A new model describing the coordination pattern of the legs of a walking stick insect

A computer (Fortran) model is proposed that describes the temporal and spatial coordination pattern of straight walking stick insects (Carausius morosus) for a broad speed range. It provides a stable pattern independent of the different starting positions. The model is based on six relaxation oscillators. The leading oscillator corresponds to a frontleg. Therefore the information flow runs from front to rear in contrast to earlier models (Graham, 1972; Wendler, 1968).Supported by DFG     

Walking in Aretaon asperrimus

This article describes basic parameters characterizing walking of the stick insect Aretaon asperrimus to allow a comparative approach with other insects studied. As in many other animals, geometrical parameters such as step amplitude and leg extreme positions do not vary with walking velocity. However, the relation between swing duration and stance duration is quite constant, in contrast to most insects studied. Therefore, velocity profiles during swing vary with walking velocity whereas time course of leg trajectories and leg angle trajectories are independent of walking velocity. Nevertheless, A. asperrimus does not show a classical tripod gait, but performs a metachronal, or tetrapod, gait, showing phase values differing from 0.5 between ipsilateral neighbouring legs. As in Carausius morosus, the detailed shape of the swing trajectory may depend on the form of the substrate. Effects describing coordinating influences between legs have been found that prevent the start of a swing as long as the posterior leg performs a swing. Further, the treading on tarsus reflex can be observed in Aretaon. No hint to the existence of a targeting influence has been found. Control of rearward walking is easiest interpreted by maintaining the basic rules but an anterior-posterior reversal of the information flow.     

The coordination of force oscillations and of leg movement in a walking insect (Carausius morosus)

As in the preceding paper stick insects walk on a treadwheel and different legs are put on platforms fixed relative to the insect's body. The movement of the walking legs is recorded in addition to the force oscillations of the standing legs. The coordination between the different legs depends upon the number and arrangement of the walking legs and the legs standing on platforms. In most experimental situations one finds a coordination which is different from that of a normal walking animal.Supported by DFG (Cr 58/1)     

Speed dependent phase shifts and gait changes in cockroaches running on substrates of different slipperiness

Background

Many legged animals change gaits when increasing speed. In insects, only one gait change has been documented so far, from slow walking to fast running, which is characterised by an alternating tripod. Studies on some fast-running insects suggested a further gait change at higher running speeds. Apart from speed, insect gaits and leg co-ordination have been shown to be influenced by substrate properties, but the detailed effects of speed and substrate on gait changes are still unclear. Here we investigate high-speed locomotion and gait changes of the cockroach Nauphoeta cinerea, on two substrates of different slipperiness.

Results

Analyses of leg co-ordination and body oscillations for straight and steady escape runs revealed that at high speeds, blaberid cockroaches changed from an alternating tripod to a rather metachronal gait, which to our knowledge, has not been described before for terrestrial arthropods. Despite low duty factors, this new gait is characterised by low vertical amplitudes of the centre of mass (COM), low vertical accelerations and presumably reduced total vertical peak forces. However, lateral amplitudes and accelerations were higher in the faster gait with reduced leg synchronisation than in the tripod gait with distinct leg synchronisation.

Conclusions

Temporally distributed leg force application as resulting from metachronal leg coordination at high running speeds may be particularly useful in animals with limited capabilities for elastic energy storage within the legs, as energy efficiency can be increased without the need for elasticity in the legs. It may also facilitate locomotion on slippery surfaces, which usually reduce leg force transmission to the ground. Moreover, increased temporal overlap of the stance phases of the legs likely improves locomotion control, which might result in a higher dynamic stability.

     

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.     

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     

Effect of walking speed on inter-joint coordination differs between young and elderly adults

Investigating inter-joint coordination at different walking speeds in young and elderly adults could provide insights to age-related changes in neuromuscular control of gait. We examined effects of walking speed and age on the pattern and variability of inter-joint coordination. Gait analyses of 10 young and 10 elderly adults were performed with different self-selected speeds, including a preferred, faster, and slower speed. Continuous relative phase (CRP), derived from phase planes of two adjacent joints, was used to assess the inter-joint coordination. CRP patterns were examined with cross-correlation measures and root-mean-square (RMS) differences when comparing ensemble mean curves of the faster or slower speed to preferred speed walking. Variability of coordination for each participant was assessed with the average value of all standard deviations calculated for each data point over a gait cycle from all CRP curves, namely the deviation phase (DP). For hip-knee CRP pattern, RMS differences were significantly greater between the slower and preferred walking speeds than between the faster and preferred walking speeds in young adults, but this was not found in elderly adults. Significant group differences in RMS differences and cross-correlation measures were detected in hip-knee CRP patterns between the slower and preferred walking speeds. No significant walking speed or age effects were detected for the knee-ankle CRP. Significant walking speed effects were also detected in hip-knee DP values. However, no significant group differences were detected for all three speeds. These findings suggested that young and elder adults compromise changes of walking speed with different neuromuscular control strategies.     

Fast axon activity and the motor pattern in cockroach legs during swimming

Abstract Electromyographic recordings were made from muscles that extend the trochanter/femur of each of the six legs of American cockroaches, Periplaneta americana (L.), while the insects swam in water. The recordings showed two novel features. (1) During swimming, muscle activity in different legs was coordinated in the alternating tripod pattern commonly seen during free walking on land, not in the pattern of synchronous leg pairs common to other large terrestrial insects in water. (2) Fast axons were usually recruited along with slow axons, even when the insect swam at a moderate pace. Fast axon activity always started after the middle of the slow axon burst in intact insects, but vanished from most bursts in the stump of the leg after amputation of the femur. The alternating tripod pattern was maintained even after amputation. Possible causes of fast axon recruitment are discussed.     

Coordination of legs during straight walking and turning in Drosophila melanogaster

Leg coordination of Drosophila melanogaster was studied using frame-by-frame film analysis. 1. For fastest walking alternating tripod coordination is observed which slightly deviates towards tetrapody as a function of step period. During acceleration or deceleration legs may transiently recover in diagonal pairs. 2. Mean step length increases with step frequency. 3. Mean recovery stroke duration increases with step period and plateaus beyond a period of about 110 ms. Middle legs recover significantly faster than others. 4. Ipsilateral footprints are transversally separated. 5. Walking is usually initiated in tripod coordination (frequently in combination with a turn), otherwise in an accelerating sequence which rapidly shifts towards tripod pattern. Flies can stop abruptly or decelerate over about one metachronal wave. 6. Short interruptions in walking are observed. Legs interrupted during swing phase stay lifted and finish recovery thereafter. 7. Slight changes in walking direction are obtained by altering step lengths only. Tight turns are composed of two or three phases with backward, zero and forward translatory components. In fast turning tripod coordination is maintained. Otherwise body sides can decouple widely. In all turns numbers of contralateral metachronal waves were equal. Results are compared to those for other walking insects and their relevance in screens for locomotor mutants is discussed.     

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

The coordination of adult stick insects walking on a light double wheel system with a fixed axle is examined as a function of friction loads applied to the wheels. Four parameters are influenced by loads parallel to the body axis in the range 0.08–1.0 p. Protraction duration at low stepping frequency falls to a value equal to that used in high speed walking and is therefore independent of step period for loads >0.4p. Above 0.4p the step period is significantly increased producing coordination patterns similar to those reported for free walking mature adults. Both the anterior (AEP) and posterior (PEP) extreme positions move forward with increasing load for all legs.     

A model of bipedal locomotion on compliant legs.

Simple mathematical models capable of walking or running are used to compare the merits of bipedal gaits. Stride length, duty factor (the fraction of the stride, for which the foot is on the ground) and the pattern of force on the ground are varied, and the optimum gait is deemed to be the one that minimizes the positive work that the muscles must perform, per unit distance travelled. Even the simplest model, whose legs have neither mass nor elastic compliance, predicts the changes of duty factor and force pattern that people make as they increase their speed of walking. It predicts a sudden change to running at a critical speed, but this is much faster than the speed at which people make the change. When elastic compliance is incorporated in the model, unnaturally fast walking becomes uncompetitive. However, a slow run with very brief foot contact becomes the optimum gait at low speeds, at which people would walk, unless severe energy dissipation occurs in the compliance. A model whose legs have mass as well as elastic compliance predicts well the relationship between speed and stride length in human walking.     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

A biologically inspired controller for hexapod walking: simple solutions by exploiting physical properties

The locomotor system of slowly walking insects is well suited for coping with highly irregular terrain and therefore might represent a paragon for an artificial six-legged walking machine. Our investigations of the stick insect Carausius morosus indicate that these animals gain their adaptivity and flexibility mainly from the extremely decentralized organization of the control system that generates the leg movements. Neither the movement of a single leg nor the coordination of all six legs (i.e., the gait) appears to be centrally pre-programmed. Thus, instead of using a single, central controller with global knowledge, each leg appears to possess its own controller with only procedural knowledge for the generation of the leg's movement. This is possible because exploiting the physical properties avoids the need for complete information on the geometry of the system that would be a prerequisite for explicitly solving the problems. Hence, production of the gait is an emergent property of the whole system, in which each of the six single-leg controllers obeys a few simple and local rules in processing state-dependent information about its neighbors.     

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.     

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).     

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.     

Gait Transitions in Human Infants: Coping with Extremes of Treadmill Speed

Spinal pattern generators in quadrupedal animals can coordinate different forms of locomotion, like trotting or galloping, by altering coordination between the limbs (interlimb coordination). In the human system, infants have been used to study the subcortical control of gait, since the cerebral cortex and corticospinal tract are immature early in life. Like other animals, human infants can modify interlimb coordination to jump or step. Do human infants possess functional neuronal circuitry necessary to modify coordination within a limb (intralimb coordination) in order to generate distinct forms of alternating bipedal gait, such as walking and running? We monitored twenty-eight infants (7–12 months) stepping on a treadmill at speeds ranging between 0.06–2.36 m/s, and seventeen adults (22–47 years) walking or running at speeds spanning the walk-to-run transition. Six of the adults were tested with body weight support to mimic the conditions of infant stepping. We found that infants could accommodate a wide range of speeds by altering stride length and frequency, similar to adults. Moreover, as the treadmill speed increased, we observed periods of flight during which neither foot was in ground contact in infants and in adults. However, while adults modified other aspects of intralimb coordination and the mechanics of progression to transition to a running gait, infants did not make comparable changes. The lack of evidence for distinct walking and running patterns in infants suggests that the expression of different functional, alternating gait patterns in humans may require neuromuscular maturation and a period of learning post-independent walking.     

Effects of circum-oesophageal lesion on the behaviour of the stick insect Carausius morosus

The co-ordination of the walking behaviour of decerebrate stick insects is examined and compared with normal behaviour. The walks are fully coordinated but undergo subtle changes in timing, have a longer average step period and show momentary pauses of 50 ms during the time course of protraction movements. In addition a new intersegmental reflex has been discovered. This tactile reflex is used to avoid errors in co-ordination that would be produced by posterior legs stepping onto the tarsi of the legs in front. The reflex has a latency of 100 ms and is easily observed in lesioned animals but is also active, although seldom seen, in slowly walking intact animals.     

Walk-, run- and gallop-like gait patterns in human sideways locomotion

The purpose of this study is to examine the characteristics of gait patterns in human preferred sideways locomotion at increasing speeds. Fifteen healthy young males were asked to step sideways on a treadmill at various speeds of 1.3–6.1 km/h. The times of foot contact and take-off were analyzed. Three gait patterns were observed. At slow speeds, all of the subjects performed a walk-like pattern. When the treadmill speed exceeded approximately 3.5 km/h, the subjects preferred gait patterns with a flight phase. Most of the subjects performed an asymmetric gait pattern that was similar to a forward gallop, whereas only two out of fifteen subjects performed a run-like gait pattern. Because the left and right legs are positioned along the movement direction, it might be more efficient to divide roles between the leading and trailing limbs at high speeds: the leading limb functions to produces breaking and vertical force, and the trailing limb mainly absorbs the impact of foot contact and generates propulsive forces.     

The effect of uphill and downhill walking on gait parameters: A self-paced treadmill study

It has been shown that gait parameters vary systematically with the slope of the surface when walking uphill (UH) or downhill (DH) (Andriacchi et al., 1977; Crowe et al., 1996; Kawamura et al., 1991; Kirtley et al., 1985; McIntosh et al., 2006; Sun et al., 1996). However, gait trials performed on inclined surfaces have been subject to certain technical limitations including using fixed speed treadmills (TMs) or, alternatively, sampling only a few gait cycles on inclined ramps. Further, prior work has not analyzed upper body kinematics. This study aims to investigate effects of slope on gait parameters using a self-paced TM (SPTM) which facilitates more natural walking, including measuring upper body kinematics and gait coordination parameters.Gait of 11 young healthy participants was sampled during walking in steady state speed. Measurements were made at slopes of +10°, 0° and −10°. Force plates and a motion capture system were used to reconstruct twenty spatiotemporal gait parameters. For validation, previously described parameters were compared with the literature, and novel parameters measuring upper body kinematics and bilateral gait coordination were also analyzed.Results showed that most lower and upper body gait parameters were affected by walking slope angle. Specifically, UH walking had a higher impact on gait kinematics than DH walking. However, gait coordination parameters were not affected by walking slope, suggesting that gait asymmetry, left-right coordination and gait variability are robust characteristics of walking. The findings of the study are discussed in reference to a potential combined effect of slope and gait speed. Follow-up studies are needed to explore the relative effects of each of these factors.