Optimal foot shape for a passive dynamic biped

Passive walking dynamics describe the motion of a biped that is able to "walk" down a shallow slope without any actuation or control. Instead, the walker relies on gravitational and inertial effects to propel itself forward, exhibiting a gait quite similar to that of humans. These purely passive models depend on potential energy to overcome the energy lost when the foot impacts the ground. Previous research has demonstrated that energy loss at heel-strike can vary widely for a given speed, depending on the nature of the collision. The point of foot contact with the ground (relative to the hip) can have a significant effect: semi-circular (round) feet soften the impact, resulting in much smaller losses than point-foot walkers. Collisional losses are also lower if a single impulse is broken up into a series of smaller impulses that gradually redirect the velocity of the center of mass rather than a single abrupt impulse. Using this principle, a model was created where foot-strike occurs over two impulses, "heel-strike" and "toe-strike," representative of the initial impact of the heel and the following impact as the ball of the foot strikes the ground. Having two collisions with the flat-foot model did improve efficiency over the point-foot model. Representation of the flat-foot walker as a rimless wheel helped to explain the optimal flat-foot shape, driven by symmetry of the virtual spoke angles. The optimal long period foot shape of the simple passive walking model was not very representative of the human foot shape, although a reasonably anthropometric foot shape was predicted by the short period solution.     

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.     

The validity of stability measures: A modelling approach

Measures calculated from unperturbed walking patterns, such as variability measures and maximum Floquet multipliers, are often used to study the stability of walking. However, it is unknown if, and to what extent, these measures correlate to the probability of falling.We studied whether in a simple model of human walking, i.e., a passive dynamic walker, the probability of falling could be predicted from maximum Floquet multipliers, kinematic state variability, and step time variability. We used an extended version of the basic passive dynamic walker with arced feet and a hip spring. The probability of falling was manipulated by varying the foot radius and hip spring stiffness, or varying these factors while co-varying the slope to keep step length constant.The simulation data indicated that Floquet multipliers and kinematic state variability correlated inconsistently with probability of falling. Step time variability correlated well with probability of falling, but a more consistent correlation with the probability of falling was found by calculating the variability of the log transform of the step time. Our findings speak against the use of maximum Floquet multipliers and suggest instead that variability of critical variables may be a good predictor of the probability to fall.     

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.     

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.     

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.     

Voluntary bipedal walking of infant chimpanzees

The voluntary bipedal walking of infant chimpanzees was studied by the analysis of foot force and by motion analysis. The infants were trained to locomote on a level platform without any restrictions on the locomotor pattern. The voluntary bipedal walking was compared with the other types of locomotion at the same age and with the trained bipedal walking performed by other chimpanzees, including adult chimpanzees. The characteristics of voluntary bipedal walking in the infant until one year of age were: (1) high-speed walking with short cycle duration; (2) short stance phase duration; (3) small braking component of the preceding leg and large acceleration of the following leg; (4) one downward peak in the vertical component; and (5) a relatively small transverse component. Bipedal walking usually continued for less than one second and ended in quadrupedal locomotion. During walking, the preceding foot touched the floor, heel first, as in the case of older chimpanzees and humans. At this age, bipedal walking was similar to high-speed locomotion. The voluntary bipedal walking of the two-year-old and frour-yearold chimpanzees was characterized as follows: (1) slower speed than during quadrupedal locomotion, (2) relatively long periods and distances; (3) well balanced accelerating and braking components; and (4) a vertical component showing two downward peaks and a trough in between during numerous trials. The last characteristic means that the body center of gravity is higher in the single stance phase, just as in the bipedal walkinbg of the adult chimpanzees and humans. The bipedal walking of infant chimpanzees was discussed in comparison with the walking of humans, including infants.     

Pre-swing deficits in forward propulsion,swing initiation and power generation by individual muscles during hemiparetic walking

Clinical studies of hemiparetic walking have shown pre-swing abnormalities in the paretic leg suggesting that paretic muscle contributions to important biomechanical walking subtasks are different than those of non-disabled individuals. Three-dimensional forward dynamics simulations of two representative hemiparetic subjects with different levels of walking function classified by self-selected walking speed (i.e., limited community=0.4–0.8 m/s and community walkers=>0.8 m/s) and a speed-matched control were generated to quantify individual muscle contributions to forward propulsion, swing initiation and power generation during the pre-swing phase (i.e., double support phase proceeding toe-off). Simulation analyses identified decreased paretic soleus and gastrocnemius contributions to forward propulsion and power generation as the primary impairment in the limited community walker compared to the control subject. The non-paretic leg did not compensate for decreased forward propulsion by paretic muscles during pre-swing in the limited community walker. Paretic muscles had the net effect to absorb energy from the paretic leg during pre-swing in the community walker suggesting that deficits in swing initiation are a primary impairment. Specifically, the paretic gastrocnemius and hip flexors (i.e., iliacus, psoas and sartorius) contributed less to swing initiation and the paretic soleus and gluteus medius absorbed more power from the paretic leg in the community walker compared to the control subject. Rehabilitation strategies aimed at diminishing these deficits have much potential to improve walking function in these hemiparetic subjects and those with similar deficits.     

Stable bipedal walking with a swing-leg protraction strategy

In bipedal locomotion, swing-leg protraction and retraction refer to the forward and backward motion, respectively, of the swing-leg before touchdown. Past studies have shown that swing-leg retraction strategy can lead to stable walking. We show that swing-leg protraction can also lead to stable walking. We use a simple 2D model of passive dynamic walking but with the addition of an actuator between the legs. We use the actuator to do full correction of the disturbance in a single step (a one-step dead-beat control). Specifically, for a given limit cycle we perturb the velocity at mid-stance. Then, we determine the foot placement strategy that allows the walker to return to the limit cycle in a single step. For a given limit cycle, we find that there is swing-leg protraction at shallow slopes and swing-leg retraction at steep slopes. As the limit cycle speed increases, the swing-leg protraction region increases. On close examination, we observe that the choice of swing-leg strategy is based on two opposing effects that determine the time from mid-stance to touchdown: the walker speed at mid-stance and the adjustment in the step length for one-step dead-beat control. When the walker speed dominates, the swing-leg retracts but when the step length dominates, the swing-leg protracts. This result suggests that swing-leg strategy for stable walking depends on the model parameters, the terrain, and the stability measure used for control. This novel finding has a clear implication in the development of controllers for robots, exoskeletons, and prosthetics and to understand stability in human gaits.     

Minimizing center of mass vertical movement increases metabolic cost in walking.

A human walker vaults up and over each stance limb like an inverted pendulum. This similarity suggests that the vertical motion of a walker's center of mass reduces metabolic cost by providing a mechanism for pendulum-like mechanical energy exchange. Alternatively, some researchers have hypothesized that minimizing vertical movements of the center of mass during walking minimizes the metabolic cost, and this view remains prevalent in clinical gait analysis. We examined the relationship between vertical movement and metabolic cost by having human subjects walk normally and with minimal center of mass vertical movement ("flat-trajectory walking"). In flat-trajectory walking, subjects reduced center of mass vertical displacement by an average of 69% (P = 0.0001) but consumed approximately twice as much metabolic energy over a range of speeds (0.7-1.8 m/s) (P = 0.0001). In flat-trajectory walking, passive pendulum-like mechanical energy exchange provided only a small portion of the energy required to accelerate the center of mass because gravitational potential energy fluctuated minimally. Thus, despite the smaller vertical movements in flat-trajectory walking, the net external mechanical work needed to move the center of mass was similar in both types of walking (P = 0.73). Subjects walked with more flexed stance limbs in flat-trajectory walking (P < 0.001), and the resultant increase in stance limb force generation likely helped cause the doubling in metabolic cost compared with normal walking. Regardless of the cause, these findings clearly demonstrate that human walkers consume substantially more metabolic energy when they minimize vertical motion.     

Effects of hip torque during step-to-step transition on center-of-mass dynamics during human walking examined with numerical simulation

Besides the leg force actuator, humans also use a hip torque actuator during the step-to-step transition to redirect the velocity of CoM (Center of Mass). Although the leg force actuator has been widely studied, few researches analyze the hip torque actuator during the step-to-step transition. In this paper, we build a powered walking model which consists of a point mass linked with two compliant legs. Each leg has a spring and a damper in parallel. Two types of active actuators, the force actuator on the leg and the torque actuator at the hip, are added to simulate the leg force and hip torque actuator during the step-to-step transition. The cycle walk is solved by numerical simulations under different hip torque strength, and the energetics and stability are evaluated. The simulation results show that the hip torque actuator can reduce the energy cost and improve the stability of walking. Further analysis shows that the hip torque actuator can reduce mechanical works of both legs with small extra energy cost. To understand the principle of hip torque actuator, the CoM dynamics is analyzed. It is shown that the hip torque actuator is efficient on the redirection of CoM. Thus, it can improve the stability and reduce required forces of both legs, which decreases the energy cost. Our work provides a fundamental understanding of the hip torque during the step-to-step transition, and may help improve the design of bipedal robots and prosthesis.     

Effects of walking speed, strength and range of motion on gait stability in healthy older adults

Falls pose a tremendous risk to those over 65 and most falls occur during locomotion. Older adults commonly walk slower, which many believe helps improve walking stability. While increased gait variability predicts future fall risk, increased variability is also caused by walking slower. Thus, we need to better understand how differences in age and walking speed independently affect dynamic stability during walking. We investigated if older adults improved their dynamic stability by walking slower, and how leg strength and flexibility (passive range of motion (ROM)) affected this relationship. Eighteen active healthy older and 17 healthy younger adults walked on a treadmill for 5min each at each of 5 speeds (80-120% of preferred). Local divergence exponents and maximum Floquet multipliers (FM) were calculated to quantify each subject's inherent local dynamic stability. The older subjects walked with the same preferred walking speeds as the younger subjects (p=0.860). However, these older adults still exhibited greater local divergence exponents (p<0.0001) and higher maximum FM (p<0.007) than the younger adults at all walking speeds. These older adults remained more locally unstable (p<0.04) even after adjusting for declines in both strength and ROM. In both age groups, local divergence exponents decreased at slower speeds and increased at faster speeds (p<0.0001). Maximum FM showed similar changes with speed (p<0.02). Both younger and older adults exhibited decreased instability by walking slower, in spite of increased variability. These increases in dynamic instability might be more sensitive indicators of future fall risk than changes in gait variability.     

Influence of simulated neuromuscular noise on the dynamic stability and fall risk of a 3D dynamic walking model

Measures that can predict risk of falling are essential for enrollment of older adults into fall prevention programs. Local and orbital stability directly quantify responses to very small perturbations and are therefore putative candidates for predicting fall risk. However, research to date is not conclusive on whether and how these measures relate to fall risk. Testing this empirically would be time consuming or may require high risk tripping experiments. Simulation studies therefore provide an important tool to initially explore potential measures to predict fall risk. This study performed simulations with a 3D dynamic walking model to explore if and how dynamic stability measures predict fall risk. The model incorporated a lateral step controller to maintain lateral stability. Neuronal noise of increasing amplitude was added to this controller to manipulate fall risk. Short-term (λ(S)(*)) local instability did predict fall risk, but long-term (λ(L)(*)) local instability and orbital stability (maxFM) did not. Additionally, λ(S)(*) was an early predictor for fall risk as it started increasing before fall risk increased. Therefore, λ(S)(*) could be a very useful tool to identify older adults whose fall risk is about to increase, so they can be enrolled in fall prevention programs before they actually fall.     

The Role of Walkers’ Needs and Expectations in Supporting Maintenance of Attendance at Walking Groups: A Longitudinal Multi-Perspective Study of Walkers and Walk Group Leaders

Background

There is good evidence that when people’s needs and expectations regarding behaviour change are met, they are satisfied with that change, and maintain those changes. Despite this, there is a dearth of research on needs and expectations of walkers when initially attending walking groups and whether and how these needs and expectations have been satisfied after a period of attendance. Equally, there is an absence of research on how people who lead these groups understand walkers’ needs and walk leaders’ actions to address them. The present study was aimed at addressing both of these gaps in the research.

Methods

Two preliminary thematic analyses were conducted on face-to-face interviews with (a) eight walkers when they joined walking groups, five of whom were interviewed three months later, and (b) eight walk leaders. A multi-perspective analysis building upon these preliminary analyses identified similarities and differences within the themes that emerged from the interviews with walkers and walk leaders.

Results

Walkers indicated that their main needs and expectations when joining walking groups were achieving long-term social and health benefits. At the follow up interviews, walkers indicated that satisfaction with meeting similar others within the groups was the main reason for continued attendance. Their main source of dissatisfaction was not feeling integrated in the existing walking groups. Walk leaders often acknowledged the same reasons for walkers joining and maintaining attendance at walking. However, they tended to attribute dissatisfaction and drop out to uncontrollable environmental factors and/or walkers’ personalities. Walk leaders reported a lack of efficacy to effectively address walkers’ needs.

Conclusions

Interventions to increase retention of walkers should train walk leaders with the skills to help them modify the underlying psychological factors affecting walkers’ maintenance at walking groups. This should result in greater retention of walkers in walking groups, thereby allowing walkers to receive the long-term social and health benefits of participation in these groups.     

Kinematic variability and local dynamic stability of upper body motions when walking at different speeds

A ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls. Many clinicians assume these patients walk slower to improve their stability, just as healthy people slow down when walking across ice. However, walking slower also leads to greater variability, which is often assumed to imply deteriorated stability. If this were true, then slowing down would be completely antithetical to the goal of maintaining stability. This study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Eleven young healthy subjects walked on a motorized treadmill at five different speeds. Three-dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking. Mean stride-to-stride standard deviations and maximum finite-time Lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability, respectively, of these movements. Quadratic regression analyses of the dependent measures vs. walking speed revealed highly significant U shaped trends for all three mean standard deviations, but highly significant linear trends, with significant or nearly significant quadratic terms, for five of the six finite-time Lyapunov exponents. Subjects exhibited consistently better local dynamic stability at slower speeds for these five measures. These results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability, even at the cost of increased variability.     

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.     

Do highly trained monkeys walk like humans? A kinematic study of bipedal locomotion in bipedally trained Japanese macaques

In this study, we examined the kinematics of bipedal walking in macaque monkeys that have been highly trained to stand and walk bipedally, and compared them to the kinematics of bipedal walking in ordinary macaques. The results revealed that the trained macaques walked with longer and less frequent strides than ordinary subjects. In addition, they appear to have used inverted pendulum mechanics during bipedal walking, which resulted in an efficient exchange of potential and kinetic energy. These gait characteristics resulted from the relatively more extended hindlimb joints of the trained macaques. By contrast, the body of the ordinary macaques translated downward during the single-limb stance phase due to more flexed hindlimb joints. This resulted in almost in-phase fluctuations of potential and kinetic energy, which indicated that energy transformation was less efficient in the ordinary macaques. The findings provide two insights into the early stage of the evolution of human bipedalism. First, the finding that training considerably improved bipedal walking a posteriori may explain why the very first bipeds that might not yet have been morphologically adapted to bipedal walking continued to walk bipedally. The evolutionary transition from quadrupedalism to bipedalism might not be as difficult as has been envisioned. In addition, the finding that macaques, which are phylogenetically distant from humans and in which bipedal walking is unlike human walking, could develop humanlike gait characteristics with training, provides strong support for the commonly held but unproven idea that the characteristics of the human gait are advantageous to human bipedalism.     

Head injuries related to the use of baby walkers.

To determine what proportion of head injuries in children under 24 months of age who presented to an emergency department were related to the use of baby walkers, we reviewed the charts of 52 such children. Walkers were involved in 42% of the head injuries in the children under 12 months of age and in none of those in the children aged 12 to 24 months. All walker-related injuries, including skull fractures in three children, involved stairs (p less than 0.001). Questionnaires were also sent to all families with children aged 3 to 18 months attending a private pediatric practice to determine the prevalence of falls involving baby walkers among these children and the factors associated with such falls. Of the 152 responding families 82% reported using or having used a walker. Thirty-six percent of the families reported that their child had a fall while in a walker, with 8.8% of the falls resulting in contact with a doctor. Walker-related falls were directly associated with time spent in the walker (p less than 0.001) and with a previous fall from the walker by an older sibling (p less than 0.03). Since there is no demonstrated benefit of walkers, their use should not be encouraged, and parents should be advised of their potential danger.     

Perceptual grouping of biological motion promotes binocular rivalry

Investigation of perceptual rivalry between conflicting stimuli presented one to each eye can further understanding of the neural underpinnings of conscious visual perception. During rivalry, visual awareness fluctuates between perceptions of the two stimuli. Here, we demonstrate that high-level perceptual grouping can promote rivalry between stimulus pairs that would otherwise be perceived as nonrivalrous. Perceptual grouping was generated with point-light walker stimuli that simulate human motion, visible only as lights placed on the joints. Although such walking figures are unrecognizable when stationary, recognition judgments as complex as gender and identity can accurately be made from animated displays, demonstrating the efficiency with which our visual system can group dynamic local signals into a globally coherent walking figure. We find that point-light walker stimuli presented one to each eye and in different colors and configurations results in strong rivalry. However, rivalry is minimal when the two walkers are split between the eyes or both presented to one eye. This pattern of results suggests that processing animated walker figures promotes rivalry between signals from the two eyes rather than between higher-level representations of the walkers. This leads us to hypothesize that awareness during binocular rivalry involves the integrated activity of high-level perceptual mechanisms in conjunction with lower-level ocular suppression modulated via cortical feedback.     

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.