Center Of Mass Oscillations Research Articles

Walking Stability of a Variable Length Inverted Pendulum Controlled with Virtual Constraints

Bipedal walking is a complex phenomenon that is not fully understood. Simplified models make it easier to highlight the important features. Here, the variable length inverted pendulum (VLIP) model is used, which has the particularity of taking into account the vertical oscillations of the center of mass (CoM). When the desired walking gait is defined as virtual constraints, i.e., as functions of a phasing variable and not on time, for the evolution of the swing foot and the vertical oscillation of the CoM, the walk will asymptotically converge to the periodic motion under disturbance with proper choice of the virtual constraints, thus a self-stabilization is obtained. It is shown that the vertical CoM oscillation, positions of the swing foot and the choice of the switching condition play crucial roles in stability. Moreover, a PI controller of the CoM velocity along the sagittal axis is also proposed such that the walking speed of the robot can converge to another periodic motion with a different walking speed. In this way, a natural walking gait is illustrated as well as the possibility of velocity adaptation as observed in human walking.

Step width and frontal plane trunk motion in bipedal chimpanzee and human walking

Human bipedalism is characterized by mediolateral oscillations of the center of mass (CoM) between the feet. The preferred step widths and CoM oscillations used by humans likely represent a trade-off of several factors (e.g., stance and swing phase costs). However, it is difficult to assess whether human frontal plane control strategies are unique given few detailed data on frontal plane motion during facultative bipedalism in apes. Here, we collected three-dimensional kinematic and kinetic data in humans and chimpanzees to investigate the relationship between step width, mediolateral CoM motion, frontal plane trunk kinematics, and CoM power during bipedalism. Chimpanzee bipedalism entails mediolateral CoM oscillations and step widths that are (scaled to lower/hind limb length) three times larger than those of humans. Chimpanzees use a combination of linear and angular motion of the trunk and list the entire trunk, and especially thorax, over the stance side foot, generating large mediolateral shifts in the CoM, whereas humans utilize little angular motion within the trunk. Larger mediolateral CoM motions do not have a significant effect on CoM power. Similarities between bipedal chimpanzees and other bipedal non-human primates (macaques and gibbons) indicate that narrow CoM motions are unique to humans and are likely due to our adducted hips and valgus knees. Valgus knees appear early in the human fossil record (∼3.6 Ma), contemporaneous with the Laetoli footprints. However, fossils attributed to Ardipithecus ramidus (∼4.4 Ma) suggest that the earliest hominins may have lacked a hominin-like degree of knee valgus. If correct, this suggests that this species may have used wide steps, larger mediolateral CoM motions, and perhaps larger trunk motions during bipedal walking. Finally, we present a novel means to estimate mediolateral CoM motion from trackway step width, and estimate that the Laetoli G track maker used CoM motions within the human range.

Sex-specific kinetic and kinematic indicators of medial tibiofemoral force during walking and running

BackgroundOur aims were to (1) Evaluate sex-specific contributions of peak knee flexion moment (pKFM) and peak knee adduction moment (pKAM) in medial tibiofemoral joint (TFJ) force during walking and running; (2) identify kinematic variables to estimate peak medial TFJ force. MethodsEighty-seven runners participated (36 females, 51 males; age=23.0±3.8years (1 standard deviation)). Kinematics and kinetics data were collected during treadmill walking (1.3m/s) and running (3.0±0.4m/s). Peak medial TFJ contact force was estimated using a musculoskeletal model. Linear regression analyses were used to assess the contribution of pKFM, pKAM and kinematic indicators to estimated joint forces. ResultsDuring walking and running, pKAM and pKFM accounted for 74.9% and 64.5% of peak medial TFJ force variance (P<0.001), respectively. Similar pKAM contribution was found between males and females during walking (51.8% vs. 47.9%), as opposed to running (50.4% vs. 26.8%). Kinematic indicators during walking were peak knee flexion and adduction angles, regardless of sex. During running, indicators were ankle dorsiflexion at foot strike and center of mass (COM) vertical displacement in females (R2=0.364, P=0.012), and peak knee abduction angle and step length in males (R2=0.508, P=0.019). ConclusionWe conclude from these results that pKAM and pKFM make significant but potentially sex-specific contributions to peak medial TFJ force during walking and running. Clinically, peak medial TFJ force during walking can be estimated using peak knee flexion and adduction angles in both sexes. During running, ankle dorsiflexion at foot strike and COM oscillation are best indicators among females, while knee abduction and step length are best among males.

Investigation on the Reduction of Center of Mass Oscillations of Flexible Flapping Fins

Nature has been a source of inspiration for developing advanced autonomous aerial and underwater vehicles. The bodies with flapping appendages produce Center of Mass (COM) oscillations as the flapping fins generate forces oscillatory in nature. The vehicles with larger COM oscillations pose the problems of control and maneuverability and this paper discusses the effect of flexibility and other operating parameters such as heaving, pitching amplitudes and operating frequency on COM oscillations. A detailed theoretical investigation has been carried out to predict the optimal operating parameters along with the fin stiffness to reduce the COM oscillations for a given Self-Propelled Speed (SPS). Experiments have been performed to validate the theoretical results. It has been observed that the flexible fins operating at larger frequencies produce lower COM oscillations compared to stiffer fins operating at lower frequencies for a given mean thrust/SPS, and that the trailing edge amplitude along with the deformation pattern play a role in the generation of COM oscillations.

Effects of a light touch on fixed or mobile supports on gait parameters in visually restricted young adults

We investigated the effects of lightly touching fixed and mobile supports on gait parameters and center of mass oscillations in visually restricted young adults. Fourteen healthy male and female adults of mean=23.6 years (SD=1.6 years). Twelve walking conditions were completed on the GAITRite measurement system, resulting from crossing 3 conditions of visual restriction (no restriction, partial restriction, blindfolded) and 4 conditions of haptic supplementation (no supplementation, with a cane used as “light touch”, with a cane sliding on the ground, while touching a soft elastic handrail). Gait speed, stance time, step length and the basis of support were measured. Accelerations of center of mass were also recorded through an accelerometer and the displacements of center of mass were analyzed. Results showed that visual restriction decreased in gait speed, reduced step length, while it increased the base of support and the amplitude of CoM displacements. In the full restriction condition, haptic supplementation provided by the use of the classic cane improved normalized stance time (%). In addition, in the no vision condition, both the classic cane and the soft handrail increased step length and reduced medio-lateral oscillations of the CoM. These results suggest that in visually restricted healthy adults, lightly touching a fixed (soft handrail) or a mobile (classic cane) support contributes to adaptation of gait parameters and postural control during locomotion.

Center of mass mechanics of chimpanzee bipedal walking.

Center of mass (CoM) oscillations were documented for 81 bipedal walking strides of three chimpanzees. Full-stride ground reaction forces were recorded as well as kinematic data to synchronize force to gait events and to determine speed. Despite being a bent-hip, bent-knee (BHBK) gait, chimpanzee walking uses pendulum-like motion with vertical oscillations of the CoM that are similar in pattern and relative magnitude to those of humans. Maximum height is achieved during single support and minimum height during double support. The mediolateral oscillations of the CoM are more pronounced relative to stature than in human walking when compared at the same Froude speed. Despite the pendular nature of chimpanzee bipedalism, energy recoveries from exchanges of kinetic and potential energies are low on average and highly variable. This variability is probably related to the poor phasic coordination of energy fluctuations in these facultatively bipedal animals. The work on the CoM per unit mass and distance (mechanical cost of transport) is higher than that in humans, but lower than that in bipedally walking monkeys and gibbons. The pronounced side sway is not passive, but constitutes 10% of the total work of lifting and accelerating the CoM. CoM oscillations of bipedally walking chimpanzees are distinctly different from those of BHBK gait of humans with a flat trajectory, but this is often described as "chimpanzee-like" walking. Human BHBK gait is a poor model for chimpanzee bipedal walking and offers limited insights for reconstructing early hominin gait evolution.

Center of mass motion in swimming fish: effects of speed and locomotor mode during undulatory propulsion

Studies of center of mass (COM) motion are fundamental to understanding the dynamics of animal movement, and have been carried out extensively for terrestrial and aerial locomotion. But despite a large amount of literature describing different body movement patterns in fishes, analyses of how the center of mass moves during undulatory propulsion are not available. These data would be valuable for understanding the dynamics of different body movement patterns and the effect of differing body shapes on locomotor force production. In the present study, we analyzed the magnitude and frequency components of COM motion in three dimensions (x: surge, y: sway, z: heave) in three fish species (eel, bluegill sunfish, and clown knifefish) swimming with four locomotor modes at three speeds using high-speed video, and used an image cross-correlation technique to estimate COM motion, thus enabling untethered and unrestrained locomotion. Anguilliform swimming by eels shows reduced COM surge oscillation magnitude relative to carangiform swimming, but not compared to knifefish using a gymnotiform locomotor style. Labriform swimming (bluegill at 0.5 body lengths/s) displays reduced COM sway oscillation relative to swimming in a carangiform style at higher speeds. Oscillation frequency of the COM in the surge direction occurs at twice the tail beat frequency for carangiform and anguilliform swimming, but at the same frequency as the tail beat for gymnotiform locomotion in clown knifefish. Scaling analysis of COM heave oscillation for terrestrial locomotion suggests that COM heave motion scales with positive allometry, and that fish have relatively low COM oscillations for their body size.

Resonance-based oscillations could describe human gait mechanics under various loading conditions

The oscillatory behavior of the center of mass (CoM) and the corresponding ground reaction force (GRF) of human gait for various gait speeds can be accurately described in terms of resonance using a spring–mass bipedal model. Resonance is a mechanical phenomenon that reflects the maximum responsiveness and energetic efficiency of a system. To use resonance to describe human gait, we need to investigate whether resonant mechanics is a common property under multiple walking conditions. Body mass and leg stiffness are determinants of resonance; thus, in this study, we investigated the following questions: (1) whether the estimated leg stiffness increased with inertia, (2) whether a resonance-based CoM oscillation could be sustained during a change in the stiffness, and (3) whether these relationships were consistently observed for different walking speeds. Seven healthy young subjects participated in over-ground walking trials at three different gait speeds with and without a 25-kg backpack. We measured the GRFs and the joint kinematics using three force platforms and a motion capture system. The leg stiffness was incorporated using a stiffness parameter in a compliant bipedal model that best fitted the empirical GRF data. The results showed that the leg stiffness increased with the load such that the resonance-based oscillatory behavior of the CoM was maintained for a given gait speed. The results imply that the resonance-based oscillation of the CoM is a consistent gait property and that resonant mechanics may be useful for modeling human gait.

Postural Responses of Adults With Cerebral Palsy to Combined Base of Support and Visual Field Rotation

We employed a virtual environment to examine the postural behaviors of adults with cerebral palsy (CP). Four adults with CP (22-32 years) and nine healthy adults (21-27 years) were tested with a Rod and Frame protocol. They then stood quietly on a platform within a three-wall virtual environment. The platform was either kept stationary or tilted 3(°) into dorsiflexion in the dark or with pitch up and down visual field rotations at 30(°)/s and 45(°)/s. While the visual field rotated, the platform was held tilted for 30 s and then slowly returned to a neutral position over 30 s. Center of pressure (CoP) was recorded and center of mass (CoM) as well as trunk and ankle angles were calculated. Electromyography (EMG) responses of the ankle and the hip muscles were recorded and analyzed using wavelets. Larger angular deviations from vertical and horizontal in the Rod and Frame test indicated that adults with CP were more visually dependent than healthy adults. Adults with CP had difficulty maintaining balance when standing on a stationary platform during pitch upward rotation of the visual scene. When the platform was tilted during visual field rotations, adults with CP took longer to stabilize their posture and had larger CoM oscillations than when in the dark. The inability to compensate for busy visual environments could impede maintenance of functional locomotion in adults with CP. Employing a visual field stimulus for assessment and training of postural behaviors would be more meaningful than testing in the dark.

Idiosyncratic control of the center of mass in expert climbers

Here, we studied posture and movement coordination adopted by expert climbers. The investigation of such expertise might be of particular interest to gain understanding about the mechanisms underlying the biomechanical control of vertical quadrupedal locomotion. A novel custom setup was developed to analyze the motion of the center-of-mass (COM) and complementary information about the dynamic distribution of vertical reaction forces under the feet during climbing in nine elite climbers (EC) and nine control subjects. Two adaptive features were found in EC. First, unexpectedly they tended to maintain larger COM distances from the wall relative to controls, during both the static and dynamic phases of vertical motion (by ∼5 cm in both cases). Second, while the control subjects tended to restrain the lateral motion of the COM, all EC demonstrated systematic COM oscillations (∼1.3 times larger) associated with a significant alternating dynamic redistribution of the body weight between the limbs during the double support phase. The latter phenomenon likely reflects an adopted basic climbing strategy in experts. Furthermore, a convergence of the optimal solution towards a more diagonal climbing strategy in EC may shed light on the origin of the diagonal gait in primates and early hominids habituated to quadrupedal vertical locomotion.

Adaptation to continuous perturbation of balance: Progressive reduction of postural muscle activity with invariant or increasing oscillations of the center of mass depending on perturbation frequency and vision conditions

We investigated the adaptation of balancing behavior during a continuous, predictable perturbation of stance consisting of 3-min backward and forward horizontal sinusoidal oscillations of the support base. Two visual conditions (eyes-open, EO; eyes-closed, EC) and two oscillation frequencies (LF, 0.2 Hz; HF, 0.6 Hz) were used. Center of Mass (CoM) and Center of Pressure (CoP) oscillations and EMG of Soleus (Sol) and Tibialis Anterior (TA) were recorded. The time course of each variable was estimated through an exponential model. An adaptation index allowed comparison of the degree of adaptation of different variables. Muscle activity pattern was initially prominent under the more challenging conditions (HF, EC and EO; LF, EC) and diminished progressively to reach a steady state. At HF, the behavior of CoM and CoP was almost invariant. The time-constant of EMG adaptation was shorter for TA than for Sol. With EC, the adaptation index showed a larger decay in the TA than Sol activity at the end of the balancing trial, pointing to a different role of the two muscles in the adaptation process. At LF, CoM and CoP oscillations increased during the balancing trial to match the platform translations. This occurred regardless of the different EMG patterns under EO and EC. Contrary to CoM and CoP, the adaptation of the muscle activities had a similar time-course at both HF and LF, in spite of the two frequencies implying a different number of oscillation cycles. During adaptation, under critical balancing conditions (HF), postural muscle activity is tuned to that sufficient for keeping CoM within narrow limits. On the contrary, at LF, when vision permits, a similar decreasing pattern of muscle activity parallels a progressive increase in CoM oscillation amplitude, and the adaptive balancing behavior shifts from the initially reactive behavior to one of passive riding the platform. Adaptive balance control would rely on on-line computation of risk of falling and sensory inflow, while minimizing balance challenge and muscle effort. The results from this study contribute to the understanding of plasticity of the balance control mechanisms under posture-challenging conditions.

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.

An Instance of Reduced Center of Mass Displacement: The Ba Gua Zhang Walking Gait

The Ba Gua Zhang walking gait was examined in an accomplished practitioner to test the hypothesis that reducing the vertical oscillation of the body center of mass (CoM) conserves energy. Compared to typical walking, center-of-mass displacement and peak vertical ground reaction force decreased during Ba Gua Zhang walking. Muscle activity in the lower extremities and lower back, however, increased. The results failed to support the concept of decreasing CoM oscillations to increase efficiency.

Employing dust particle chains as a wakefield diagnostic

Dust particles often form vertical chains due to the influence of the wakefield produced by streaming ions in the plasma sheath produced within an experimental dusty plasma. These particle chains are proving to be a unique diagnostic tool for investigating the physics behind the basic properties of the ion wakefield in the plasma sheath. In this paper, an experimental method is presented for investigating the wakefield employing a new oscillation technique designed to perturb a two-particle vertical chain. Damped attenuated oscillations are generated via an external dc bias on the lower electrode. A fast Fourier transform is used to produce a spectrum of the oscillation data collected, and a center of mass oscillation is identified.

How locomotor parameters adapt to gravity and body structure changes during gait development in children.

The principles of direct dynamics and oscillating systems have been used to study the development of gait parameters in children, with respect to their kinetic consequences on the oscillations of body center of mass (CM). In particular the equations established (a) a natural body frequency (NBF), a body parameter specific to oscillating movements which is invariant for adults and decreases with age for children, and (b) the amplitude ratio of CM to center-of-foot pressure (CP) oscillations as a parametric function of the step frequency, whose parameter is the NBF. This function was used to analyze the development of gait locomotors with respect to their kinetic effects on balance in the frontal plane. Five children were examined longitudinally during their first 5 years of independent walking (IW), and two cross-sectional groups between 5 and 7 years of IW were also considered. The results showed a shift toward the low end of step frequency bands as the NBF decreased along with invariances in the amplitudes of CM oscillation in both the frontal and sagittal planes, regardless of age and gait velocity. The biomechanical meaning of the NBF, of its decrease and of postural invariances associated with the decrease of the frequency, are discussed as well as how the programming of locomotor parameters adapts to changes in body structure during gait development.

Why we walk the way we do.

By using inverse dynamics and forceplate recordings, this study established the principle of oscillating systems and the influence of gravity and body parameters on the programming of the gait parameters, step frequency and length. Calculation of the ratio of the amplitude of the center of mass (CM) and the center of foot pressure (CP) oscillations yielded an equation and established a biomechanical constant, the natural body frequency (NBF). NBF appears to be an absolute invariant parameter, specific to human standing posture and gait in terrestrial gravity, which influences the relative positions of CM and CP and whose value separates the frequency bands of standing posture from those for gait. This equation was tested by using the experimental paradigm of stepping in place and then used in calculating the magnitude of CM oscillations during gait. The biomechanical analysis of the experimental observations allows one to establish the relationships between body parameters and gravity and the central programming of locomotor parameters.