Stability and Control of Human Trunk Movement During Walking

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov' stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.     

A model of cerebrocerebello-spinomuscular interaction in the sagittal control of human walking

A computationally developed model of human upright balance control (Jo and Massaquoi on Biol cybern 91:188–202, 2004) has been enhanced to describe biped walking in the sagittal plane. The model incorporates (a) non-linear muscle mechanics having activation level -dependent impedance, (b) scheduled cerebrocerebellar interaction for control of center of mass position and trunk pitch angle, (c) rectangular pulse-like feedforward commands from a brainstem/ spinal pattern generator, and (d) segmental reflex modulation of muscular synergies to refine inter-joint coordination. The model can stand when muscles around the ankle are coactivated. When trigger signals activate, the model transitions from standing still to walking at 1.5 m/s. Simulated natural walking displays none of seven pathological gait features. The model can simulate different walking speeds by tuning the amplitude and frequency in spinal pattern generator. The walking is stable against forward and backward pushes of up to 70 and 75 N, respectively, and with sudden changes in trunk mass of up to 18%. The sensitivity of the model to changes in neural parameters and the predicted behavioral results of simulated neural system lesions are examined. The deficit gait simulations may be useful to support the functional and anatomical correspondences of the model. The model demonstrates that basic human-like walking can be achieved by a hierarchical structure of stabilized-long loop feedback and synergy-mediated feedforward controls. In particular, internal models of body dynamics are not required.     

A mathematical model of the stability control of human thorax and pelvis movements during walking

A mathematical model is developed to study the human thorax and pelvis movements in the frontal plane during normal walking. The model comprises of two-link base-excited inverted pendulums with one-degree of rotational freedom for each link. Since the linear motion of the pelvis has a significant effect on the upper body stability, this effect is included in the model by having a base point moving in the frontal plane in a general way. Furthermore, because the postural stability is the primary requirement of normal human walking, the control law is developed based on Lyapunov's stability theory, which guarantees the stability of the pendulum system around the up-right position. To evaluate the model, the simulation results, including the angular displacement of each link and the torque applied on each link, are compared with those from gait measurements. It is shown that the simulation results match those from gait measurements closely. These results suggest that the proposed model can provide a useful framework for analysis of postural control mechanisms.     

A Mathematical Model of the Stability Control of Human Thorax and Pelvis Movements During Walking

A mathematical model is developed to study the human thorax and pelvis movements in the frontal plane during normal walking. The model comprises of two-link base-excited inverted pendulums with one-degree of rotational freedom for each link. Since the linear motion of the pelvis has a significant effect on the upper body stability, this effect is included in the model by having a base point moving in the frontal plane in a general way. Furthermore, because the postural stability is the primary requirement of normal human walking, the control law is developed based on Lyapunov's stability theory, which guarantees the stability of the pendulum system around the up-right position. To evaluate the model, the simulation results, including the angular displacement of each link and the torque applied on each link, are compared with those from gait measurements. It is shown that the simulation results match those from gait measurements closely. These results suggest that the proposed model can provide a useful framework for analysis of postural control mechanisms.     

Distinct Motor Strategies Underlying Split-Belt Adaptation in Human Walking and Running

The aim of the present study was to elucidate the adaptive and de-adaptive nature of human running on a split-belt treadmill. The degree of adaptation and de-adaptation was compared with those in walking by calculating the antero-posterior component of the ground reaction force (GRF). Adaptation to walking and running on a split-belt resulted in a prominent asymmetry in the movement pattern upon return to the normal belt condition, while the two components of the GRF showed different behaviors depending on the gaits. The anterior braking component showed prominent adaptive and de-adaptive behaviors in both gaits. The posterior propulsive component, on the other hand, exhibited such behavior only in running, while that in walking showed only short-term aftereffect (lasting less than 10 seconds) accompanied by largely reactive responses. These results demonstrate a possible difference in motor strategies (that is, the use of reactive feedback and adaptive feedforward control) by the central nervous system (CNS) for split-belt locomotor adaptation between walking and running. The present results provide basic knowledge on neural control of human walking and running as well as possible strategies for gait training in athletic and rehabilitation scenes.     

Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator

The central pattern generators (CPGs) in the spinal cord strongly contribute to locomotor behavior. To achieve adaptive locomotion, locomotor rhythm generated by the CPGs is suggested to be functionally modulated by phase resetting based on sensory afferent or perturbations. Although phase resetting has been investigated during fictive locomotion in cats, its functional roles in actual locomotion have not been clarified. Recently, simulation studies have been conducted to examine the roles of phase resetting during human bipedal walking, assuming that locomotion is generated based on prescribed kinematics and feedback control. However, such kinematically based modeling cannot be used to fully elucidate the mechanisms of adaptation. In this article we proposed a more physiologically based mathematical model of the neural system for locomotion and investigated the functional roles of phase resetting. We constructed a locomotor CPG model based on a two-layered hierarchical network model of the rhythm generator (RG) and pattern formation (PF) networks. The RG model produces rhythm information using phase oscillators and regulates it by phase resetting based on foot-contact information. The PF model creates feedforward command signals based on rhythm information, which consists of the combination of five rectangular pulses based on previous analyses of muscle synergy. Simulation results showed that our model establishes adaptive walking against perturbing forces and variations in the environment, with phase resetting playing important roles in increasing the robustness of responses, suggesting that this mechanism of regulation may contribute to the generation of adaptive human bipedal locomotion.     

Spinal Mechanisms May Provide a Combination of Intermittent and Continuous Control of Human Posture: Predictions from a Biologically Based Neuromusculoskeletal Model

Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called “paradoxical” behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.     

Dynamic stability of a human standing on a balance board

The neuromuscular system used to stabilize upright posture in humans is a nonlinear dynamical system with time delays. The analysis of this system is important for improving balance and for early diagnosis of neuromuscular disease. In this work, we study the dynamic coupling between the neuromuscular system and a balance board—an unstable platform often used to improve balance in young athletes, and older or neurologically impaired patients. Using a simple inverted pendulum model of human posture on a balance board, we describe a surprisingly broad range of divergent and oscillatory CoP/CoM responses associated with instabilities of the upright equilibrium. The analysis predicts that a variety of sudden changes in the stability of upright postural equilibrium occurs with slow continuous deterioration in balance board stiffness, neuromuscular gain, and time delay associated with the changes in proprioceptive/vestibular/visual-neuromuscular feedback. The analysis also provides deeper insight into changes in the control of posture that enable stable upright posture on otherwise unstable platforms.     

Neural adaptive control of nonlinear multivariable systems with application to a class of inverted pendulums

In this paper multilayer neural networks (MNNs) are used to control the balancing of a class of inverted pendulums. Unlike normal inverted pendulums, the pendulum discussed here has two degrees of rotational freedom and the base-point moves randomly in three-dimensional space. The goal is to apply control torques to keep the pendulum in a prescribed position in spite of the random movement at the base-point. Since the inclusion of the base-point motion leads to a non-autonomous dynamic system with time-varying parametric excitation, the design of the control system is a challenging task. A feedback control algorithm is proposed that utilizes a set of neural networks to compensate for the effect of the system's nonlinearities. The weight parameters of neural networks updated on-line, according to a learning algorithm that guarantees the Lyapunov stability of the control system. Furthermore, since the base-point movement is considered unmeasurable, a neural inverse model is employed to estimate it from only measured state variables. The estimate is then utilized within the main control algorithm to produce compensating control signals. The examination of the proposed control system, through simulations, demonstrates the promise of the methodology and exhibits positive aspects, which cannot be achieved by the previously developed techniques on the same problem. These aspects include fast, yet well-maintained damped responses with reasonable control torques and no requirement for knowledge of the model or the model parameters. The work presented here can benefit practical problems such as the study of stable locomotion of human upper body and bipedal robots.     

Synthesis of two-dimensional human walking: a test of the <Emphasis Type="Italic">λ</Emphasis>-model

To test the -model version of the equilibrium point hypothesis both for feasibility and validity with respect to the control of terrestrial locomotion, we developed a two-dimensional, eleven-segment musculoskeletal model of the human body including 14 muscle-tendon complexes per leg, three-segment feet, and a physiologically based model of foot-ground interaction. Human walking was synthesized by numerical integration of the coupled muscle-tendon and rigid body dynamics. To this end a control algorithm based on the -model was implemented in the model providing muscle stimulation patterns that guaranteed dynamically stable walking including a balanced trunk. Thus, the timing of the movement is not preset by a central pattern generator but emerges from the interaction of the musculoskeletal system with the control algorithm. The control parameters were found in a trial-and-error approach. The feedforward part of the control scheme consists of just two target configurations each of which is composed of a set of one nominal length per muscle (-model). Variation of gravity reveals that (1) the synthesized walking patterns are close to ballistic walking and (2) this muscularly induced natural walking can only be initiated and maintained in the range between about a tenth and three times earth-bound gravity. Our walking patterns are robust both against parameter variations and shuffling of the swing leg. We discuss our model with respect to gravity scaling, speed control, feedback delay, and the terms equilibrium point hypothesis and central pattern generator.     

Dynamic model of the equine hindlimb during the swing phase

A dynamic model is developed to describe the swing phase of the hindlimb of a normally walking horse. The limb was represented by four rigid segments constrained to move in a sagittal plane only. The mathematical equations of motion of this four-element pendulum were formulated using Lagrange's theorem. The morphometric parameters from the hindlimb segments of 3 horses were determined using high-speed film analysis. Five muscle groups were incorporated in the model. Muscle activity was derived from earlier EMG measurements. Optimization of muscle moments resulted in a simulated swing movement that approximated that in the living animal.     

Relative Roles of the Ankle and Hip Muscles in Human Postural Control in the Frontal Plane during Standing

The main goal was to evaluate the relative roles of the ankle and hip muscles in human postural control in the frontal plane during normal upright standing. Experiments were designed to compare upright standing with and without the involvement of the ankle joint. The results demonstrated that standing balance in the frontal plane depended largely on the hip muscles and just slightly on the ankle muscles, which performed only small adjusting movements in the frontal plane. During quiet standing, the human body swayed in the frontal plane as a two-component inverted pendulum or, when no ankle joint torque was permitted, as an inverted pendulum consisting of only one component.     

Segment and joint angles of hind limb during bipedal and quadrupedal walking of the bonobo (Pan paniscus)

We describe segment angles (trunk, thigh, shank, and foot) and joint angles (hip, knee, and ankle) for the hind limbs of bonobos walking bipedally ("bent-hip bent-knee walking," 17 sequences) and quadrupedally (33 sequences). Data were based on video recordings (50 Hz) of nine subjects in a lateral view, walking at voluntary speed. The major differences between bipedal and quadrupedal walking are found in the trunk, thigh, and hip angles. During bipedal walking, the trunk is approximately 33-41 degrees more erect than during quadrupedal locomotion, although it is considerably more bent forward than in normal human locomotion. Moreover, during bipedal walking, the hip has a smaller range of motion (by 12 degrees ) and is more extended (by 20-35 degrees ) than during quadrupedal walking. In general, angle profiles in bonobos are much more variable than in humans. Intralimb phase relationships of subsequent joint angles show that hip-knee coordination is similar for bipedal and quadrupedal walking, and resembles the human pattern. The coordination between knee and ankle differs much more from the human pattern. Based on joint angles observed throughout stance phase and on the estimation of functional leg length, an efficient inverted pendulum mechanism is not expected in bonobos.     

A model of neuro-musculo-skeletal system for human locomotion under position constraint condition

The human locomotion was studied on the basis of the interaction of the musculo-skeletal system, the neural system and the environment. A mathematical model of human locomotion under position constraint condition was established. Besides the neural rhythm generator, the posture controller and the sensory system, the environment feedback controller and the stability controller were taken into account in the model. The environment feedback controller was proposed for two purposes, obstacle avoidance and target position control of the swing foot. The stability controller was proposed to imitate the self-balancing ability of a human body and improve the stability of the model. In the stability controller, the ankle torque was used to control the velocity of the body gravity center. A prediction control algorithm was applied to calculate the torque magnitude of the stability controller. As an example, human stairs climbing movement was simulated and the results were given. The simulation result proved that the mathematical modeling of the task was successful.     

Ankle torque control that shifts the center of pressure from heel to toe contributes non-zero sagittal plane angular momentum during human walking

A principle objective of human walking is controlling angular motion of the body as a whole to remain upright. The force of the ground on each foot (F) reflects that control, and recent studies show that in the sagittal plane F exhibits a specific coordination between F direction and center-of-pressure (CP) that is conducive to remaining upright. Typical walking involves the CP shifting relative to the body due to two factors: posterior motion of the foot with respect to the hip (stepping) and motion of the CP relative to the foot (foot roll-over). Recent research has also shown how adjusting ankle torque alone to shift CP relative to the foot systematically alters the direction of F, and thus, could play a key role in upright posture and the F measured during walking. This study explores how the CP shifts due to stepping and foot roll-over contribute to the observed F and its role in maintaining upright posture. Experimental walking kinetics and kinematics were combined with a mechanical model of the human to show that variation in F that was not attributable to foot roll-over had systematic correlation between direction and CP that could be described by an intersection point located near the center-of-mass. The findings characterize a component of walking motor control, describe how typical foot roll-over contributes to postural control, and provide a rationale for the increased fall risk observed in individuals with atypical ankle muscle function.     

Impedance characteristics of a neuromusculoskeletal model of the human arm II. Movement control

The modulation of neuromusculoskeletal impedance during movements is analysed using a motor control model of the human arm. The motor control system combines feedback and feedforward control and both control modes are determined in one optimization process. In the model, the stiffness varies at the double movement frequency for 2-Hz oscillatory elbow movements and has high values at the movement reversals. During goal-directed two-degrees-of-freedom arm movements, the stiffness is decreased during the movement and may be increased in the initial and final phases, depending on the movement velocity. The stiffness has a considerable curl during the movement, as was also observed in experimental data. The dynamic stiffness patterns of the model can be explained basically by the α−γ coactivation scheme where feedback gains covary with motor control signals. In addition to the modulation of the gain factors, it is argued that the variation of the intrinsic stiffness has a considerable effect on movement control, especially during fast movements. Received: 14 October 1997 / Accepted in revised form: 18 May 1999     

Similar sensorimotor transformations control balance during standing and walking

Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.     

Independent Walking as a Major Skill for the Development of Anticipatory Postural Control: Evidence from Adjustments to Predictable Perturbations

Although there is suggestive evidence that a link exists between independent walking and the ability to establish anticipatory strategy to stabilize posture, the extent to which this skill facilitates the development of anticipatory postural control remains largely unknown. Here, we examined the role of independent walking on the infants’ ability to anticipate predictable external perturbations. Non-walking infants, walking infants and adults were sitting on a platform that produced continuous rotation in the frontal plane. Surface electromyography (EMG) of neck and lower back muscles and the positions of markers located on the platform, the upper body and the head were recorded. Results from cross-correlation analysis between rectified and filtered EMGs and platform movement indicated that although muscle activation already occurred before platform movement in non-walking infants, only walking infants demonstrated an adult-like ability for anticipation. Moreover, results from further cross-correlation analysis between segmental angular displacement and platform movement together with measures of balance control at the end-points of rotation of the platform evidenced two sorts of behaviour. The adults behaved as a non-rigid non-inverted pendulum, rather stabilizing head in space, while both the walking and non-walking infants followed the platform, behaving as a rigid inverted pendulum. These results suggest that the acquisition of independent walking plays a role in the development of anticipatory postural control, likely improving the internal model for the sensorimotor control of posture. However, despite such improvement, integrating the dynamics of an external object, here the platform, within the model to maintain balance still remains challenging in infants.     

Possible functional roles of phase resetting during walking

The walking rhythm is known to show phase shift or "reset" in response to external impulsive perturbations. We tried to elucidate functional roles of the phase reset possibly used for the neural control of locomotion. To this end, a system with a double pendulum as a simplified model of the locomotor control and a model of bipedal locomotion were employed and analyzed in detail. In these models, a movement corresponding to the normal steady-state walking was realized as a stable limit cycle solution of the system. Unexpected external perturbations applied to the system can push the state point of the system away from its limit cycle, either outside or inside the basin of attraction of the limit cycle. Our mathematical analyses of the models suggested functional roles of the phase reset during walking as follows. Function 1: an appropriate amount of the phase reset for a given perturbation can contribute to relocating the system's state point outside the basin of attraction of the limit cycle back to the inside. Function 2: it can also be useful to reduce the convergence time (the time necessary for the state point to return to the limit cycle). In experimental studies during walking of animals and humans, the reset of walking rhythm induced by perturbations was investigated using the phase transition curve (PTC) or the phase resetting curve (PRC) representing phase-dependent responses of the walking. We showed, for the simple double-pendulum model, the existence of the optimal phase control and the corresponding PTC that could optimally realize the aforementioned functions in response to impulsive force perturbations. Moreover, possible forms of PRC that can avoid falling against the force perturbations were predicted by the biped model, and they were compared with the experimentally observed PRC during human walking. Finally, physiological implications of the results were discussed.     

A mathematical modeling study of inter-segmental coordination during stick insect walking

The biomechanical conditions for walking in the stick insect require a modeling approach that is based on the control of pairs of antagonistic motoneuron (MN) pools for each leg joint by independent central pattern generators (CPGs). Each CPG controls a pair of antagonistic MN pools. Furthermore, specific sensory feedback signals play an important role in the control of single leg movement and in the generation of inter-leg coordination or the interplay between both tasks. Currently, however, no mathematical model exists that provides a theoretical approach to understanding the generation of coordinated locomotion in such a multi-legged locomotor system. In the present study, I created such a theoretical model for the stick insect walking system, which describes the MN activity of a single forward stepping middle leg and helps to explain the neuronal mechanisms underlying coordinating information transfer between ipsilateral legs. In this model, CPGs that belong to the same leg, as well as those belonging to different legs, are connected by specific sensory feedback pathways that convey information about movements and forces generated during locomotion. The model emphasizes the importance of sensory feedback, which is used by the central nervous system to enhance weak excitatory and inhibitory synaptic connections from front to rear between the three thorax-coxa-joint CPGs. Thereby the sensory feedback activates caudal pattern generation networks and helps to coordinate leg movements by generating in-phase and out-of-phase thoracic MN activity.