Behaviour-based modelling of hexapod locomotion: linking biology and technical application

Walking in insects and most six-legged robots requires simultaneous control of up to 18 joints. Moreover, the number of joints that are mechanically coupled via body and ground varies from one moment to the next, and external conditions such as friction, compliance and slope of the substrate are often unpredictable. Thus, walking behaviour requires adaptive, context-dependent control of many degrees of freedom. As a consequence, modelling legged locomotion addresses many aspects of any motor behaviour in general. Based on results from behavioural experiments on arthropods, we describe a kinematic model of hexapod walking: the distributed artificial neural network controller walknet. Conceptually, the model addresses three basic problems in legged locomotion. (I) First, coordination of several legs requires coupling between the step cycles of adjacent legs, optimising synergistic propulsion, but ensuring stability through flexible adjustment to external disturbances. A set of behaviourally derived leg coordination rules can account for decentralised generation of different gaits, and allows stable walking of the insect model as well as of a number of legged robots. (II) Second, a wide range of different leg movements must be possible, e.g. to search for foothold, grasp for objects or groom the body surface. We present a simple neural network controller that can simulate targeted swing trajectories, obstacle avoidance reflexes and cyclic searching-movements. (III) Third, control of mechanically coupled joints of the legs in stance is achieved by exploiting the physical interactions between body, legs and substrate. A local positive displacement feedback, acting on individual leg joints, transforms passive displacement of a joint into active movement, generating synergistic assistance reflexes in all mechanically coupled joints.     

The contralateral coordination of walking legs in the crayfish Astacus leptodactylus

The coupling mechanisms which coordinate the movement of ipsilateral walking legs in the crayfish have been described in earlier investigations. Concerning the coupling between contralateral legs it was only known that these influences are weaker than those acting between ipsilateral legs. The nature of these coupling mechanisms between contralateral legs of the crayfish are investigated here by running left and right legs on separate walking belts at different speeds. The results show that coordination is performed by a phase-dependent shift of the anterior extreme position of the influenced leg. This backward shift leads to a shortening of both the return stroke and the following power stroke. As the coupling influence is only weak, several steps might be necessary to retain normal coordination after a disturbance. This corresponds to v. Holst's relative coordination. The influences act in both directions, from left to right and vice versa. However, one side may be more or less dominant. A gradient was found in the way that anterior leg pairs show less strong coordination than posterior legs. In some cases the coupling between diagonally neighbouring legs was found to be stronger than between contralateral legs of the same segment. The interpretation of this result is still open.     

Tight turns in stick insects

We investigated insects Carausius morosus walking whilst hanging upside down along a narrow 3 mm horizontal beam. At the end of the beam, the animal takes a 180° turn. This is a difficult situation because substrate area is small and moves relative to the body during the turn. We investigated how leg movements are organised during this turn. A non-contact of either front leg appears to indicate the end of the beam. However, a turn can only begin if the hind legs stand in an appropriate position relative to each other; the outer hind leg must not be placed posterior to the inner hind leg. When starting the turn, both front legs are lifted and usually held in a relatively stable position and then the inner middle leg performs a swing-and-search movement: The leg begins a swing, which is continued by a searching movement to the side and to the rear, and eventually grasps the beam. At the same time the body is turned usually being supported by the outer middle leg and both hind legs. Then front legs followed by the outer middle leg reach the beam. A scheme describing the turns based on a few simple behavioural elements is proposed.     

Rotational locomotion by the cockroach Blattella germanica

Locomotion on complex substrata can be expressed in a plane by two geometric components of body movement: linear locomotion and rotational locomotion. This study examined pure rotation by analysing the geometry of leg movements and stepping patterns during the courtship turns of male Blattella germanica. Strict rotation or translation by an insect requires that each side of the body cover equal distance with respect to the substrate. There are three mechanisms by which the legs can maintain this equality: frequency of stepping, magnitude of the leg arcs relative to the body and the degree to which legs flex and extend during locomotion. During the courtship behaviour of Blattella germanica selected males executed turns involving body rotation along with leg movements in which the legs on the outside of the turn swung through greater average arcs than those on the inside of the turn. This difference should have resulted in a translation component. However, legs on the inside of the turn compensated by flexion and extension movements which were greater than those of opposing legs. The net effect was that both sides of the body covered equal average ground. These cockroaches used a wide variety of stepping combinations to effect rotation. The frequency of these combinations was compared to an expected frequency distribution of stepping combinations and further to an expected frequency of these stepping combinations used for straight walking. These comparisons demonstrated a similarity between interleg coordination during straight walking and that during turning in place.     

Influence of a movable support under one leg on human vertical posture during standing with asymmetrical load on legs

Changes in the vertical posture maintenance were studied when the legs were placed on supports of different degrees of mobility and part of the body weight was voluntarily transferred to one leg. The aim of these experiments was to explore how the mobility of support under the feet affects the balance and how this effect depends on the load distribution between the legs during standing. When both legs were on rigid immovable supports, the vertical posture was maintained by control of the center of pressure (CP) on both legs. When the subject transferred the weight to one foot, the posture was maintained mainly due to the control of CP of the loaded leg. When the legs were on supports of different degrees of mobility, the balance was maintained by the leg on the immovable support. This result was observed both when the subject stood with symmetrical load on the legs and when the load was transferred to one leg. Even when the leg was unloaded but placed on the immovable support, its CP moved more compared to the CP of the loaded leg on a movable support. The results obtained show that the support mobility is a factor that determines the mechanisms of posture maintenance, and this factor is more significant than load distribution between the legs. Thus, the upright posture is maintained with the physical properties of support under the feet taken into account.     

Sexually dimorphic legs in a neotropical harvestman (Arachnida,Opiliones): Ornament or weapon?

The evolution of sexually dimorphic traits has been the focus of much theoretical work, but empirical approaches to this topic have not been equally prolific. Males of the neotropical family Gonyleptidae usually present a strong fourth pair of legs armed with spines, but their functional significance is unknown. We investigated the putative functions of the leg armature in the harvestman Neosadocus maximus. Being a non-visual species, the spines on male legs can only be perceived by females through physical contact. Thus, we could expect females to touch the armature on the legs of their mates if they were to evaluate it. However, we found no support for this hypothesis. We did show that (1) leg armature is used as a weapon in contests between males and (2) spines and associated sensilla are sexually dimorphic structures involved in "nipping behavior", during which a winner emerged in most fights. Finally, we demonstrate that five body structures directly involved in male-male fights show positive allometry in males, presenting slopes higher than 1, whereas the same structures show either no or negative allometry in the case of females. In conclusion, leg armature in male harvestmen is clearly used as a device in intrasexual contests.     

Kinematic and kinetic analysis of the fouetté turn in classical ballet

The fouetté turn in classical ballet dancing is a continuous turn with the whipping of the gesture leg and the arms and the bending and stretching of the supporting leg. The knowledge of the movement intensities of both legs for the turn would be favorable for the conditioning of the dancer's body. The purpose of this study was to estimate the intensities. The hypothesis of this study was that the intensities were higher in the supporting leg than in the gesture leg. The joint torques of both legs were determined in the turns performed by seven experienced female classical ballet dancers with inverse dynamics using three high-speed cine cameras and a force platform. The hip abductor torque, knee extensor and plantar flexor torques of the supporting leg were estimated to be exerted up to their maximum levels and the peaks of the torques were larger than the peaks of their matching torques of the gesture leg. Thus, the hypothesis was partly supported. Training of the supporting leg rather than the gesture leg would help ballet dancers perform many revolutions of the fouetté turn continuously.     

External body dimensions ofPan paniscus andPan troglodytes chimpanzees

Postcranial skeletal studies have demonstrated thatPan paniscus is a more gracile animal thanPan troglodytes, with different arm to leg proportions. Published data on external body dimensions are extremely rare forPan paniscus, however. We present here a series of such measures for a sample ofpaniscus, and we compare these to similar measures forPan troglodytes. This comparison further clarifies the morphological distinctions between the two chimpanzee species, and indicates that bonobos have longer legs and smaller chest girths relative to overall body height than doPan troglodytes chimpanzees.     

Precise tuning of barnacle leg length to coastal wave action

Both spatial and temporal variation in environmental conditions can favour intraspecific plasticity in animal form. But how precise is such environmental modulation? Individual Balanus glandula Darwin, a common northeastern Pacific barnacle, produce longer feeding legs in still water than in moving water. We report here that, on the west coast of Vancouver Island, Canada, the magnitude and the precision of this phenotypic variation is impressive. First, the feeding legs of barnacles from protected bays were nearly twice as long (for the same body mass) as those from open ocean shores. Second, leg length varied surprisingly precisely with wave exposure: the average maximum velocities of breaking waves recorded in situ explained 95.6-99.5% of the variation in average leg length observed over a threefold range of wave exposure. The decline in leg length with increasing wave action was less than predicted due to simple scaling, perhaps due to changes in leg shape or material properties. Nonetheless, the precision of this relationship reveals a remarkably close coupling between growth environment and adult form, and suggests that between-population differences in barnacle leg length may be used for estimating differences in average wave exposure easily and accurately in studies of coastal ecology.     

Comparative Density of Hair Sensilla on the Legs of Cavernicolous and Epigean Harvestmen (Arachnida: Opiliones)

To allow an animal to behave appropriately, the location of sensorial structures is expected to be related to their function. As the different leg pairs of arachnids may have different functions (probing x supporting the body), one could expect them to have a different density of sensilla. Moreover, different regions of the same leg (dorsal, lateral, and ventral) would also be expected to have different densities of sensilla, according to the use of each region (e.g., the ventral part is often in contact with the substrate while the dorsal part is not). As cavernicolous animals are expected to be more sensitive than their epigean relatives, one could also expect a different density of sensilla when comparing cavernicolous and epigean animals. Using three epigean and three cavernicolous species of harvestmen (Arachnida, Opiliones), this study aimed at describing the morphology of hair sensilla on the legs and answering three questions: (1) Are there differences in the density of hair sensilla between the dorsal, lateral and ventral regions of each leg pair of the same individual? (2) Are there differences in the density of hair sensilla between the leg pairs of the same individual? (3) Are there differences in the density of hair sensilla when comparing the leg pairs of individuals of cavernicolous and non-cavernicolous species? The tarsi and metatarsi of all right legs of the six studied species were analyzed under a scanning electron microscope. The results (P < 0.05) showed that, in general: the ventral region of the tarsus was denser in sensilla trichodea than the lateral and dorsal regions, particularly on legs I and II; the density of sensilla chaetica did not differ on legs III and IV, but was greater on the dorsal region of legs I and II; the ventral part of legs I had the higher density of sensilla trichodea of the four pairs, whereas the second pair had the lower density; Holcobunus citrinus (Eupnoi) was the species with higher density of sensilla trichodea, on all legs; the cavernicolous species had a lower density of sensilla than the epigean species. The results are tentatively related to harvestmen behavior.     

The control of walking movements in the leg of the rock lobster

1. Experiments with rock lobsters walking on a treadmill were undertaken to obtain information upon the system controlling the movement of the legs. Results show that the position of the leg is an important parameter affecting the cyclic movement of the walking leg. Stepping can be interrupted when the geometrical conditions for terminating either a return stroke or a power stroke are not fullfilled. 2. The mean value of anterior and posterior extreme positions (AEP and PEP respectively) of the walking legs do not depend on the walking speed (Fig. 1). 3. When one leg is isolated from the other walking legs by placing it on a platform the AEPs and PEPs of the other legs show a broader distribution compared to controls (Figs. 2 and 3). 4. Force measurements (Fig. 4) are in agreement with the hypothesis that the movement of the leg is controlled by a position servomechanism. 5. When one leg stands on a stationary force transducer this leg develops forces which oscillate with the step rhythm of the other legs (Fig. 5). 6. A posteriorly directed influence is found, by which the return stroke of a leg can be started when the anterior leg performs a backward directed movement. 7. Results are compared with those obtained from stick insects. The systems controlling the movement of the individual leg are similar in both, lobster and stick insect but the influences between the legs seem to be considerably different.     

Maintenance of Human Vertical Posture upon Asymmetric Leg Loading and Fixation of the Knee Joint of One Leg

Maintenance of a vertical posture was studied in standing subjects with a fixed knee joint of one leg and a different weight distribution between the legs. Knee fixation on one leg did not affect the speed of movements of the common center of pressure (CP) at any weight distribution between the legs, and the stability of vertical posture was therefore unchanged. However, the relative contributions of the legs to the posture control changed when knee movements of one leg were restricted. The speed of CP movements of the free leg was independent of the weight loading on the leg. The speed of CP movements of the leg with the knee fixed depended on the weight distribution and was higher when the leg was loaded. Thus, the leg with the fixed knee joint made a greater contribution to maintaining vertical posture when the leg was loaded. Yet its contribution was comparable with that of the unloaded free contralateral leg even in this case, as was evident from lack of differences in CP movements between the two legs. It was assumed that the leg with the free knee joint played a major role in maintaining equilibrium of vertical posture, while the leg with the fixed knee joint mostly acted to more finely adjust the body position.     

Wings versus legs in the avian bauplan: Development and evolution of alternative locomotor strategies

Wings have long been regarded as a hallmark of evolutionary innovation, allowing insects, birds, and bats to radiate into aerial environments. For many groups, our intuitive and colloquial perspective is that wings function for aerial activities, and legs for terrestrial, in a relatively independent manner. However, insects and birds often engage their wings and legs cooperatively. In addition, the degree of autonomy between wings and legs may be constrained by tradeoffs, between allocating resources to wings versus legs during development, or between wing versus leg investment and performance (because legs must be carried as baggage by wings during flight and vice versa). Such tradeoffs would profoundly affect the development and evolution of locomotor strategies, and many related aspects of animal ecology. Here, we provide the first evaluation of wing versus leg investment, performance and relative use, in birds—both across species, and during ontogeny in three precocial species with different ecologies. Our results suggest that tradeoffs between wing and leg modules help shape ontogenetic and evolutionary trajectories, but can be offset by recruiting modules cooperatively. These findings offer a new paradigm for exploring locomotor strategies of flying organisms and their extinct precursors, and thereby elucidating some of the most spectacular diversity in animal history.     

Resonant frequencies of arms and legs identify different walking patterns

The present study is aimed at investigating changes in the coordination of arm and leg movements in young healthy subjects. It was hypothesized that with changes in walking velocity there is a change in frequency and phase coupling between the arms and the legs. In addition, it was hypothesized that the preferred frequencies of the different coordination patterns can be predicted on the basis of the resonant frequencies of arms and legs with a simple pendulum model. The kinematics of arms and legs during treadmill walking in seven healthy subjects were recorded with accelerometers in the sagittal plane at a wide range of different velocities (i.e., 0.3-1. 3m/s). Power spectral analyses revealed a statistically significant change in the frequency relation between arms and legs, i.e., within the velocity range 0.3-0.7m/s arm movement frequencies were dominantly synchronized with the step frequency, whereas from 0.8m/s onwards arm frequencies were locked onto stride frequency. Significant effects of walking speed on mean relative phase between leg and arm movements were found. All limb pairs showed a significantly more stable coordination pattern from 0.8 to 1.0m/s onwards. Results from the pendulum modelling demonstrated that for most subjects at low-velocity preferred movement frequencies of the arms are predicted by the resonant frequencies of individual arms (about 0.98Hz), whereas at higher velocities these are predicted on the basis of the resonant frequencies of the individual legs (about 0.85Hz). The results support the above-mentioned hypotheses, and suggest that different patterns of coordination, as shown by changes in frequency coupling and phase relations, can exist within the human walking mode.     

Hexapod Walking: an expansion to Walknet dealing with leg amputations and force oscillations

The control of the legs of a walking hexapod is a complex problem as the legs have three joints each, resulting in a total of 18 degrees of freedom. We addressed this problem using a decentralized architecture termed Walknet, which consists of peripheral pattern generators being coordinated through influences acting mainly between neighbouring legs. Both, the coordinating influences and the local control modules (each acting only on one leg), are biologically inspired. This investigation shows that it is possible to adapt this approach to account for additional biological data by (1) changing the structure of the selector net in a biological plausible way (including force as an analog variable), (2) introducing a biologically motivated coordination influence for coactivation between legs and (3) adding a hypothetical influence between hind and front legs. This network of controllers has been tested using a dynamic simulation. It is able to describe (a) the behaviour of animals walking with one or two legs being amputated and (b) force oscillations that occur in a specific experimental situation, the standing legs of a walking animal.     

Mass-induced oscillations in the femur-tibia control system of stick insects

Attaching an inert mass to a freely moving tibia of an otherwise fixed stick insect Carausius morosus, induces undamped oscillations of the tibia. We describe the use of a rotational pendulum to observe these oscillations applying various amounts of inertia. The dependence of the frequency of these oscillations on the moment of inertia is similar to that of a purely mechanical system. The sequence of the oscillatory behavior can be separated into 3 distinct behavioural states. The transitions between some of these states could be elicited by external stimuli and partly showed characteristics of habituation and dishabituation. With a rotational pendulum on each middle leg, simultaneous oscillations of both legs were measured to investigate coupling effects between the neural control systems of the two legs. In some cases, significant coupling effects could be observed in phase and frequency. In many other cases, no coupling was found. The habituation and dishabituation effects were not transferred between the middle legs.     

The control of body position in the stick insect (Carausius morosus), when walking over uneven surfaces

An investigation has been made of the way, in which the height of the body of an insect (Carausius morosus) is controlled when walking over an uneven terrain. The animals have been filmed from the side while walking over different types of irregularity (step up, step down, obstacle, ditch). A frame by frame analysis of the height of the three thoracic segments of the insect has been performed. A computer model has been set up, which is able to describe the experimental results within the exactness of measurement. This model consists of three independent height controllers, each having a unique characteristic. The coupling of these three controllers is performed mechanically. One possible interpretation of this model is that the height of each segment is controlled by a closed loop mechanism with a proportional element as a controller.Supported by the Deutsche Forschungsgemeinschaft     

Relationships between legs bone mineral density, anthropometry and jumping height in prepubertal children

The aim of this study was to determine how the legs bone mineral density (BMD) is influenced by anthropometry and vertical jumping height in prepubertal children. In total, 64 8-11-year-old schoolchildren (27 boys and 37 girls) were studied. All children were at Tanner stage 1. The subjects' height and body mass were measured and BMI calculated. The following anthropometric parameters directly connected with leg were measured: skinfolds--front thigh and medial calf girths--gluteal, thigh, mid-thigh, calf and ankle; lengths--iliospinale height, trochanterion height, trochanteriontibiale laterale, tibiale-laterale height and tibiale mediale-spyrion tibiale; and breadths--biiliocristal, foot length and biepicondylar femur. Total body and legs fat mass and fat %, lean body mass (LBM) and both legs BMD were measured by DXA. Maximal jumping height was measured on the contact mat. Stepwise multiple regression analysis indicated that body height in boys (54.6%; R2 x 100) and body mass in girls (57.3%) were the most important basic anthropometric parameters that influenced BMD in legs. From the measured skinfolds, that of the front thigh characterized legs BMD by 24.9-35.6%. From the girths, the most important parameter to characterize legs BMD was that of calf (50.0-59.1%). Tibiale laterale height was the only length parameter which was highly related with legs BMD (51.1-54.5%). Biepicondylar femur was the most important breadth parameter which characterized legs BMD (51.0-54.8%). Femur breadth and tibiale-laterale height were selected (68.7%) in boys, and tibiale-laterale height and front thigh skinfold thickness (66.0%) in girls when all measured leg anthropometric parameters were analyzed together. From the body composition parameters, the most important parameter to characterize legs BMD was legs LBM (48.9-59.5%). Jumping height did not correlate with legs BMD in any studied groups. In summary, the present study demonstrated that legs LBM together with tibiale-laterale height are the main predictors of legs BMD in prepubertal children.     

Common motor mechanisms support body load in serially homologous legs of cockroaches in posture and walking

We studied the mechanisms underlying support of body load in posture and walking in serially homologous legs of cockroaches. Activities of the trochanteral extensor muscle in the front or middle legs were recorded neurographically while animals were videotaped. Body load was increased via magnets attached to the thorax and varied through a coil below the substrate. In posture, tonic firing of the slow trochanteral extensor motoneuron (Ds) in each leg was strongly modulated by changing body load. Rapid load increases produced decreases in body height and sharp increments in extensor firing. The peak of extensor activity more closely approximated the maximum velocity of body displacement than the body position. In walking, extensor bursts in front and middle legs were initiated during swing and continued into the stance phase. Moderate tonic increases in body load elicited similar, specific, phase dependent changes in both legs: extensor firing was not altered in swing but was higher after foot placement in stance. These motor adjustments to load are not anticipatory but apparently depend upon sensory feedback. These data are consistent with previous findings in the hind legs and support the idea that body load is countered by common motor mechanisms in serially homologous legs.     

Studying the Neural Basis of Adaptive Locomotor Behavior in Insects

Studying the neural basis of walking behavior, one often faces the problem that it is hard to separate the neuronally produced stepping output from those leg movements that result from passive forces and interactions with other legs through the common contact with the substrate. If we want to understand, which part of a given movement is produced by nervous system motor output, kinematic analysis of stepping movements, therefore, needs to be complemented with electrophysiological recordings of motor activity. The recording of neuronal or muscular activity in a behaving animal is often limited by the electrophysiological equipment which can constrain the animal in its ability to move with as many degrees of freedom as possible. This can either be avoided by using implantable electrodes and then having the animal move on a long tether (i.e. Clarac et al., 1987; Duch & Pflüger, 1995; Böhm et al., 1997; Gruhn & Rathmayer, 2002) or by transmitting the data using telemetric devices (Kutsch et al, 1993; Fischer et al., 1996; Tsuchida et al. 2004; Hama et al., 2007; Wang et al., 2008). Both of these elegant methods, which are successfully used in larger arthropods, often prove difficult to apply in smaller walking insects which either easily get entangled in the long tether or are hindered by the weight of the telemetric device and its batteries. In addition, in all these cases, it is still impossible to distinguish between the purely neuronal basis of locomotion and the effects exerted by mechanical coupling between the walking legs through the substrate. One solution for this problem is to conduct the experiments in a tethered animal that is free to walk in place and that is locally suspended, for example over a slippery surface, which effectively removes most ground contact mechanics. This has been used to study escape responses (Camhi and Nolen, 1981; Camhi and Levy, 1988), turning (Tryba and Ritzman, 2000a,b; Gruhn et al., 2009a), backward walking (Graham and Epstein, 1985) or changes in velocity (Gruhn et al., 2009b) and it allows the experimenter easily to combine intra- and extracellular physiology with kinematic analyses (Gruhn et al., 2006).We use a slippery surface setup to investigate the timing of leg muscles in the behaving stick insect with respect to touch-down and lift-off under different behavioral paradigms such as straight forward and curved walking in intact and reduced preparations.