Leg coordination during turning on an extremely narrow substrate in a bug, Mesocerus marginatus (Heteroptera, Coreidae)

The turning movement of a bug, Mesocerus marginatus, is observed when it walks upside-down below a horizontal beam and, at the end of the beam, performs a sharp turn by 180 degrees . The turn at the end of the beam is accomplished in three to five steps, without strong temporal coordination among legs. During the stance, leg endpoints (tarsi) run through rounded trajectories, rotating to the same side in all legs. During certain phases of the turn, a leg is strongly depressed and the tarsus crosses the midline. Swing movements rotate to the same side as do leg endpoints in stance, in strong contrast to the typical swing movements found in turns or straight walk on a flat surface. Terminal location is found after the search through a trajectory that first moves away from the body and then loops back to find substrate. When a leg during stance has crossed the midline, in the following swing movement the leg may move even stronger on the contralateral side, i.e. is stronger depressed, in contrast to swing movements in normal walking, where the leg is elevated. These results suggest that the animals apply a different control strategy compared to walking and turning on a flat surface.     

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.     

Mechanisms of stick insect locomotion in a gap-crossing paradigm

Locomotion of stick insects climbing over gaps of more than twice their step length has proved to be a useful paradigm to investigate how locomotor behaviour is adapted to external conditions. In this study, swing amplitudes and extreme positions of single steps from gap-crossing sequences have been analysed and compared to corresponding parameters of undisturbed walking. We show that adaptations of the basic mechanisms concern movements of single legs as well as the coordination between the legs. Slowing down of stance velocity, searching movements of legs in protraction and the generation of short steps are crucial prerequisites in the gap-crossing task. The rules of leg coordination described for stick insect walking seem to be modified, and load on the supporting legs is assumed to have a major effect on coordination especially in slow walking. Stepping into the gap with a front leg and antennal contact with the far edge of the gap provide information, as both events influence the following leg movements, whereas antennal non-contact seems not to contain information. Integration of these results into the model of the walking controller can improve our understanding of insect locomotion in highly irregular environments.Abbreviations AEP anterior extreme position - fAEP fictive anterior extreme position - PEP posterior extreme position - TOT treading-on-tarsus     

Differential control of temporal and spatial aspects of cockroach leg coordination

Ensembles of neuronal networks and sensory pathways participate in controlling the kinematic and dynamic parameters of animal movement necessary to achieve motor coordination. Determining the relative contribution of proprioceptive feedback is essential for understanding how animals sustain stable, coordinated locomotion in complex natural environments. Here, we focus on the role of chordotonal organs (COs), proprioceptors found in insect legs, in the spatial and temporal regulation of walking. We compare gait parameters of intact cockroaches (Periplaneta americana) and sensory-impaired ones, injected with pymetrozine, a chemical previously shown to abolish CO function in locusts. We verify that afferent CO activity in pymetrozine-treated cockroaches is inhibited, and analyze the effect of this sensory deprivation on inter-leg coordination. We find significant changes in tarsi placement and leg path trajectories after pymetrozine treatment. Leg touchdown accuracy, measured from relative tarsi positions of adjacent legs, is reduced in treated animals. Interestingly, despite poorer spatial coordination in both stance and swing, temporal properties of the gait remain largely the same as in the intact preparations, apart from changes in ipsilateral phase differences between front and middle legs. These findings provide insights into the role of COs in insect gait control and establish pymetrozine as a useful tool for further studies of insect locomotion.     

Gait transitions in simulated reduced gravity

Gravity has a strong effect on gait and the speed of gait transitions. A gait has been defined as a pattern of locomotion that changes discontinuously at the transition to another gait. On Earth, during gradual speed changes, humans exhibit a sudden discontinuous switch from walking to running at a specific speed. To study the effects of altered gravity on both the stance and swing legs, we developed a novel unloading exoskeleton that allows a person to step in simulated reduced gravity by tilting the body relative to the vertical. Using different simulation techniques, we confirmed that at lower gravity levels the transition speed is slower (in accordance with the previously reported Froude number ～0.5). Surprisingly, however, we found that at lower levels of simulated gravity the transition between walking and running was generally gradual, without any noticeable abrupt change in gait parameters. This was associated with a significant prolongation of the swing phase, whose duration became virtually equal to that of stance in the vicinity of the walk-run transition speed, and with a gradual shift from inverted-pendulum gait (walking) to bouncing gait (running).     

Kinematics and motor activity during tethered walking and turning in the cockroach, <Emphasis Type="Italic">Blaberus discoidalis</Emphasis>

When insects turn from walking straight, their legs have to follow different motor patterns. In order to examine such pattern change precisely, we stimulated single antenna of an insect, thereby initiating its turning behavior, tethered over a lightly oiled glass plate. The resulting behavior included asymmetrical movements of prothoracic and mesothoracic legs. The mesothoracic leg on the inside of the turn (in the apparent direction of turning) extended the coxa-trochanter and femur-tibia joints during swing rather than during stance as in walking, while the outside mesothoracic leg kept a slow walking pattern. Electromyograms in mesothoracic legs revealed consistent changes in the motor neuron activity controlling extension of the coxa-trochanter and femur-tibia joints. In tethered walking, depressor trochanter activity consistently preceded slow extensor tibia activity. This pattern was reversed in the inside mesothoracic leg during turning. Also for turning, extensor and depressor motor neurons of the inside legs were activated in swing phase instead of stance. Turning was also examined in free ranging animals. Although more variable, some trials resembled the pattern generated by tethered animals. The distinct inter-joint and inter-leg coordination between tethered turning and walking, therefore, provides a good model to further study the neural control of changing locomotion patterns.     

Stick insects walking along inclined surfaces

In the experiments stick insects walk on an inclined substratesuch that the legs of one side of the body point uphill andthe legs of the other side point downhill. In this situationthe vertical axis of the body is rotated against the inclinationof the substrate as if to compensate for the effect of substrateinclination. A very small effect has been found when the experimentwas performed with animals standing on a tilted platform whichshows that the effect depends on the behavioral context. When,however, animals first walked along the inclined surface andthen, before measurement, stopped walking spontaneously, a rotationof the body has been observed similar to that in walking animals.In a second experiment it was tested whether the observed bodyrotation is caused by the change of direction of gravity vectoror by the fact that on an inclined surface gravity necessarilyhas a component pulling the body sideways. Experiments withanimals standing on horizontal ground and additional weightsapplied pulling the body to the side showed similar body rotationssupporting the latter idea. In a simulation study it could beshown that the combined activity of proportional feedback controllersin the leg joints is sufficient to explain the observed behavior.This is however only possible if the gain factors of coxa-trochanterjoint controller and of femur-tibia joint controller show aratio in the order of 1 : 0.05 to 1 : 1.8. In order to describethe behavior of animals standing on a tilted platform, a ratioof 1 : 1.7 is necessary. In walking animals, this body rotationrequires to change the trajectories of stance and swing movements.The latter have been studied in more detail. During swing, thefemur-tibia joint is more extended in the uphill legs. Conversely,the coxa-trochanter joint appears to be more elevated in thedownhill legs which compensates the smaller lift in the femur-tibiajoint. The results are discussed in the context of differenthypotheses.     

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.     

Walking in the American cockroach: the timing of motor activity in the legs during straight walking

The timing of bursts of motor activity in extensor muscles in the coxae of pairs of legs in intact freely walking American cockroaches was studied. The timing of bursts in adjacent and non-adjacent leg pairs generally reflected the common alternating tripod gait of these insects. Detailed study of the timing further revealed two previously unreported features. (1) The timing of extensor bursts in the middle legs relative to bursts in the rear legs was more variable than it was relative to those in the front legs. This difference in variability was statistically significant for the means of bursts when all insects were considered together as well as for bursts in individual insects. An apparent difference in variability of the timing of burst starts compared to burst ends for any one leg pair was not significant. (2) There was a shift in the timing of motor bursts relative to one another when an insect walked fast such that motor bursts in the middle legs tended to lag farther behind those in the front legs, and those in the rear legs tended to lag farther behind those in the middle legs compared to the timing during slow walking. This shift was apparent in both burst starts and burst ends, although more obvious in the former. It occurred in both ipsilateral and contralateral leg pairs, and in both the mean data and the data for individual insects. The implications of these characteristics of the timing data are discussed in terms of the neural organization of insect walking.     

Kinematics of walking in the hermit crab,Pagurus pollicarus

Hermit crabs are decapod crustaceans that have adapted to life in gastropod shells. Among their adaptations are modifications to their thoracic appendages or pereopods. The 4th and 5th pairs are adapted for shell support; walking is performed with the 2nd and 3rd pereopods, with an alternation of diagonal pairs. During stance, the walking legs are rotated backwards in the pitch plane. Two patterns of walking were studied to compare them with walking patterns described for other decapods, a lateral gait, similar to that in many brachyurans, and a forward gait resembling macruran walking.Video sequences of free walking and restrained animals were used to obtain leg segment positions from which joint angles were calculated. Leading legs in a lateral walk generated a power stroke by flexion of MC and PD joints; CB angles often did not change during slow walks. Trailing legs exhibited extension of MC and PD with a slight levation of CB. The two joints, B/IM and CP, are aligned at 90° angles to CB, MC and PD, moving dorso-anteriorly during swing and ventro-posteriorly during stance. A forward step was more complex; during swing the leg was rotated forward (yaw) and vertically (pitch), due to the action of TC. At the beginning of stance, TC started to rotate posteriorly and laterally, CB was depressed, and MC flexed. As stance progressed and the leg was directed laterally, PD and MC extended, so that at the end of stance the dactyl tip was quite posterior. During walks of the animal out of its shell, the legs were extended more anterior-laterally and the animal often toppled over, indicating that during walking in a shell its weight stabilized the animal.An open chain kinematic model in which each segment was approximated as a rectangular solid, the dimensions of which were derived from measurements on animals, was developed to estimate the CM of the animal under different load conditions. CM was normally quite anterior; removal of the chelipeds shifted it caudally. Application of forces simulating the weight of the shell on the 5th pereopods moved CM just anterior to the thoracic-abdominal junction. However, lateral and vertical coordinates were not altered under these different load conditions. The interaction of the shell aperture with proximal leg joints and with the CM indicates that the oblique angles of the legs, due primarily to the rotation of the TC joints, is an adaptation that confers stability during walking.     

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.     

Influence of loading parallel to the body axis on the walking coordination of an insect

It is often reported in the early literature that insects walk with the legs protacting in diagonal pairs rather than the triplet of three legs associated with the tripod step pattern. The diagonal pattern implies that legs of the same segment have a phase relationship significantly different from 0.5. Such a pattern of leg recovery has been demonstrated quantitatively for the stick insect (Graham, 1972). Such patterns occur in several insects and systematic asymmetry can even be detected in the earliest quantitative study on cockroaches (Hughes, 1957) when the animals are walking slowly. More recently Spirito and Mushrush (1979) have reported systematic deviations from a phase of 0.5 similar to those observed in stick insects. Asymmetry has also been quantitatively demonstrated in Katydids (Graham, 1978) and has recently been observed in Mantid walking (Thomson, personal communication). This phenomenon seems to be a general characteristic of slow walking coordination in insects. In stick insects asymmetry only becomes obvious in gait II at slow speeds although there can be systematic differences in ipsilateral coordination on right and left sides even at the highest speeds in this gait (Graham, 1972).     

Characteristics of sit-to-stand and gait coordination in patients with total hip replacement

Upright posture, standing up from a chair, and gait were analyzed in patients after one-sided total hip replacement and in healthy subjects (control). It was found that the patients predominantly loaded the unoperated leg when they stood quietly or rose from a chair. Subjects’ walking on a 10-m podograph treadmill showed that their walking speed was slower than that of healthy subjects and the swing phase on the side of hip replacement was longer than on the unoperated side. It was assumed that the unequal load on legs during walking, standing, and sit-to-stand performance in patients with total hip replacement was related to the sensory deficit of the artificial joint, leading to the overstrain of the unoperated leg and coxarthrosis in it.     

Controlling propulsive forces in gait initiation in transfemoral amputees

During prosthetic gait initiation, transfemoral (TF) amputees control the spatial and temporal parameters that modulate the propulsive forces, the positions of the center of pressure (CoP), and the center of mass (CoM). Whether their sound leg or the prosthetic leg is leading, the TF amputees reach the same end velocity. We wondered how the CoM velocity build up is influenced by the differences in propulsive components in the legs and how the trajectory of the CoP differs from the CoP trajectory in able bodied (AB) subjects. Seven TF subjects and eight AB subjects were tested on a force plate and on an 8 m long walkway. On the force plate, they initiated gait two times with their sound leg and two times with their prosthetic leg. Force measurement data were used to calculate the CoM velocity curves in horizontal and vertical directions. Gait initiated on the walkway was used to determine the leg preference. We hypothesized that because of the differences in propulsive components, the motions of the CoP and the CoM have to be different, as ankle muscles are used to help generate horizontal ground reaction force components. Also, due to the absence of an active ankle function in the prosthetic leg, the vertical CoM velocity during gait initiation may be different when leading with the prosthetic leg compared to when leading with the sound leg. The data showed that whether the TF subjects initiated a gait with their prosthetic leg or with their sound leg, their horizontal end velocity was equal. The subjects compensated the loss of propulsive force under the prosthesis with the sound leg, both when the prosthetic leg was leading and when the sound leg was leading. In the vertical CoM velocity, a tendency for differences between the two conditions was found. When initiating gait with the sound leg, the downward vertical CoM velocity at the end of the gait initiation was higher compared to when leading with the prosthetic leg. Our subjects used a gait initiation strategy that depended mainly on the active ankle function of the sound leg; therefore, they changed the relative durations of the gait initiation anticipatory postural adjustment phase and the step execution phase. Both legs were controlled in one single system of gait propulsion. The shape of the CoP trajectories, the applied forces, and the CoM velocity curves are described in this paper.     

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.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Phase-Dependent Effects of Transcutaneous Spinal Cord Stimulation on Regulation of Kinematics of Human Stepping Motions

The effect of transcutaneous electrical spinal cord stimulation on the kinematic parameters of movement of the ipsilateral and contralateral legs in healthy subjects during treadmill walking at speeds of 1.5 to 1.7 km/h has been studied. The stimulation electrodes were placed 2.5 cm lateral from the right and left sides of the spinal midline at L1 and T11 levels. During the stance phase, stimulation was administered at L1 level at a frequency of 15 Hz; during the swing phase the stimuli was delivered to T11 at a frequency of 30 Hz, followed by alternating stimulation at L1 and T11. The stimulation during the swing phase (T11) was more effective than that during the stance phase (L1); the most impressive changes in kinematic parameters were observed when combined delivery of stimulations to L1 and T11 was performed. With unilateral spinal stimulation, the amplitude of the angles in the hip, knee and/or ankle joints, the length of the transfer, and the height of the leg elevation increased in the ipsilateral leg. Similar but less pronounced changes were observed in the contralateral leg. A 10% increase in the duration of stimulation in the swing phase caused a change in the kinematic stepping parameters both in ipsilateral and contralateral legs. The maximum effect was observed when bilateral alternating stimulation was used. These data show that phasic transcutaneous electrical spinal cord stimulation, using a wide range of natural walking speeds, can be applied to control kinematic movement parameters.

     

Effects of arm swing on mechanical parameters of human gait

The aim of this study was to investigate the influence of the upper limb swing on human gait. Measurements were performed on 52 subjects by using the Elite system with two cameras and a Kistler force platform. The recording of trajectories of characteristic body points on the subjects and the measurement of ground reaction forces have been performed at normal walking and at walking with emphasised rhythmic upper limb swing. The trajectory of the whole body mass centre, central dynamic moments of inertia and ground reaction forces have been calculated for every subject and mean curves of the entire group have been determined for walking with the natural and the emphasised upper limb swing. The determined mean values of normalised mechanical parameters have been compared and differences between the gait with the natural and the emphasised upper limb swing have been described.