Center Of Mass Dynamics Research Articles

Impact of visual rotations on heading direction and center of mass control during steady-state gait.

Visual information is essential to navigate the environment and maintain postural stability during gait. Visual field rotations alter the perceived heading direction, resulting in gait trajectory deviations, known as visual coupling. It is unclear how center of mass (CoM) control relative to a continuously changing base of support (BoS) is adapted to facilitate visual coupling. This study aimed to characterize mediolateral (ML) balance control during visual coupling in steady-state gait. Sixteen healthy participants walked on an instrumented treadmill, naive to sinusoidal low-frequency (0.1 Hz) rotations of the virtual environment around the vertical axis. Rotations were continuous with 1) high or 2) low amplitude or were 3) periodic with 10-s intervals. Visual coupling was characterized with cross-correlations between CoM trajectory and visual rotations. Balance control was characterized with the ML margin of stability (MoSML) and by quantifying foot placement control as the relation between CoM dynamics and lateral foot placement. Visual coupling was strong on a group level (continuous low: 0.88, continuous high: 0.91, periodic: 0.95) and moderate to strong on an individual level. Higher rotation amplitudes induced stronger gait trajectory deviations. The MoSML decreased toward the deviation direction and increased at the opposite side. Foot placement control was similar compared with regular gait. Furthermore, pelvis and foot reorientation toward the rotation direction was observed. We concluded that visual coupling was facilitated by reorientating the body and shifting the extrapolated CoMML closer to the lateral BoS boundary toward the adjusted heading direction while preserving CoM excursion and foot placement control.NEW & NOTEWORTHY Healthy, naive participants were unaware of subtle, low-frequency rotations of the visual field but still coupled their gait trajectory to a rotating virtual environment. In response, participants decreased their margin of stability toward the new heading direction, without changing the center of mass excursion magnitude and foot placement strategy.

Skipping without and with hurdles in bipedal macaque: global mechanics.

Macaques trained to perform bipedally used running gaits across a wide range of speeds. At higher speeds they preferred unilateral skipping (galloping). The same asymmetric stepping pattern was used while hurdling across two low obstacles placed at the distance of a stride within our experimental track. In bipedal macaques during skipping, we expected a differential use of the trailing and leading legs. The present study investigated global properties of the effective and virtual leg, the location of the virtual pivot point (VPP), and the energetics of the center of mass (CoM), with the aim of clarifying the differential leg operation during skipping in bipedal macaques. When skipping, macaques displayed minor double support and aerial phases during one stride. Asymmetric leg use was indicated by differences in leg kinematics. Axial damping and tangential leg work did not influence the indifferent peak ground reaction forces and impulses, but resulted in a lift of the CoM during contact of the leading leg. The aerial phase was largely due to the use of the double support. Hurdling amplified the differential leg operation. Here, higher ground reaction forces combined with increased double support provided the vertical impulse to overcome the hurdles. Following CoM dynamics during a stride, skipping and hurdling represented bouncing gaits. The elevation of the VPP of bipedal macaques resembled that of human walking and running in the trailing and leading phases, respectively. Because of anatomical restrictions, macaque unilateral skipping differs from that of humans, and may represent an intermediate gait between grounded and aerial running.

Quantifying changes in individual-specific template-based representations of center-of-mass dynamics during walking with ankle exoskeletons using Hybrid-SINDy

Ankle exoskeletons alter whole-body walking mechanics, energetics, and stability by altering center-of-mass (CoM) motion. Controlling the dynamics governing CoM motion is, therefore, critical for maintaining efficient and stable gait. However, how CoM dynamics change with ankle exoskeletons is unknown, and how to optimally model individual-specific CoM dynamics, especially in individuals with neurological injuries, remains a challenge. Here, we evaluated individual-specific changes in CoM dynamics in unimpaired adults and one individual with post-stroke hemiparesis while walking in shoes-only and with zero-stiffness and high-stiffness passive ankle exoskeletons. To identify optimal sets of physically interpretable mechanisms describing CoM dynamics, termed template signatures, we leveraged hybrid sparse identification of nonlinear dynamics (Hybrid-SINDy), an equation-free data-driven method for inferring sparse hybrid dynamics from a library of candidate functional forms. In unimpaired adults, Hybrid-SINDy automatically identified spring-loaded inverted pendulum-like template signatures, which did not change with exoskeletons (p > 0.16), except for small changes in leg resting length (p < 0.001). Conversely, post-stroke paretic-leg rotary stiffness mechanisms increased by 37–50% with zero-stiffness exoskeletons. While unimpaired CoM dynamics appear robust to passive ankle exoskeletons, how neurological injuries alter exoskeleton impacts on CoM dynamics merits further investigation. Our findings support Hybrid-SINDy’s potential to discover mechanisms describing individual-specific CoM dynamics with assistive devices.

Center of Mass Dynamics and Contact-Aided Invariant Filtering for Biped Robot State Estimation

Center of Mass Dynamics and Contact-Aided Invariant Filtering for Biped Robot State Estimation

‘Virtual pivot point’ in human walking: Always experimentally observed but simulations suggest it may not be necessary for stability

The intersection of ground reaction forces near a point above the center of mass has been observed in computer simulation models and human walking experiments. Observed so ubiquitously, the intersection point (IP) is commonly assumed to provide postural stability for bipedal walking. In this study, we challenge this assumption by questioning if walking without an IP is possible. Deriving gaits with a neuromuscular reflex model through multi-stage optimization, we found stable walking patterns that show no signs of the IP-typical intersection of ground reaction forces. The non-IP gaits found are stable and successfully rejected step-down perturbations, which indicates that an IP is not necessary for locomotion robustness or postural stability. A collision-based analysis shows that non-IP gaits feature center of mass (CoM) dynamics with vectors of the CoM velocity and ground reaction force increasingly opposing each other, indicating an increased mechanical cost of transport. Although our computer simulation results have yet to be confirmed through experimental studies, they already indicate that the role of the IP in postural stability should be further investigated. Moreover, our observations on the CoM dynamics and gait efficiency suggest that the IP may have an alternative or additional function that should be considered.

Stabilized Walking of Humanoid NAO Using Enhanced Spring-Loaded Inverted Pendulum Model on Uneven Terrain

In the coming decades, humanoid robots will play a rising role in society. The present article discusses their walking control and obstacle avoidance on uneven terrain using enhanced spring-loaded inverted pendulum model (ESLIP). The SLIP model is enhanced by tuning it with an adaptive particle swarm optimization (APSO) approach. It helps the humanoid robot to reach closer to the obstacles in order to optimize the turning angle to optimize the path length. The desired trajectory, along with the sensory data, is provided to the SLIP model, which creates compatible COM (center of mass) dynamics for stable walking. This output is fed to APSO as input, which adjusts the placement of the foot during interaction with uneven surfaces and obstacles. It provides an optimum turning angle for shunning the obstacles and ensures the shortest path length. Simulation has been carried out in a 3D simulator based on the proposed controller and SLIP controller in uneven terrain.

Towards an Integrative “Lightness” of Being

Towards an Integrative “Lightness” of Being

Meaningful measurements of maneuvers: People with incomplete spinal cord injury \u2018step up\u2019 to the challenges of altered stability requirements

BackgroundMany people with incomplete spinal cord injury (iSCI) have the ability to maneuver while walking. However, neuromuscular impairments create challenges to maintain stability. How people with iSCI maintain stability during walking maneuvers is poorly understood. Thus, this study compares maneuver performance in varying external conditions between persons with and without iSCI to better understand maneuver stabilization strategies in people with iSCI.MethodsParticipants with and without iSCI walked on a wide treadmill and were prompted to perform lateral maneuvers between bouts of straight walking. Lateral force fields applied to the participants’ center of mass amplified or attenuated the participants’ movements, thereby increasing the capability of the study to capture behavior at varied levels of challenge to stability.ResultsBy examining metrics of stability, step width, and center of mass dynamics, distinct strategies emerged following iSCI. The minimum margin of stability (MOSmin) on each step during maneuvers indicated persons with iSCI generally adapted to amplified and attenuated force fields with increased stability compared to persons without iSCI, particularly using increased step width and reduced center of mass excursion on maneuver initiation. In the amplified field, however, persons with iSCI had a reduced MOSmin when terminating a maneuver, likely due to the challenge of the force field opposing the necessary lateral braking. Persons without iSCI were more likely to rely on or oppose the force field when appropriate for movement execution. Compared to persons with iSCI, they reduced their MOSmin to initiate maneuvers in the attenuated and amplified fields and increased their MOSmin to arrest maneuvers in the amplified field.ConclusionsThe different force fields were successful in identifying relatively subtle strategy differences between persons with and without iSCI. Specifically, persons with iSCI adopted increased step width and reduction in center of mass excursion to increase maneuver stability in the amplified field. The amplified field may provoke practice of stable and efficient initiation and arrest of walking maneuvers. Overall, this work allows better framing of the stability mechanisms used following iSCI to perform walking maneuvers.

Post-Stroke Adaptation of Lateral Foot Placement Coordination in Variable Environments.

Individuals with stroke often have difficulty modulating their lateral foot placement during gait, a primary strategy for maintaining lateral stability. Our purpose was to understand how individuals with and without stroke adapt their lateral foot placement when walking in an environment that alters center of mass (COM) dynamics and the mechanical requirement to maintain lateral stability. The treadmill walking environments included: 1) a Null Field – where no forces were applied, and 2) a Damping Field – where external forces opposed lateral COM velocity. To evaluate the response to the changes in environment, we quantified the correlation between lateral COM state and lateral foot placement (FP), as well as step width mean and variability. We hypothesized the Damping Field would produce a stabilizing effect and reduce both the COM-FP correlation strength and step width compared to the Null Field. We also hypothesized that individuals with stroke would have a significantly weaker COM-FP correlation than individuals without stroke. Surprisingly, we found no differences in COM-FP correlations between the Damping and Null Fields. We also found that compared to individuals without stroke in the Null Field, individuals with stroke had weaker COM-FP correlations (Paretic < Control: p = 0.001, Non-Paretic < Control: p = 0.007) and wider step widths (p = 0.001). Our results suggest that there is a post-stroke shift towards a non-specific lateral stabilization strategy that relies on wide steps that are less correlated to COM dynamics than in individuals without stroke.

An extended statically equivalent serial chain—Identification of whole body center of mass with dynamic motion

Background:Tracking the whole body center of mass (CoM) trajectory of balance-impaired individuals with a personalized model is useful in the development of customized fall prevention strategies. A personalized CoM estimate can be obtained using the statically equivalent serial chain (SESC) method, but the subject has to perform an identification procedure to determine the set of subject-specific SESC parameters. During this identification, the subject must hold a series of static poses, some of which are unsuitable for balanced-impaired individuals. Research question:Can non-static poses be used to replace the static poses during SESC parameter identification? Methods:A new method that extends the range of postures used to determine SESC parameters is presented. It takes advantage of CoM dynamics and can be executed by predominantly using dynamic motions with a few static frames. Furthermore, it is implemented using a Kalman filter to allow automatic switching between the dynamic and static models. The proposed method was tested with motion data obtained from seven healthy adults using a Vicon motion capture system and an AMTI force platform. Results:We found that dynamic motions could be used to estimate the SESC parameter and even reproduce ground reaction forces; however a small number of static poses are still required to determine the subject’s CoM position. The SESC-based CoM estimate obtained with this new approach was similar to that obtained using conventional full-static identification, except that the subject did not have to assume and maintain static poses. Significance:Our proposed extension of the conventional SESC method would facilitate its application in the field of neuro-rehabilitation, especially in patients who need balance training. This personalized CoM method could be applicable for patients who are not able to maintain a static posture. In addition, this method helps minimize the total identification time by increasing the number of usable recorded frames.

Dynamic and Versatile Humanoid Walking via Embedding 3D Actuated SLIP Model With Hybrid LIP Based Stepping

In this paper, we propose an efficient approach to generate dynamic and versatile humanoid walking with non-constant center of mass (COM) height. We exploit the benefits of using reduced order models (ROMs) and stepping control to generate dynamic and versatile walking motion. Specifically, we apply the stepping controller based on the Hybrid Linear Inverted Pendulum Model (H-LIP) to perturb a periodic walking motion of a 3D actuated Spring Loaded Inverted Pendulum (3D-aSLIP), which yields versatile walking behaviors of the 3D-aSLIP, including various 3D periodic walking, fixed location tracking, and global trajectory tracking. The 3D-aSLIP walking is then embedded on the fully-actuated humanoid via the task space control on the COM dynamics and ground reaction forces. The proposed approach is realized on the robot model of Atlas in simulation, wherein versatile dynamic motions are generated.

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.

Robust Bipedal Locomotion Based on a Hierarchical Control Structure

SummaryTo improve biped locomotion’s robustness to internal and external disturbances, this study proposes a hierarchical structure with three control levels. At the high level, a foothold sequence is generated so that the Center of Mass (CoM) trajectory tracks a planned path. The planning procedure is simplified by selecting the midpoint between two consecutive Center of Pressure (CoP) points as the feature point. At the middle level, a novel robust hybrid controller is devised to drive perturbed system states back to the nominal trajectory within finite cycles without chattering. The novelty lies in that the hybrid controller is not subject to linear CoM dynamic constraints. The hybrid controller consists of two sub-controllers: an oscillation controller and a smoothing controller. For the oscillation controller, the desired CoM height is specified as a sine-shaped function, avoiding a new attractive limit cycle. However, this controller results in the inevitable chattering because of discontinuities. A smoothing controller provides continuous properties and thus can inhibit the chattering problem, but has a smaller region of attraction compared with the oscillation controller. A hybrid controller merges the two controllers for a smooth transition. At the low level, the desired CoM motion is defined as tasks and embedded in a whole body operational space (WBOS) controller to compute the joint torques analytically. The novelty of the low-level controller lies in that within the WBOS framework, CoM motion is not subject to fixed CoM dynamics and thus can be generalized.

Linking Gait Dynamics to Mechanical Cost of Legged Locomotion.

For millenia, legged locomotion has been of central importance to humans for hunting, agriculture, transportation, sport, and warfare. Today, the same principal considerations of locomotor performance and economy apply to legged systems designed to serve, assist, or be worn by humans in urban and natural environments. Energy comes at a premium not only for animals, wherein suitably fast and economical gaits are selected through organic evolution, but also for legged robots that must carry sufficient energy in their batteries. Although a robot's energy is spent at many levels, from control systems to actuators, we suggest that the mechanical cost of transport is an integral energy expenditure for any legged system—and measuring this cost permits the most direct comparison between gaits of legged animals and robots. Although legged robots have matched or even improved upon total cost of transport of animals, this is typically achieved by choosing extremely slow speeds or by using regenerative mechanisms. Legged robots have not yet reached the low mechanical cost of transport achieved at speeds used by bipedal and quadrupedal animals. Here we consider approaches used to analyze gaits and discuss a framework, termed mechanical cost analysis, that can be used to evaluate the economy of legged systems. This method uses a point mass perspective to evaluate the entire stride as well as to identify individual events that accrue mechanical cost. The analysis of gait began at the turn of the last century with spatiotemporal analysis facilitated by the advent of cine film. These advances gave rise to the “gait diagram,” which plots duty factors and phase separations between footfalls. This approach was supplanted in the following decades by methods using force platforms to determine forces and motions of the center of mass (CoM)—and analytical models that characterize gait according to fluctuations in potential and kinetic energy. Mechanical cost analysis draws from these approaches and provides a unified framework that interprets the spatiotemporal sequencing of leg contacts within the context of CoM dynamics to determine mechanical cost in every instance of the stride. Diverse gaits can be evaluated and compared in biological and engineered systems using mechanical cost analysis.

Analysis of biases in dynamic margins of stability introduced by the use of simplified center of mass estimates during walking and turning

The ability to control the body’s center of mass (CoM) is critical for preventing falls, which are a major health concern in aging populations. Control of the CoM has been assessed by characterizing dynamic margins of stability (MoS) which capture the dynamic relationship between the CoM and the base of support. Accurate estimation of CoM dynamics is best accomplished using a full-body marker set. However, a number of simplified estimates have been used throughout literature. Here, we determined the biases and sources of bias when computing MoS using four simplified CoM models, and we characterized how these biases varied in straight walking versus turning. CoM kinematics were characterized using a full-body marker set, the lower extremities and trunk, lower extremities only, an average of four pelvic markers, and one pelvic marker alone. Significant bias was demonstrated for most methods and was larger during turning tasks compared to straight walking. In the fore-aft direction, only overestimates in the MoS were observed, and these ranged from 15 to 110% larger than the true MoS value. In the mediolateral direction, both under- and over-estimates were observed and ranged from −175 to 225%. Across tasks, bias was smallest when using the lower extremity plus trunk (−23 to 62%) and pelvis average methods (−71 to 43%). Sources of bias were attributed to misestimates of CoM height, velocity, and position. Together, our findings suggest that the 1) lower extremity and trunk model and 2) pelvis average model should be considered in future studies to minimize bias when simplified models of CoM dynamics are desired.

A springy pendulum could describe the swing leg kinetics of human walking

The dynamics of human walking during various walking conditions could be qualitatively captured by the springy legged dynamics, which have been used as a theoretical framework for bipedal robotics applications. However, the spring-loaded inverted pendulum model describes the motion of the center of mass (CoM), which combines the torso, swing and stance legs together and does not explicitly inform us as to whether the inter-limb dynamics share the springy legged dynamics characteristics of the CoM. In this study, we examined whether the swing leg dynamics could also be represented by springy mechanics and whether the swing leg stiffness shows a dependence on gait speed, as has been observed in CoM mechanics during walking. The swing leg was modeled as a spring-loaded pendulum hinged at the hip joint, which is under forward motion. The model parameters of the loaded mass were adopted from body parameters and anthropometric tables, whereas the free model parameters for the rest length of the spring and its stiffness were estimated to best match the data for the swing leg joint forces. The joint forces of the swing leg were well represented by the springy pendulum model at various walking speeds with a regression coefficient of R2>0.8. The swing leg stiffness increased with walking speed and was correlated with the swing frequency, which is consistent with previous observations from CoM dynamics described using the compliant leg. These results suggest that the swing leg also shares the springy dynamics, and the compliant walking model could be extended to better present swing leg dynamics.

Aging and the recovery of postural stability from taking a step

The study examined the effect of aging adults (young: 18-26 years vs. old: 66-73 years) on the recovery of postural stability from taking a single volitional step that varied in direction (forward, backward, sideways) onto force platforms. The recovery of postural stability (as indexed by an exponential decay function) was determined from the dynamic stability of the motions of the center of pressure (COP), center of mass (COM) and virtual time to contact (VTC). The findings showed that in all step directions the older adults required more time to securely perform the step and were less stable after the second foot contact with the surface of support. The decay rate of the recovery of the COP, COM and VTC stable dynamics was reduced and the minimum of VTC lower in the old in contrast to the young adults. The findings reveal that even in taking a single step with preferred spatial–temporal dynamics older adults are slower and less stable in recovery of stance through more closely challenging the limits of the postural stability boundary and its associated potential of a fall.

Coupled internal-state and center-of-mass dynamics of Rydberg atoms in a magnetic guide

We study cold rubidium Rydberg atoms, initially prepared in state 59D5/2, guided along a two-wire magnetic atom guide. The evolution of the atoms is driven by the combined effects of internal-state transitions and dipole forces acting on the center-of-mass degree of freedom. State-selective field ionization, applied at a variable delay time, is used to investigate the evolution of the internal-state distribution. We observe a broadening of the field ionization spectrum caused by population transfer between Rydberg states. At late times, the distribution of the remaining Rydberg atoms becomes biased toward states with high principal quantum numbers. The population transfer is attributed to thermal transitions and, to a lesser extent, initial state mixing due to Rydberg-Rydberg collisions. Characteristic components in spatially and temporally resolved distributions of the ion signal are interpreted in the context of the underlying physics. The system is simulated with a model in which the centerof-mass dynamics are treated classically, while the internal-state dynamics are treated quantum mechanically. The simulation qualitatively reproduces most experimental findings and provides experimentally inaccessible information.

Center of mass acceleration feedback control for standing by functional neuromuscular stimulation: A simulation study

The potential efficacy of total body center of mass (COM) acceleration for feedback control of standing balance by functional neuromuscular stimulation (FNS) following spinal cord injury (SCI) was investigated. COM acceleration may be a viable alternative to conventional joint kinematics because of its rapid responsiveness, focal representation of COM dynamics, and ease of measurement. A computational procedure was developed using an anatomically realistic, three-dimensional, bipedal biomechanical model to determine optimal patterns of muscle excitations to produce targeted effects upon COM acceleration from erect stance. The procedure was verified with electromyographic data collected from standing nondisabled subjects undergoing systematic perturbations. Using 16 muscle groups targeted by existing implantable neuroprostheses, we generated data to train an artificial neural network (ANN)-based controller in simulation. During forward simulations, proportional feedback of COM acceleration drove the ANN to produce muscle excitation patterns countering the effects of applied perturbations. Feedback gains were optimized to minimize upper-limb (UL) loading required to stabilize against disturbances. Compared with the clinical case of maximum constant excitation, the controller reduced UL loading by 43% in resisting external perturbations and by 51% during simulated one-arm reaching. Future work includes performance assessment against expected measurement errors and development of user-specific control systems.

Approximate mathematical model of the orientation of profiled joints with the use of passive adaptation and low-frequency vibrations

The article presents the approximate mathematical model of the center of mass dynamics of workpiece in relation to the basic part.