Stability of an underactuated bipedal gait

A self-excited biped walking mechanism consisting of two legs that are connected in series at the hip joint through a servomotor is studied as a cyclic system with collisions. A torque proportional to angle between the shank of the swinging leg and the vertical is seen to sustain a gait. Each leg has a thigh and a shank connected at a passive knee joint that has a knee stopper restricting hyperextension similar to the human knee. A mathematical model for the dynamics of the system including the impact equations is used to analyse the stability of the system through examination of phase plane plots. Attractor lines along which the system approaches stability have been identified. A leg length for optimal stability has been identified. The biological basis for the proposed system has been identified by comparison with human gait.     

A methodology for studying the effects of various types of prosthetic feet on the biomechanics of trans-femoral amputee gait.

This paper reports on a methodology developed for studying the effects of various types of prosthetic feet on the gait of trans-femoral amputees. It is shown that an analysis in three planes of motion of not only the prosthetic, but also the sound limb provides important information on the performance of prosthetic feet. Two male trans-femoral amputees were tested with four different prosthetic feet; the Springlite II, Carbon Copy III, Seattle LightFoot and the Multiflex foot. A detailed analysis of the results of one amputee and a summary of the most important results of a second subject is presented. The tests were carried out at normal (1.16 m s(-1)) and fast (1.56 m s(-1)) walking speeds. Three dimensional gait analysis was carried out to derive the time curves of the joint angles, intersegmental moments and power at the ankle, knee and hip joints at both the prosthetic and sound sides. A higher first peak of the ground reaction force at the sound side with the Seattle LightFoot compared to that with the Springlite II, may be the result of the lower late stance dorsiflexion angle with the former. Compared to the other two feet, the Carbon Copy III and the Springlite II showed higher prosthetic dorsiflexing moments and positive power at late stance, which could assist in the push-off. The 3D intersegmental loads at the ankle and knee can be used as a guide for design and for compilation of standards for testing of lower limb prostheses incorporating flexible feet.     

Predicting the metabolic cost of incline walking from muscle activity and walking mechanics

The goal of this study was to identify which muscle activation patterns and gait features best predict the metabolic cost of inclined walking. We measured muscle activation patterns, joint kinematics and kinetics, and metabolic cost in sixteen subjects during treadmill walking at inclines of 0%, 5%, and 10%. Multivariate regression models were developed to predict the net metabolic cost from selected groups of the measured variables. A linear regression model including incline and the squared integrated electromyographic signals of the soleus and vastus lateralis explained 96% of the variance in metabolic cost, suggesting that the activation patterns of these large muscles have a high predictive value for metabolic cost. A regression model including only the peak knee flexion angle during stance phase, peak knee extension moment, peak ankle plantarflexion moment, and peak hip flexion moment explained 89% of the variance in metabolic cost; this finding indicates that kinematics and kinetics alone can predict metabolic cost during incline walking. The ability of these models to predict metabolic cost from muscle activation patterns and gait features points the way toward future work aimed at predicting metabolic cost when gait is altered by changes in neuromuscular control or the use of an assistive technology.     

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.     

Hip joint contact force in the emu (Dromaius novaehollandiae) during normal level walking

The emu is a large, (bipedal) flightless bird that potentially can be used to study various orthopaedic disorders in which load protection of the experimental limb is a limitation of quadrupedal models. An anatomy-based analysis of normal emu walking gait was undertaken to determine hip contact forces for comparison with human data. Kinematic and kinetic data captured for two laboratory-habituated emus were used to drive the model. Muscle attachment data were obtained by dissection, and bony geometries were obtained by CT scan. Inverse dynamics calculations at all major lower-limb joints were used in conjunction with optimization of muscle forces to determine hip contact forces. Like human walking gait, emu ground reaction forces showed a bimodal distribution over the course of the stance phase. Two-bird averaged maximum hip contact force was approximately 5.5 times body weight, directed nominally axially along the femur. This value is only modestly larger than optimization-based hip contact forces reported in literature for humans. The interspecies similarity in hip contact forces makes the emu a biomechanically attractive animal in which to model loading-dependent human orthopaedic hip disorders.     

The locomotion of the camel (Camelus dromedarius)

The feet and gaits of many camels Camelus dromedarius were studied and filmed in Mauritania, Africa. The camel has a digitigrade stance, large feet to support the animal in soft sand, and soles of flexible pads that step readily onto small stones where necessary. The walking stride is long and slow, with the body supported for much of each stride on the two right or two left legs. The pattern of supporting legs was significantly different in slow compared to fast walking camels, and in young compared to adult camels and compared to adults pulling water at the wells. There was no difference in pattern in one individual's walk, when it was either loaded or unloaded. The angles that the leg bones made with each other and with the horizon are depicted for the walk and the pace. The camel is the only animal which paces often and never trots. The pace is an unstable gait only suitable for flat terrain such as that in deserts. It may have evolved from the pace-like walk which is by far the dominant gait in this animal, which spends most of each day walking from plant to plant browsing or grazing. The pace is not used by all camelids, as one author has claimed. The pace and the gallop were only used by the camels at wells, when the animals were chased from the water by men.     

Virtual slope control of a forward dynamic bipedal walker

Active joint torques are the primary source of power and control in dynamic walking motion. However the amplitude, rate, timing and phasic behavior of the joint torques necessary to achieve a natural and stable performance are difficult to establish. The goal of this study was to demonstrate the feasibility and stable behavior of an actively controlled bipedal walking simulation wherein the natural system dynamics were preserved by an active, nonlinear, state-feedback controller patterned after passive downhill walking. A two degree-of-freedom, forward-dynamic simulation was implemented with active joint torques applied at the hip joints and stance leg ankle. Kinematic trajectories produced by the active walker were similar to passive dynamic walking with active joint torques influenced by prescribed walking velocity. The control resulted in stable steady-state gait patterns, i.e. eigenvalue magnitudes of the stride function were less than one. The controller coefficient analogous to the virtual slope was modified to successfully control average walking velocity. Furture developments are necessary to expand the range of walking velocities.     

Walking with increased ankle pushoff decreases hip muscle moments

In a simple bipedal walking model, an impulsive push along the trailing limb (similar to ankle plantar flexion) or a torque at the hip can power level walking. This suggests a tradeoff between ankle and hip muscle requirements during human gait. People with anterior hip pain may benefit from walking with increased ankle pushoff if it reduces hip muscle forces. The purpose of our study was to determine if simple instructions to alter ankle pushoff can modify gait dynamics and if resulting changes in ankle pushoff have an effect on hip muscle requirements during gait. We hypothesized that changes in ankle kinetics would be inversely related to hip muscle kinetics. Ten healthy subjects walked on a custom split-belt force-measuring treadmill at 1.25m/s. We recorded ground reaction forces and lower extremity kinematic data to calculate joint angles and internal muscle moments, powers and angular impulses. Subjects walked under three conditions: natural pushoff, decreased pushoff and increased pushoff. For the decreased pushoff condition, subjects were instructed to push less with their feet as they walked. Conversely, for the increased pushoff condition, subjects were instructed to push more with their feet. As predicted, walking with increased ankle pushoff resulted in lower peak hip flexion moment, power and angular impulse as well as lower peak hip extension moment and angular impulse (p<0.05). Our results emphasize the interchange between hip and ankle kinetics in human walking and suggest that increased ankle pushoff during gait may help to compensate for hip muscle weakness or injury and reduce hip joint forces.     

Leg and Joint Stiffness in Children with Spastic Diplegic Cerebral Palsy during Level Walking

Individual joint deviations are often identified in the analysis of cerebral palsy (CP) gait. However, knowledge is limited as to how these deviations affect the control of the locomotor system as a whole when striving to meet the demands of walking. The current study aimed to bridge the gap by describing the control of the locomotor system in children with diplegic CP in terms of their leg stiffness, both skeletal and muscular components, and associated joint stiffness during gait. Twelve children with spastic diplegia CP and 12 healthy controls walked at a self-selected pace in a gait laboratory while their kinematic and forceplate data were measured and analyzed during loading response, mid-stance, terminal stance and pre-swing. For calculating the leg stiffness, each of the lower limbs was modeled as a non-linear spring, connecting the hip joint center and the corresponding center of pressure, with varying stiffness that was calculated as the slope (gradient) of the axial force vs. the deformation curve. The leg stiffness was further decomposed into skeletal and muscular components considering the alignment of the lower limb. The ankle, knee and hip of the limb were modeled as revolute joints with torsional springs whose stiffness was calculated as the slope of the moment vs. the angle curve of the joint. Independent t-tests were performed for between-group comparisons of all the variables. The CP group significantly decreased the leg stiffness but increased the joint stiffness during stance phase, except during terminal stance where the leg stiffness was increased. They appeared to rely more on muscular contributions to achieve the required leg stiffness, increasing the muscular demands in maintaining the body posture against collapse. Leg stiffness plays a critical role in modulating the kinematics and kinetics of the locomotor system during gait in the diplegic CP.     

Form in the context of function: Fundamentals of an energy effective striding walk,the role of the plantigrade foot and its expected size

What morphological and functional factors allow for the unique and characteristic upright striding walk of the hominin lineage? Predictive models of locomotion that arise from considering mechanisms of energy loss indicate that collision-like losses at the transition between stance limbs are important determinants of bipedal gait. Theoretical predictions argue that these collisional losses can be reduced by having “functional extra legs” which are physically the heel and the toe part of a single anatomical foot. The ideal spacing for these “functional legs” are up to a quarter of a stride length, depending on the model employed. We evaluate the foot in the context of the dynamics of a bipedal system and compare predictions of optimal foot size against empirical data from modern humans, the Laetoli footprint trackways, and chimpanzees walking bipedally. The dynamics-based modeling approach provides substantial insight into how, and why, walking works as it does, even though current models are too simple to make predictions at a level adequate to anticipate specific morphology except at the most general level.     

Estimation of Quasi-Stiffness of the Human Hip in the Stance Phase of Walking

This work presents a framework for selection of subject-specific quasi-stiffness of hip orthoses and exoskeletons, and other devices that are intended to emulate the biological performance of this joint during walking. The hip joint exhibits linear moment-angular excursion behavior in both the extension and flexion stages of the resilient loading-unloading phase that consists of terminal stance and initial swing phases. Here, we establish statistical models that can closely estimate the slope of linear fits to the moment-angle graph of the hip in this phase, termed as the quasi-stiffness of the hip. Employing an inverse dynamics analysis, we identify a series of parameters that can capture the nearly linear hip quasi-stiffnesses in the resilient loading phase. We then employ regression analysis on experimental moment-angle data of 216 gait trials across 26 human adults walking over a wide range of gait speeds (0.75–2.63 m/s) to obtain a set of general-form statistical models that estimate the hip quasi-stiffnesses using body weight and height, gait speed, and hip excursion. We show that the general-form models can closely estimate the hip quasi-stiffness in the extension (R² = 92%) and flexion portions (R² = 89%) of the resilient loading phase of the gait. We further simplify the general-form models and present a set of stature-based models that can estimate the hip quasi-stiffness for the preferred gait speed using only body weight and height with an average error of 27% for the extension stage and 37% for the flexion stage.     

Passive bipedal walking with phasic muscle contraction

The existence of self-organizing walking patterns is often considered the result of a mechanical system interacting with the environment and a (neural) oscillating unit. The pattern generators might be thought of as an indispensable component for the existence of limit cycle behavior. This paper shows that this is not a necessity for the existence of a self-organizing bipedal walking pattern. Stable walking cycles emerge from a simple passive bipedal structure, with an energy source inevitably present to sustain the oscillation. In this work the energy source is chosen to be phasic muscle contraction. A two-dimensional model is composed of two legs and a hip mass, symbolizing the trunk. The stance leg stiffness is generated by two muscles. The hip stiffness is generated by four muscles. Muscle activation is caused by two reflex-like trigger signals, without feedback control. Human equivalent model parameters such as geometry and mass distribution were assumed. With return map analysis, the model is analyzed on periodic behavior. Stable walking cycles were found and could be manipulated during walking by varying the muscle or reflex parameters, forcing the oscillation to converge to a new attractor. Received: 5 November 1998 / Accepted in revised form: 26 March 1999     

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.     

Behavioural and physical reactions of the Colorado potato beetle, Leptinotarsa decemlineata (Say) (Coleoptera: Chrysomelidae) walking on a slanted surface

 A natural reaction of the adult Colorado potato beetle [Leptinotarsa decemlineata (Say)] is to walk uphill on sloped surfaces. The geotaxis reaction of the beetle was observed on slopes of 20° or steeper. It was demonstrated that the uphill orientation behaviour was not a consequence of physical limitation for across-slope locomotion. The walking speed of insects deviating from the fall line did not change within the range of slope angles tested. The speed of adult beetles decreased with an increase in the slope of the substrate as a reaction to the increased gravitational force vector opposing uphill movement. The larger size of the hind legs might make uphill locomotion more efficient than traversing a sloped surface. As the angle of the slope increased, the gait changed from a 3/3 to a 5/1, as did the posterior and anterior extreme position of the legs. This behaviour might be triggered by the need to maintain balance on slanted surfaces as the vertical projection of the centre of mass on the substrate moved outside the support base pattern at the steeper angles. In one experiment beetles were made to pull a load when walking over a horizontal surface. The loads pulled were equivalent to the gravitational loads opposing forward motion when walking up a slope. No differences in forward speed or gait were observed at the lower-angle equivalent compared to beetles walking on slopes. Differences in speed were noted at slope angles higher than 40° indicating that adaptation of the walking strategy might be needed on steeply slanted surfaces. Received: 2 May 2000 / Accepted in revised form: 11 September 2000     

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).     

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.     

The effects of railroad ballast surface and slope on rearfoot motion in walking

The purpose of this study was to investigate the effects of transversely sloped ballasted walking surface on gait and rearfoot motion (RFM) parameters. Motion analysis was performed with 20 healthy participants (15 male and 5 female) walking in six surface-slope conditions: two surfaces (solid and ballasted) by three slopes (0, 5, and 10 degrees). The gait parameters (walking velocity, step length, step rate, step width, stance time, and toe-out angle) showed significant surface effect (p = .004) and surface-slope interaction (p = .017). The RFM motion parameters (peak everted/inverted position, eversion/inversion velocity, and acceleration) revealed significant surface (p = .004) and slope (p = .024) effects. The ballasted conditions showed more cautious gait patterns with lower walk velocity, step length, and step rate and longer stance time. In the RFM parameters, the slope effect was more notable in the solid conditions due to the gait adaptations in the ballasted conditions. Ballast conditions showed reduced inversion and increased eversion and RFM range. The RFM data were comparable to other typical walking conditions but smaller than those from running.     

An upper-body can improve the stability and efficiency of passive dynamic walking

The compass-gait walker proposed by McGeer can walk down a shallow slope with a self-stabilizing gait that requires no actuation or control. However, as the slope goes to zero so does the walking speed, and dynamic gait stability is only possible over a very narrow range of slopes. Gomes and Ruina have results demonstrating that by adding a torso to the compass-gait walker, it can walk passively on level-ground with a non-infinitesimal constant average speed. However, the gait involves exaggerated joint movements, and for energetic reasons horizontal passive dynamic walking cannot be stable. We show in this research that in addition to collision-free walking, adding a torso improves stability and walking speed when walking downhill. Furthermore, adding arms to the torso results in a collision-free periodic gait with natural-looking torso and limb movements. Overall, in contrast to the suggestions that active control may be needed to balance an upper-body on legs, it turns out that the upper and lower bodies can be integrated to improve the stability, efficiency and speed of a passive dynamic walker.