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.     

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.     

Reflex modulation in locusts walking on a treadwheel intracellular recordings from motoneurons

Summary In locusts (Locusta migratoria) walking on a treadwheel, afferents of tarsal hair sensilla were stimulated via chronically implanted hook electrodes (Fig. 1). Stimuli applied to the middle leg tarsus elicited avoidance reflexes (Fig. 2). In quiescent animals, the leg was lifted off the ground and the femur adducted. In walking locusts, the response was phase-dependent. During the stance phase, no reaction was observed except occasional, premature triggering of swing movements; stimuli applied near the end of the swing phase were able to elicit an additional, short leg protraction.Central nervous correlates of phase-dependent reflex modulation were observed by recording intracellularly from motoneuron somata in walking animals. As a rule, motoneurons recruited during the swing phase showed excitatory stimulus-related responses around the end of the swing movement, correlated to the triggering of additional leg protractions (Figs. 3, 4, 5). Motoneurons active during the stance phase were often inhibited by tarsal stimulation, some showed only weak responses (Figs. 8, 9, 10). Common inhibitory motoneuron 1 was excited by tarsal stimulation during all phases of the leg movement (Figs. 6, 7). In one type of flexor tibiae motoneuron, a complex response pattern was observed, involving the inversion of stimulus-related synaptic potentials from excitatory, recorded during rest, to inhibitory, observed during long-lasting stance phases (Figs. 11, 12).The results demonstrate how reflex modulation is represented on the level of synaptic input to motoneurons. They further suggest independent gain control in parallel, antagonistic pathways converging onto the same motoneuron as a mechanism for reflex reversal during locomotion.Abbreviations CI ₁ common inhibitory motoneuron (1) - EMG electromyogram - Feti fast extensor muscle of the tibia     

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.     

Mechanical energetic contributions from individual muscles and elastic prosthetic feet during symmetric unilateral transtibial amputee walking: a theoretical study

Energy storage and return (ESAR) foot-ankle prostheses have been developed in an effort to improve gait performance in lower-limb amputees. However, little is known about their effectiveness in providing the body segment mechanical energetics normally provided by the ankle muscles. The objective of this theoretical study was to use muscle-actuated forward dynamics simulations of unilateral transtibial amputee and non-amputee walking to identify the contributions of ESAR prostheses to trunk support, forward propulsion and leg swing initiation and how individual muscles must compensate in order to produce a normal, symmetric gait pattern. The simulation analysis revealed the ESAR prosthesis provided the necessary trunk support, but it could not provide the net trunk forward propulsion normally provided by the plantar flexors and leg swing initiation normally provided by the biarticular gastrocnemius. To compensate, the residual leg gluteus maximus and rectus femoris delivered increased energy to the trunk for forward propulsion in early stance and late stance into pre-swing, respectively, while the residual iliopsoas delivered increased energy to the leg in pre- and early swing to help initiate swing. In the intact leg, the soleus, gluteus maximus and rectus femoris delivered increased energy to the trunk for forward propulsion in the first half of stance, while the iliopsoas increased the leg energy it delivered in pre- and early swing. Thus, the energy stored and released by the ESAR prosthesis combined with these muscle compensations was able to produce a normal, symmetric gait pattern, although various neuromuscular and musculoskeletal constraints may make such a pattern non-optimal.     

Development of an advanced mechanised gait trainer, controlling movement of the centre of mass, for restoring gait in non-ambulant subjects.

The study aimed at further development of a mechanised gait trainer which would allow non-ambulant people to practice a gait-like motion repeatedly. To simulate normal gait, discrete stance and swing phases, lasting 60% and 40% of the gait cycle respectively, and the control of the movement of the centre of mass were required. A complex gear system provided the gait-like movement of two foot plates with a ratio of 60% to 40% between the stance and swing phases. A controlled propulsion system adjusted its output according to patient's efforts. Two eccenters on the central gear controlled phase-adjusted the vertical and horizontal position of the centre of mass. The patterns of sagittal lower limb joint kinematics and of muscle activation of a normal subject were similar when using the mechanised trainer and when walking on a treadmill. A non-ambulatory hemiparetic subject required little help from one therapist on the gait trainer, while two therapists supported treadmill walking. Gait movements on the trainer were highly symmetrical, impact-free, and less spastic. The weight-bearing muscles were activated in a similar fashion during both conditions. The vertical displacement of the centre of mass was bi-instead of mono-phasic during each gait cycle on the new device. In conclusion, the gait trainer allowed wheelchair-bound subjects the repetitive practice of a gait-like movement without overstraining therapists.     

Compliant bipedal model with the center of pressure excursion associated with oscillatory behavior of the center of mass reproduces the human gait dynamics

Although the compliant bipedal model could reproduce qualitative ground reaction force (GRF) of human walking, the model with a fixed pivot showed overestimations in stance leg rotation and the ratio of horizontal to vertical GRF. The human walking data showed a continuous forward progression of the center of pressure (CoP) during the stance phase and the suspension of the CoP near the forefoot before the onset of step transition. To better describe human gait dynamics with a minimal expense of model complexity, we proposed a compliant bipedal model with the accelerated pivot which associated the CoP excursion with the oscillatory behavior of the center of mass (CoM) with the existing simulation parameter and leg stiffness. Owing to the pivot acceleration defined to emulate human CoP profile, the arrival of the CoP at the limit of the stance foot over the single stance duration initiated the step-to-step transition. The proposed model showed an improved match of walking data. As the forward motion of CoM during single stance was partly accounted by forward pivot translation, the previously overestimated rotation of the stance leg was reduced and the corresponding horizontal GRF became closer to human data. The walking solutions of the model ranged over higher speed ranges (~1.7 m/s) than those of the fixed pivoted compliant bipedal model (~1.5 m/s) and exhibited other gait parameters, such as touchdown angle, step length and step frequency, comparable to the experimental observations. The good matches between the model and experimental GRF data imply that the continuous pivot acceleration associated with CoM oscillatory behavior could serve as a useful framework of bipedal model.     

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.     

Modular control of human walking: A simulation study

Recent evidence suggests that performance of complex locomotor tasks such as walking may be accomplished using a simple underlying organization of co-active muscles, or “modules”, which have been assumed to be structured to perform task-specific biomechanical functions. However, no study has explicitly tested whether the modules would actually produce the biomechanical functions associated with them or even produce a well-coordinated movement. In this study, we generated muscle-actuated forward dynamics simulations of normal walking using muscle activation modules (identified using non-negative matrix factorization) as the muscle control inputs to identify the contributions of each module to the biomechanical sub-tasks of walking (i.e., body support, forward propulsion, and leg swing). The simulation analysis showed that a simple neural control strategy involving five muscle activation modules was sufficient to perform the basic sub-tasks of walking. Module 1 (gluteus medius, vasti, and rectus femoris) primarily contributed to body support in early stance while Module 2 (soleus and gastrocnemius) contributed to both body support and propulsion in late stance. Module 3 (rectus femoris and tibialis anterior) acted to decelerate the leg in early and late swing while generating energy to the trunk throughout swing. Module 4 (hamstrings) acted to absorb leg energy (i.e., decelerate it) in late swing while increasing the leg energy in early stance. Post-hoc analysis revealed an additional module (Module 5: iliopsoas) acted to accelerate the leg forward in pre- and early swing. These results provide evidence that the identified modules can act as basic neural control elements that generate task-specific biomechanical functions to produce well-coordinated walking.     

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.     

Comparing predictive validity of four ballistic swing phase models of human walking

It is unclear to what extent ballistic walking models can be used to qualitatively predict the swing phase at comfortable walking speed. Different study findings regarding the accuracy of the predictions of the swing phase kinematics may have been caused by differences in (1) kinematic input, (2) model characteristics (e.g. the number of segments), and (3) evaluation criteria. In the present study, the predictive validity of four ballistic swing phase models was evaluated and compared, that is, (1) the ballistic walking model as originally introduced by Mochon and McMahon, (2) an extended version of this model in which heel-off of the stance leg is added, (3) a double pendulum model, consisting of a two-segment swing leg with a prescribed hip trajectory, and (4) a shank pendulum model consisting of a shank and rigidly attached foot with a prescribed knee trajectory. The predictive validity was evaluated by comparing the outcome of the model simulations with experimentally derived swing phase kinematics of six healthy subjects. In all models, statistically significant differences were found between model output and experimental data. All models underestimated swing time and step length. In addition, statistically significant differences were found between the output of the different models. The present study shows that although qualitative similarities exist between the ballistic models and normal gait at comfortable walking speed, these models cannot adequately predict swing phase kinematics.     

Energetics of actively powered locomotion using the simplest walking model

We modified an irreducibly simple model of passive dynamic walking to walk on level ground, and used it to study the energetics of walking and the preferred relationship between speed and step length in humans. Powered walking was explored using an impulse applied at toe-off immediately before heel strike, and a torque applied on the stance leg. Although both methods can supply energy through mechanical work on the center of mass, the toe-off impulse is four times less costly because it decreases the collision loss at heel strike. We also studied the use of a hip torque on the swing leg that tunes its frequency but adds no propulsive energy to gait. This spring-like actuation can further reduce the collision loss at heel strike, improving walking energetics. An idealized model yields a set of simple power laws relating the toe-off impulses and effective spring constant to the speed and step length of the corresponding gait. Simulations incorporating nonlinear equations of motion and more realistic inertial parameters show that these power laws apply to more complex models as well.     

Gait acts as a gate for reflexes from the foot

During human gait, electrical stimulation of the foot elicits facilitatory P2 (medium latency) responses in TA (tibialis anterior) at the onset of the swing phase, while the same stimuli cause suppressive responses at the end of swing phase, along with facilitatory responses in antagonists. This phenomenon is called phase-dependent reflex reversal. The suppressive responses can be evoked from a variety of skin sites in the leg and from stimulation of some muscles such as rectus femoris (RF). This paper reviews the data on reflex reversal and adds new data on this topic, using a split-belt paradigm. So far, the reflex reversal in TA could only be studied for the onset and end phases of the step cycle, simply because suppression can only be demonstrated when there is background activity. Normally there are only 2 TA bursts in the step cycle, whereas TA is normally silent during most of the stance phase. To know what happens in the stance phase, one needs to have a means to evoke some background activity during the stance phase. For this purpose, new experiments were carried out in which subjects were asked to walk on a treadmill with a split-belt. When the subject was walking with unequal leg speeds, the walking pattern was adapted to a gait pattern resembling limping. The TA then remained active throughout most of the stance phase of the slow-moving leg, which was used as the primary support. This activity was a result of coactivation of agonistic and antagonistic leg muscles in the supporting leg, and represented one of the ways to stabilize the body. Electrical stimulation was given to a cutaneous nerve (sural) at the ankle at twice the perception threshold. Nine of the 12 subjects showed increased TA activity during stance phase while walking on split-belts, and 5 of them showed pronounced suppressions during the first part of stance when stimuli were given on the slow side. It was concluded that a TA suppressive pathway remains open throughout most of the stance phase in the majority of subjects. The suggestion was made that the TA suppression increases loading of the ankle plantar flexors during the loading phase of stance.     

Interruption of searching movements of partly restrained front legs of stick insects,a model situation for the start of a stance phase?

Stick insects (Cuniculina impigra) possessing only one foreleg with restrained coxa performed searching movements. A force transducer was introduced as an obstacle into the plane of movement of femur or tibia. Depending on where it was introduced and whether it was touched for the first time during an upward or a downward movement, different kinds of behaviour of the leg were released. For these different movements, the forces applied to the obstacle and the electrical activity of the depressor, levator, retractor and protractor muscles are described. In addition the alterations occurring after ablation of several sense organs including the trochanteral campaniform sensilla are mentioned. The described movements were similar to the corresponding behaviours during walking at the end of swing phase and the beginning of stance phase. Therefore there is some probability that results obtained by this experimental paradigm can also be applied to the swing-stance transition.     

Effects of load inversion in cockroach walking

To examine how walking patterns are adapted to changes in load, we recorded leg movements and muscle activities when cockroaches (Periplaneta americana) walked upright and on an inverted surface. Animals were videotaped to measure the hindleg femoro-tibial joint angle while myograms were taken from the tibial extensor and flexor muscles. The joint is rapidly flexed during swing and extended in stance in upright and inverted walking. When inverted, however, swing is shorter in duration and the joint traverses a range of angles further in extension. In slow upright walking, slow flexor motoneurons fire during swing and the slow extensor in stance, although a period of co-contraction occurs early in stance. In inverted walking, patterns of muscle activities are altered. Fast flexor motoneurons fire both in the swing phase and early in stance to support the body by pulling the animal toward the substrate. Extensor firing occurs late in stance to propel the animal forward. These findings are discussed within the context of a model in which stance is divided into an early support and subsequent propulsion phase. We also discuss how these changes in use of the hindleg may represent adaptations to the reversal of the effects of gravity.     

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.     

A self-organizing model of walking patterns of insects

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathemati cal models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector orga n. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increme nt or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system. Received: 8 February 1993/Accepted in revised form: 12 November 1993     

Kinematic analysis quantifies gait abnormalities associated with lameness in broiler chickens and identifies evolutionary gait differences

This is the first time that gait characteristics of broiler (meat) chickens have been compared with their progenitor, jungle fowl, and the first kinematic study to report a link between broiler gait parameters and defined lameness scores. A commercial motion-capturing system recorded three-dimensional temporospatial information during walking. The hypothesis was that the gait characteristics of non-lame broilers (n = 10) would be intermediate to those of lame broilers (n = 12) and jungle fowl (n = 10, tested at two ages: immature and adult). Data analysed using multi-level models, to define an extensive range of baseline gait parameters, revealed inter-group similarities and differences. Natural selection is likely to have made jungle fowl walking gait highly efficient. Modern broiler chickens possess an unbalanced body conformation due to intense genetic selection for additional breast muscle (pectoral hypertrophy) and whole body mass. Together with rapid growth, this promotes compensatory gait adaptations to minimise energy expenditure and triggers high lameness prevalence within commercial flocks; lameness creating further disruption to the gait cycle and being an important welfare issue. Clear differences were observed between the two lines (short stance phase, little double-support, low leg lift, and little back displacement in adult jungle fowl; much double-support, high leg lift, and substantial vertical back movement in sound broilers) presumably related to mass and body conformation. Similarities included stride length and duration. Additional modifications were also identified in lame broilers (short stride length and duration, substantial lateral back movement, reduced velocity) presumably linked to musculo-skeletal abnormalities. Reduced walking velocity suggests an attempt to minimise skeletal stress and/or discomfort, while a shorter stride length and time, together with longer stance and double-support phases, are associated with instability. We envisage a key future role for this highly quantitative methodology in pain assessment (associated with broiler lameness) including experimental examination of therapeutic agent efficacy.