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.     

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.     

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.     

Activity of neuromodulatory neurones during stepping of a single insect leg

Octopamine plays a major role in insect motor control and is released from dorsal unpaired median (DUM) neurones, a group of cells located on the dorsal midline of each ganglion. We were interested whether and how these neurones are activated during walking and chose the semi-intact walking preparation of stick insects that offers to investigate single leg-stepping movements. DUM neurones were characterized in the thoracic nerve cord by backfilling lateral nerves. These backfills revealed a population of 6-8 efferent DUM cells per thoracic segment. Mesothoracic DUM cells were subsequently recorded during middle leg stepping and characterized by intracellular staining. Seven out of eight identified individual different types of DUM neurones were efferent. Seven types except the DUMna nl2 were tonically depolarized during middle leg stepping and additional phasic depolarizations in membrane potential linked to the stance phase of the middle leg were observed. These DUM neurones were all multimodal and received depolarizing synaptic drive when the abdomen, antennae or different parts of the leg were mechanically stimulated. We never observed hyperpolarising synaptic inputs to DUM neurones. Only one type of DUM neurone, DUMna, exhibited spontaneous rhythmic activity and was unaffected by different stimuli or walking movements.     

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).     

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.     

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     

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.     

How locomotion sub-functions can control walking at different speeds?

Inspired from template models explaining biological locomotory systems and Raibert׳s pioneering legged robots, locomotion can be realized by basic sub-functions: elastic axial leg function, leg swinging and balancing. Combinations of these three can generate different gaits with diverse properties. In this paper we investigate how locomotion sub-functions contribute to stabilize walking at different speeds. Based on this trilogy, we introduce a conceptual model to quantify human locomotion sub-functions in walking. This model can produce stable walking and also predict human locomotion sub-function control during swing phase of walking. Analyzing experimental data based on this modeling shows different control strategies which are employed to increase speed from slow to moderate and moderate to fast gaits.     

Bipedal walking and running with spring-like biarticular muscles

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.     

Motor neurone responses during a postural reflex in solitarious and gregarious desert locusts

Desert locusts show extreme phenotypic plasticity and can change reversibly between two phases that differ radically in morphology, physiology and behaviour. Solitarious locusts are cryptic in appearance and behaviour, walking slowly with the body held close to the ground. Gregarious locusts are conspicuous in appearance and much more active, walking rapidly with the body held well above the ground. During walking, the excursion of the femoro-tibial (F-T) joint of the hind leg is smaller in solitarious locusts, and the joint is kept more flexed throughout an entire step. Under open loop conditions, the slow extensor tibiae (SETi) motor neurone of solitarious locusts shows strong tonic activity that increases at more extended F-T angles. SETi of gregarious locusts by contrast showed little tonic activity. Simulated flexion of the F-T joint elicits resistance reflexes in SETi in both phases, but regardless of the initial and final position of the leg, the spiking rate of SETi during these reflexes was twice as great in solitarious compared to gregarious locusts. This increased sensory-motor gain in the neuronal networks controlling postural reflexes in solitarious locusts may be linked to the occurrence of pronounced behavioural catalepsy in this phase similar to other cryptic insects such as stick insects.     

A self-organizing model of walking patterns of insects

It is well known that the motor systems of animals are controlled by a hierarchy consisting of a brain, central pattern generator, and effector organs. An animal's walking patterns change depending on its walking velocities, even when it has been decerebrated, which indicates that the walking patterns may, in fact, be generated in the subregions of the neural systems of the central pattern generator and the effector organs. In order to explain the self-organization of the walking pattern in response to changing circumstances, our model incorporates the following ideas: (1) the brain sends only a few commands to the central pattern generator (CPG) which act as constraints to self-organize the walking patterns in the CPG; (2) the neural network of the CPG is composed of oscillating elements such as the KYS oscillator, which has been shown to simulate effectively the diversity of the neural activities; and (3) we have introduced a rule to coordinate leg movement, in which the excitatory and inhibitory interactions among the neurons act to optimize the efficiency of the energy transduction of the effector organs. We describe this mechanism as the least dissatisfaction for the greatest number of elements, which is a self-organization rule in the generation of walking patterns. By this rule, each leg tends to share the load as efficiently as possible under any circumstances. Using this self-organizing model, we discuss the control mechanism of walking patterns.     

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.     

Mechanical energy and effective foot mass during impact loading of walking and running

The human heel pad is considered an important structure for attenuation of the transient force caused by heel-strike. Although the mechanical properties of heel pads are relatively well understood, the mechanical energy (Etot) absorbed by the heel pad during the impact phase has never been documented directly because data on the effective foot mass (Meff) was previously unavailable during normal forward locomotion. In this study, we use the impulse-momentum method (IMM) for calculating Meff from moving subjects. Mass-spring-damper models were developed to evaluate errors and to examine the effects of pad property, upper body mass, and effective leg spring on Meff. We simultaneously collected ground reaction forces, pad deformation, and lower limb kinematics during impact phase of barefoot walking, running, and crouched walking. The latter was included to examine the effect of knee angle on Meff. The magnitude of Meff as a percentage of body mass (M(B)) varies with knee angle at impact and significantly differs among gaits: 6.3%M(B) in walking, 5.3%M(B) in running, and 3.7%M(B) in crouched walking. Our modeling results suggested that Meff is insensitive to heel pad resilience and effective leg stiffness. At the instant prior to heel strike, Etot ranges from 0.24 to 3.99 J. The combination of video and forceplate data used in this study allows analyses of Etot and Etot as a function of heel-strike kinematics during normal locomotion. Relationship between Meff and knee angle provides insights into how changes in posture moderate impact transients at different gaits.     

Molecular patterning mechanism underlying metamorphosis of the thoracic leg in Manduca sexta

The tobacco hornworm Manduca sexta, like many holometabolous insects, makes two versions of its thoracic legs. The simple legs of the larva are formed during embryogenesis, but then are transformed into the more complex adult legs at metamorphosis. To elucidate the molecular patterning mechanism underlying this biphasic development, we examined the expression patterns of five genes known to be involved in patterning the proximal-distal axis in insect legs. In the developing larval leg of Manduca, the early patterning genes Distal-less and Extradenticle are already expressed in patterns comparable to the adult legs of other insects. In contrast, Bric-a-brac and dachshund are expressed in patterns similar to transient patterns observed during early stages of leg development in Drosophila. During metamorphosis of the leg, the two genes finally develop mature expression patterns. Our results are consistent with the hypothesis that the larval leg morphology is produced by a transient arrest in the conserved adult leg patterning process in insects. In addition, we find that, during the adult leg development, some cells in the leg express the patterning genes de novo suggesting that the remodeling of the leg involves changes in the patterning gene regulation.     

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.     

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.     

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.