boundary conditions are set by morphology (body mass and body height: the results of evolution), gravitation (a natural constant) and elasticity (material properties, which seem to have remained remarkably unchanged during mammalian evolution). Timing is restricted by neural mechanisms that may be derived from reptile precursors more than 140 million years ago. Because, within one species such as Homo sapiens, proportions and mass distribution are fairly common for all individuals (indeed, these features formed the basis for the differentiation of species in zoological terms), locomotor capabilities are quite constrained by our evolutionary heritage.
The functional morphology of human bipedalism as a prerequisite for the construction of humanoid walking machines
Scientific analyses of human bipedalism in the modern era began in the early 19th century with Ernst and Wilhelm Weber's Über die Mechanik der menschlichen Gehwerkzeuge (On the Mechanics of Human Walking Tools), published in 1836 (Weber & Weber, 1836). These studies were initiated by the Prussian government in order to improve the performance of the infantry, after their army had been defeated by Napoleon's forces at Jena and Auerstedt. They covered aspects of biomechanics as well as of physiology. Technical advances in chronophotography developed by Étienne Jules Marey and Eadweard Muybridge permitted true motion analyses. NASA programmes in the 1960s drove steady methodological optimization towards the present state, in which modern optical motion analysers have a recording frequency of some 1000 Hz and spatial resolution of some 0.1 mm. As a result, the mechanical action of the human walking apparatus now appears to be well described, although it is not yet completely understood.
Some synthetic approaches combine anatomical and physiological data with the use of ‘neuronal networks’, provided by computer models of cyclically stable anthropomorphic gaits. Hardware implementation of these began with the ‘McGeer walker’ and led to anthropomorphic walking machines with kinematics well matched to human data (the most impressive systems – the Honda® robots – must certainly be mentioned here). However, in spite of the high biomimetic effort underlying them, their movements – even those of the newest systems – still appear rather artificial.
We believe that the main reason for the current almost saturation-level of development in the construction of walking machines intended to achieve anthropomorphic bipedal gait (which is more of an impression than a fact given our knowledge of the high level of effort and investment needed to achieve really better machines year by year) is the restriction to mining descriptive data that answer the deductive question, ‘how?’ Doing so avoids a search for answers to the more inductive question ‘why?’ and its derivatives ‘why so?’ and ‘why not otherwise?’ These questions may only be answered by looking at the relatives and ancestors of humans as references for the flow of evolution, in other words, by functional morphology. ‘Functional’ in this context means mechanical as well as neuronal, while ‘morphology’, as the science dealing with comparative anatomy, includes aspects of historical development – either of a species (phylogeny) or of individuals within those species (ontogeny).
As noted before, the main misconception of human bipedalism is to see humans as completely different from all other animals. But what, in the light of functional morphology, is genuinely special about human bipedalism? We must recognize, more clearly than has previously been the case, that cyclical deformations of the trunk during walking do occur to a measurable degree, and occur in other modes than are observable in our mammalian relatives. The twisting about the longitudinal axis of the trunk that occurs during walking reveals, in particular, interdependencies of amplitude and velocity (see Fig. 1), which point to an interaction with the well-known mechanical behaviour of the legs and arms. In the case in hand, axial torsion of the trunk has a relative minimum at a velocity of about 1 m s−1, which has been identified as ‘energetically optimal’ for the whole body (Margaria et al. 1963; Pugh, 1971; Cavagna et al. 1977). At this velocity the gravitational pendula of legs and arms are resonant (see Fig. 2), and adapted to the resonance frequency of the leg acting as an inverted pendulum (cf. Mochon & McMahon, 1980a,b) with a torsional spring at its lower end (see Fig. 3). Resonant systems need minimal energy input; the trunk as a driving system may have a relative minimum amplitude exciting the pivots of the legs and trunk. Outside the range of resonant frequencies of the pendula, the trunk is required to influence movements of the limbs to a greater degree. Whether energy is transferred between trunk and limbs is hardly controversial, but in any case the effector control information is provided by the trunk, in a standard manner: cranio-caudal excitation waves run down the spinal cord even in phylogenetically old forms such as lizards, initiated and modulated by central pattern generators (CPGs) and locomotor primitives. These waves are distributed to the muscles by a species-specific cable network called the ‘neural plexus’. The mechanical interactions, between the swinging pendula formed by the arms and legs and the trunk, tend to rotate the latter. On the one hand, these rotations are recruited for locomotor purposes – pelvic rotation around the vertical elongates step lengths – on the other, pelvic rotation transferred from the hip to the foot optimizes joint posture for self-stabilization of the legs. The overall impression is, especially in comparison with other mammals, that rotations are reduced (and this, for example, limits perturbation of the brain and sensory organs). This purpose is served without additional cost to the individual inasmuch as the volume and mass of the trunk is determined by other (in the biomechanical context, extrinsic) factors, such as the necessity of circulation, breathing, nutrition, excretion and reproduction, and occurs by two means. The first is the distribution of mass so as to maximize mass moments of inertia. In the frontal and lateral perspective, mass is shifted to the ends of the trunk, giving it an hourglass shape with the typical human waist. Mass relationships between the pectoral and pelvic girdles are roughly comparable with the mass ratio of the upper and lower limbs, giving relatively short lever arms between the centre of gravity (CG) and hip joints and the (heavier) legs, compared with the longer lever arms between the CG and the shoulder joints, for the (lighter) arms (see Fig. 4). The second means is the out-of-phase swing of the contralateral arm and leg, providing joint forces, at the pivot, which act in a counter-rotating manner on the trunk (see Fig. 5). Owing to additional activity of the trunk musculature, these out-of-phase pivotal reaction forces do not necessarily lead to out-of-phase rotations of the pectoral girdle and pelvic girdle (see Fig. 1). Around longitudinal axes, the mass moments of inertia are maximized by a high ratio of the transverse and sagittal diameters of the trunk diameter, leading to elliptical cross-sections, and the typically human transversely oval trunk (see Fig. 6). In our nearest primate relatives such as chimpanzees, these cross-sections are in contrast more or less circular, and in quadrupedal mammals the ratio of diameters is actually in inverse proportion to the case in humans – the thorax, in particular, is narrow but deep.
These interpretations, based on rigid body mechanics, need to be complemented by some elasto-mechanics. Even in standing, the human locomotor apparatus stores elastic energy to a significant degree (Witte et al. 1997). In addition to the collagen in tendons and fascia – for which the relatively small amount in humans suggests may be of more importance in quadrupeds – the muscle bellies have an elastic giant protein content, that is the substrate of this elastic energy storage. Titin, as the main representative of a whole group of elastic giant proteins, is orientated in parallel to the active apparatus of the muscle (see Fig. 7).
As a consequence of the regionalization of the electrical activation patterns of muscles (cf. Scholle et al. 2001) muscle may form a tunable spring. In the human trunk, these muscle springs are situated crosswise, at some 45° to the longitudinal axis. In their ideal form, they actively, and elastically, drive trunk torsion (see Fig. 8). As a consequence, the linear connection between thorax and pelvis, formed by these muscle springs, yields the hyperboloid external contour we call the waist.
In contrast to the usual discussions of human locomotion, our functional morphological analyses of the limbs may be quite brief. In view of the restriction of the motion of the fore- and hindlimbs of cyclically moving mammals into the parasagittal plane and so into approximately two-dimensional (and hence mechanically simple) motion, the main aspect of interest is mass distribution, which may be explained as a means by which to shorten the pendular period, while elongating the step length, by concentrating mass at the proximal ends (i.e. near the trunk: see Fig. 9).
The length ratios of the long segments may to some extent be regarded as adaptations to minimize joint rotation per linear displacement of the feet and hands. Their fine-tuning is determined by adaptations to the needs of self-stabilization (‘intelligent mechanics’; cf. Seyfarth et al. 2001). The need to use the ankle joint as a torsional spring leads to adaptation of the shape and structure of the feet, while grasping determines the shape of hands, and leads to a concentration of muscle mass in the lower arms. It therefore provides comparable pendulum lengths of arms and legs, even if overall dimensional lengths are different.
The spatial excursion of a pendulum is proportional to its length, and the swing time is proportional to the square root of the (pendulum) length. If swing is converted into spatial gain, velocity at resonance, as the ratio of spatial excursion and swing time, is proportional to the square root of length. Therefore, in energetic terms, the longer the limbs, the higher the optimal velocity. This tendency is limited by the need for coordinated interaction of gravitational and elastic mechanisms (see Fig. 10).
When expressing the above conclusions quantitatively, as is required for engineering design, our main problem is a lack of information concerning the pattern of trunk motions dependent on walking velocity: are relationships like that illustrated in Fig. 1 for an individual typical of humans? According to data recorded by Thurston & Harris (1983) at given velocities, it is supposed to be more or less self-evident (cf. Inman et al. 1981) that trunk motion is recruited in walking, and quantification of such motion is even applied in matched-pair comparisons for clinical purposes (e.g. Wagenaar & Beek, 1992). But we currently have no answer as to whether there is a velocity-dependent pattern of trunk motion in walking, nor do we even have a standard quantification of such motion. Thus experimental data were required to support the argument of this paper.
Volunteers walked on a treadmill at velocities of 2.0–6.0 km h−1 with increments of 0.5 km h−1. Motion of the pectoral and pelvic girdles was documented for periods of 30 s at each velocity, during a stepwise increase and decrease of treadmill speed (ascending ramp: 2.0 km h−1; 2.5 km h−1 up to 6.0 km h−1; descending ramp: 6.0 km h−1; 5.5 km h−1 down to 2.0 km h−1).
The frequency profiles of shoulder and pelvic movements were first determined using a six-camera Qualisys® MCU 1000 motion analysis system, using an acquisition frequency of 240 Hz, in a pilot study on five volunteers. Movements of the pectoral girdle were represented by a marker triplet over the sternum, and those of the pelvic girdle were tracked by a marker triplet over the sacrum (Fig. 11, left). Cyclical translational and rotational movements were found to be periodic to a high degree, but only in the frontal and transverse planes. The highest basic frequencies in a fast Fourier transformation (FFT) were equal to the (double) step frequency. Harmonics with amplitudes higher than the predicted error occurred up to frequencies of 3 Hz.
For the main study, following the Shannon–Nyquist theorem, we chose a sampling frequency in excess of eight times the highest resolvable harmonics, at a minimum of 24 Hz. Analysis was subsequently made using a Zebris® CMS 50 ultrasonic motion analyser with a single-marker acquisition frequency of 26 Hz. To reduce any interference with subjects caused by gluing marker triplets to the skin, an alternative marker set-up was evaluated (Fig. 11, right). Motion of the scapula was represented by motion of the acromion processes. The anterior superior iliac spines (ASIS) were chosen as anatomical landmarks for the pelvic girdle. This set-up provides reliable data for two of the three diagonal components of the rotational matrices of the pectoral and pelvic girdles: axial rotation leading to torsion of the trunk in the transverse plane, and frontal tilting, leading to frontal bending, of the trunk. Sagittal tilting, leading to sagittal bending, was not recorded, but because the pilot study could not identify periodic sagittal bending, such motion is outside the purview of this study.
Marker motion was tracked using cartesian coordinates. Rotations of the shoulder and the pelvic girdle were represented by rotations of projections of the two lines connecting each acromion process to the ASIS. Axial torsion and frontal bending of the trunk were represented by changes in those angles between corresponding frames. Periodicity of all data taken was checked by FFT analyses. Normalized cross correlations of data were calculated to identify any coupling of the motion of the pectoral and pelvic girdle, using DIADEM® (GfS®, Aachen, Germany) software. Statistics were calculated using SPSS® (SPSS GmbH, Munich, Germany).
The 30 female and 30 male volunteers, who lacked any known disorder of the locomotor apparatus, showed no significant morphometric differences from the anthropometric standards of Flügel et al. (1986) (Table 1). Kinematic results showed no significant differences between the induction pattern of the ascending and the descending ramps of the velocity profile. Treadmill speed was established, independently of the volunteer's weight, to lie within ±0.05 km h−1 tolerance.
Table 1. Anthropometric descriptors of volunteers
Females (n = 30)
Males (n = 30)
23.1 ± 4.1
25.5 ± 4.3
Body height (cm)
171.6 ± 5.6
181.2 ± 6.1
Body weight (kg)
62.0 ± 8.1
77.0 ± 10.0
Biglenoidal width (cm)
39.1 ± 1.6
42.7 ± 2.9
Biacetabular width (cm)
24.5 ± 2.4
25.6 ± 2.6
The male volunteers showed no significant differences in choice of step length and step frequency at equivalent velocities from those of a sample of 24 male volunteers observed during unrestrained walking on a sports field (Witte, 1992). Thanks to strict control of environmental disturbance (e.g. temperature and air flow) the theoretical single marker resolution of the Zebris® system (±1 mm) was nearly achieved, error being within ±1.3 mm. Moreover, pelvic width of female volunteers, which was the smallest landmark pair examined, showed a rotational error of only ±0.6°, giving an expected error for trunk torsion and frontal bending of ±0.9°.
When the volunteers were walking, torsional twist and frontal bending of the trunk occurred according to the pattern described by Thurston & Harris (1983). The variables that did change with walking velocity were the amplitude of rotation and the phase relationship between the rotations of the pectoral and pelvic girdles. In the transverse plane (Fig. 12), the amplitude of rotation of the pectoral girdle at basic frequencies decreases with increasing speed. Pelvic rotation shows an absolute minimum at 4.0 km h−1, the ‘energetically optimal’ speed (Margaria et al. 1963; Pugh, 1971; Cavagna et al. 1977). The resulting effect on trunk torsion is at its relative minimum at the same speed. This is not self-evident from the velocity-dependent phase shift of the shoulder and pelvic rotations, which increases more or less linearly from low velocities to one-quarter of cycle duration (90° or π/2) at the ‘energetically optimal’ speed. At higher velocities, phase shift approaches one-third of cycle duration asymptotically and never reaches the value of half a cycle, which represents cross-wise or diagonal movements (cf. the gait definitions of Hildebrand, 1985). At all velocities above the ‘energetically optimal’, significant gender differences occur (Table 2).
In the frontal plane (Fig. 13), the amplitude of shoulder and pelvic tilt at basic frequencies increases with increasing velocity. Frontal bending in male volunteers tends to show an absolute minimum at the ‘energetically optimal speed’, but differences with neighbouring velocities are not significant. Frontal bending in female volunteers is constant and thus velocity-independent. Phase shift between shoulder and pelvic tilt is slightly less than a half cycle at all velocities. Results for the frontal plane, however, show no significant gender differences.
The phase difference between shoulder and pelvic tilt in the frontal plane, constantly under a half cycle, indicates that the measurements used in this study are insufficient to describe completely the pattern of trunk movements in the frontal plane. This results from temporary blockage of frontal pelvic rotations during double support, leading to a resting period with constant values in double support, which is not clearly defined by FFT. In addition, although the values of rotations are far beyond the predicted range of error, this is not the case for their difference: pelvic tilt. Owing to these problems, our results on the velocity-dependent pattern of frontal bending in walking should be taken only as indicative of the possible direction of further studies, and will be discussed no further.
In contrast to this, our results for rotational movements of the trunk in the transverse plane do not suffer from these restrictions. Movements are periodic without overlay of intersecting constant phases, and values recorded are well outside the predicted range of error.
In the group of young adults studied, we found that both men and women perform periodic motions of the trunk around longitudinal axes while walking, and these change systematically with walking velocity. Our interpretation of this observation is that the trunk is systematically employed for locomotor purposes. The relative minimum of trunk torsion at energetically optimal speeds indicates an interplay between the trunk and limbs. At speeds at which the limb pendula swing in resonance (as discussed at the present symposium by Preuschoft, following Weber & Weber, 1836, and later studies), torsion of the trunk is lower than at either lower or higher velocities. We consider that this resembles the relative minima in power consumption of the limbs when swinging resonantly; the trunk is not required to drive the limbs. Under this hypothesis, we require in future to test whether any such ‘driving’ is the consequence only of timing of the interaction of trunk and limbs. The occurrence of such phenomena would be a logical consequence of our phylogenetic heritage, even if expressed in terms of CPGs (cf. Grillner & Zangger, 1975; Selverston, 1999; Grillner et al. 2000), or of motor primitives (Mussa-Ivaldi et al. 1988, 1994; Mussa-Ivaldi & Bizzi, 2000). However, owing to the fact that the resonance effects observed here are expressed in terms of mechanics, it seems reasonable to doubt a hypothesis that no relevant energy transfer between trunk and limbs occurs in human locomotion (cf. Czerniecki et al. 1996; Krabbe et al. 1997). Because the huge methodological problems in determining energy flows within compliant mechanisms such as human beings will not be solved within the near future, humanoid robotics might provide alternative test beds.
Humans, like many other animals, are unusual in many respects (e.g. their bipedalism, and their grasping and sitting abilities), but from a zoological viewpoint they are nothing special. Humans are tetrapods – land-living vertebrates – and as such embody the evolutionary heritage of early tetrapods, some 200 million years ago. Vertebrates that in effect consist simply of a trunk (e.g. snakes) are well able to move despite being limbless; limbs without a musculoskeletal trunk, however, do not and cannot exist. Thus, all human movement has to be understood to originate from the trunk, even if at the present state of knowledge, we are not able to decide whether this means the generation or simply the initiation of movement. All neuronal information for the activation of muscles originates from the spinal cord, an axial organ situated in the trunk, and in the early phylogenetic stages was evolved to drive the trunk. In cyclical locomotion, vertebrate trunks show systematic deformations in all three rotatory degrees of freedom.
Thus, in addition to the large amount of information collected about human bipedalism since Weber, future models of human locomotion must explicitly incorporate the dynamic and kinetic interaction between trunk and extremities. The implicit integration of multibody models does lead to correct results in both inverse and forward dynamic analyses, but disguises the underlying principles. Understanding such principles, however, is the basis of bionic approaches. As biomimetic duplicates of animals are impossible for many reasons, lack of adequate materials being the most obvious, engineers have to try to realize function by different mechanisms. Experience shows that this work is facilitated if mass distribution (body shape) and mechanical functions (such as locomotion) fit together in the manner that has been identified in the natural paragons of bionic inspiration. In the case of human robotics, it seems necessary for psychological reasons for machines both to look like humans (anthropomorphic machines) and to show similar functional interactions with the environment to humans (anthropofunctional machines). This is no general paradigm for bionically inspired robotics: a quadrupedal machine searching for victims in emergency situations does not necessarily have to look like a dog.
By contrast, anthropomorphic (with respect to mass distribution, motion abilities and ranges and to elasticity) robots with anthropofunctional guidance and control will we hope allow for testing hypotheses of functional morphology and related natural sciences concerning human bipedalism and locomotion.
Research leading to this paper was supported by Deutsche Forschungsgemeinschaft (Bonn, Germany), Berufsgenossenschaft Gaststaetten und Nahrungsmittel (Erfurt/Mannheim, Gemany) and Gesellschaft zur Foerderung Kynologischer Forschung (Bonn, Germany).