Walking-like Movement Research Articles

Feedback equivalence of the chained mechanical system to the almost linear form and its use for the sustainable multi-step walking design

The main theoretical novelty of this paper is the state and feedback equivalence of the underactuated 4-degrees of freedom planar walking-like mechanical chain system with 3 actuators to its 8-dimensional almost linear form with 3 virtual inputs. Moreover, the only residual nonlinearity vanishes on the 4-dimensional linear subspace being forward invariant when 2 of 3 virtual inputs are set to be zero. Dynamics inside that subsystem is actually the chain of 4 integrators fed by the remaining single virtual input and it can be interpreted as a rich variety of synchronous movements of torsos and legs. In such a way, the seemingly abstract and purely theoretical result can be used to design the walking-like movement during the single-support phase. The impact effect during the impulsive-like double-support phase is then attenuated by further special trajectories tuning and finite-time stabilization technique which provides the sustainable multi-step walking design. Moreover, the target walking-like trajectory is attracted by nearby trajectories. This further justify the importance and usefulness of the mentioned state and feedback equivalence. Its viability is further demonstrated by the simulations of various scenarios of the walking-like movement and the respective torsos behaviors.

Activation of human spinal locomotor circuitry using transvertebral magnetic stimulation.

Transvertebral magnetic stimulation (TVMS) of the human lumbar spinal cord can evoke bilateral rhythmic leg movements, as in walking, supposedly through the activation of spinal locomotor neural circuitry. However, an appropriate stimulus intensity that can effectively drive the human spinal locomotor circuitry to evoke walking-like movements has not been determined. To address this issue, TVMS was delivered over an intervertebral space of the lumbar cord (L1–L3) at different stimulus intensities (10–70% of maximum stimulator output) in healthy human adults. In a stimulus intensity-dependent manner, TVMS evoked two major patterns of rhythmic leg movements in which the left-right movement cycles were coordinated with different phase relationships: hopping-like movements, in which both legs moved in the same direction in phase, and walking-like movements, in which both legs moved alternatively in anti-phase; uncategorized movements were also observed which could not be categorized as either movement type. Even at the same stimulation site, the stimulus-evoked rhythmic movements changed from hopping-like movements to walking-like movements as stimulus intensity was increased. Different leg muscle activation patterns were engaged in the induction of the hopping- and walking-like movements. The magnitude of the evoked hopping- and walking-like movements was positively correlated with stimulus intensity. The human spinal neural circuitry required a higher intensity of magnetic stimulation to produce walking-like leg movements than to produce hopping-like movements. These results suggest that TVMS activates distinct neural modules in the human spinal cord to generate hopping- and walking-like movements.

A Step Forward: Functional Diversity and Emerging Themes of Slow-Speed Locomotion in Vertebrates.

Walking can be defined broadly as a slow-speed movement produced when appendages interact with the ground to generate forward propulsion. Until recently, most studies of walking have focused on humans and a handful of domesticated vertebrates moving at a steady rate over highly simplified, static surfaces, which may bias our understanding of the unifying principles that underlie vertebrate locomotion. In the last few decades, studies have expanded to include a range of environmental contexts (e.g., uneven terrain, perturbations, deformable substrates) and greater phylogenetic breadth (e.g., non-domesticated species, small and/or ectothermic tetrapods and fishes); these studies have revealed that even a gait as superficially simple as walking is far more complex than previously thought. In addition, technological advances and accessibility of imaging systems and computational power have recently expanded our capabilities to test hypotheses about the locomotor movements of extant and extinct organisms in silico. In this symposium, scientists showcased diverse taxa (from extant fishes to extinct dinosaurs) moving through a range of variable conditions (speed perturbations, inclines, and deformable substrates) to address the causes and consequences of functional diversity in locomotor systems and discuss nascent research areas and techniques. From the symposium contributions, several themes emerged: (1) slow-speed, appendage-based movements in fishes are best described as walking-like movements rather than true walking gaits, (2) environmental variation (e.g., deformable substrates) and dynamic stimuli (e.g., perturbations) trigger kinematic and neuromuscular changes in animals that make defining a single gait or the transition between gaits more complicated than originally thought, and (3) computational advances have increased the ability to process large data sets, emulate the 3D motions of extant and extinct taxa, and even model species interactions in ancient ecosystems. Although this symposium allowed us to make great strides forward in our understanding of vertebrate walking, much ground remains to be covered. First, there is a much greater range of vertebrate appendage-based locomotor behaviors than has been previously recognized and existing terminology fails to accurately capture and describe this diversity. Second, despite recent efforts, the mechanisms that vertebrates use modify locomotor behaviors in response to predictable and unpredictable locomotor challenges are still poorly understood. Third, while computer-based models and simulations facilitate a greater understanding of the kinetics and kinematics of movement in both extant and extinct animals, a universal, one-size-fits-all, predictive model of appendage-based movement in vertebrates remains elusive.

Development of an Improved Rotational Orthosis for Walking With Arm Swing and Active Ankle Control.

Based on interlimb neural coupling, gait robotic systems should produce walking-like movement in both upper and lower limbs for effective walking restoration. Two orthoses were previously designed in our lab to provide passive walking with arm swing. However, an active system for walking with arm swing is desirable to serve as a testbed for investigation of interlimb neural coupling in response to voluntary input. Given the important function of the ankle joint during normal walking, this work aimed to develop an improved rotational orthosis for walking with arm swing, which is called ROWAS II, and especially to develop and evaluate the algorithms for active ankle control. After description of the mechanical structure and control schemes of the overall ROWAS II system, the closed-loop position control and adjustable admittance control algorithms were firstly deduced, then simulated in Matlab/Simulink and finally implemented in the ROWAS II system. Six able-bodied participants were recruited to use the ROWAS II system in passive mode, and then to estimate the active ankle mechanism. It was showed that the closed-loop position control algorithms enabled the ROWAS II system to track the target arm-leg walking movement patterns well in passive mode, with the tracking error of each joint <0.7°. The adjustable admittance control algorithms enabled the participants to voluntarily adjust the ankle movement by exerting various active force. Higher admittance gains enabled the participants to more easily adjust the movement trajectory of the ankle mechanism. The ROWAS II system is technically feasible to produce walking-like movement in the bilateral upper and lower limbs in passive mode, and the ankle mechanism has technical potential to provide various active ankle training during gait rehabilitation. This novel ROWAS II system can serve as a testbed for further investigation of interlimb neural coupling in response to voluntary ankle movement and is technically feasible to provide a new training paradigm of walking with arm swing and active ankle control.

Stable walking gaits for a three-link planar biped robot with two actuators based on the collocated virtual holonomic constraints and the cyclic unactuated variable

Abstract Paper presents the current state of the laboratory model of the planar walking robot built in laboratory in UTIA. Moreover, it presents simulation results of the walkinglike movement of the simplified version - the so-called three-link, alternatively also called Acrobot with torso. Method for the walking design is based on the use of the collocated virtual holonomic constraints. Collocated constraints include the directly actuated variables only. Restricted system then conserves cyclic property of the unactuated variable and can be controlled using its three dimensional exact feedback linearization.

Hybrid invariance of the collocated virtual holonomic constraints and its application in underactuated walking

Abstract: The hybrid invariance of the collocated virtual holonomic constraints for general underactuated mechanical systems is studied here. The collocated virtual holonomic constraints involve directly actuated coordinates only and they preserve the kinetic symmetry and the Lagrangian character of the corresponding restricted dynamics. Their hybrid invariance can be combined with the walking design during the swing phase based on the kinetic symmetry to achieve the exponential stable multi-step walking. Results are illustrated by the case study of the planar four link mechanical chain and its walking-like movement.

Activation of NMDA receptors is required for the initiation and maintenance of walking-like activity in the mudpuppy (Necturus Maculatus)

We hypothesized that blocking the activation of N-methyl-D-aspartate (NMDA) receptors prevents the initiation of walking-like activity and abolishes the ongoing rhythmic activity in the spinal cord-forelimb preparation from the mudpuppy. Robust walking-like movements of the limb and rhythmic alternating elbow flexor-extensor EMG pattern characteristic of walking were elicited when continuous perfusion of the spinal cord with solution containing D-glutamate. The frequency of the walking-like activity was dose-dependent on the concentration of D-glutamate in the bath over a range of 0.2 to 0.9 mmol/L. Elevation of potassium concentrations failed to induce walking-like activity. Application of the selective antagonist 2-amino-5-phosphonovalerate (AP-5) produced dose-dependent block of the initiation and maintenance of walking-like activity induced by D-glutamate. Complete block of the activity was achieved when the concentration of AP-5 reached 20 micromol/L. Furthermore, application of L-701,324 (a selective antagonist of the strychnine-insensitive glycine site of NMDA receptor) (1-10 micromol/L) also resulted in complete block of the walking-like activity. In contrast, application of the non-NMDA receptor antagonist 6-cyno-7-nitroquinoxaline-2,3-dione (CNQX) (1-50 micromol/L) induced a dose-dependent inhibition of the burst frequency but failed to result in a complete block. Only at concentration as high as 100 micromol/L, did CNQX cause complete block of the rhythmic activity, presumably through nonspecific action on the strychnine-insensitive glycine site of NMDA receptors. These results suggest that activation of NMDA receptors is required for the initiation and maintenance of walking-like activity. Operation of non-NMDA receptors plays a powerful role in the modulation of the walking-like activity in the mudpuppy.

Control of flexor motoneuron activity during single leg walking of the stick insect on an electronically controlled treadwheel.

In the present study, motoneurons innervating the flexor tibiae muscle of the stick insect (Cuniculina impigra) middle leg were recorded intracellularly while the single leg performed walking-like movements on a treadwheel. Different levels of belt friction (equivalent to a change in load) were used to study the control of activity of flexor motoneurons. During slow leg movements no fast motoneurons were active, but a recruitment of these neurons could be observed during faster leg movements. The firing rate of slow and fast motoneurons increased with incremented belt friction. Also, the force applied to the treadwheel at different frictional levels was adapted closely to the friction of the treadwheel to be overcome. The motoneurons innervating the flexor tibiae were recruited progressively during the stance phase, with the slow motoneurons being active earlier than the fast (half-maximal spike frequency after 10-15% and 50-60% of the stance phase, respectively). The resting membrane potential was more hyperpolarized in fast motoneurons (64.6 +/- 6.5 mV) than in slow motoneurons (-52.9 +/- 5.4 mV). However, the threshold for the initiation of action potentials was not statistically significantly different in both types of flexor motoneurons. Therefore, action potentials were generated in fast motoneurons after a longer period of depolarization and thus later during the stance phase than in slow motoneurons. We show that motoneurons of the flexor tibiae receive substantial common excitatory inputs during the stance phase and that the difference in resting membrane potential between slow and fast motoneurons is likely to play a crucial role in their consecutive recruitment.

Differential distribution of interneurons in the neural networks that control walking in the mudpuppy (Necturus maculatus) spinal cord.

Locomotor behavior is believed to be produced by interneuronal networks that are intrinsically organized to generate the underlying complex spatiotemporal patterns. In order to study the temporal correlation between the firing of individual interneurons and the pattern of locomotion, we utilized the spinal cord-forelimb preparation from the mudpuppy, in which electrophysiological recordings of neuronal activity were achieved during walking-like movement of the forelimb induced by bath application of N-methyl- D-aspartate (NMDA). Intra- and extracellular recordings were made in the C2 and C3 segments of the spinal cord. These segments contain independent flexor and extensor centers for the forelimb movement about the elbow joint during walking. Among the 289 cells recorded in the intermediate gray matter (an area between the ventral and dorsal horns) of the C2 and C3 segments, approximately 40% of the cells fired rhythmically during "walking." The firing rates were 6.4+/-0.4 impulses/s (mean +/- SE). These rhythmically active cells were classified into four types based on their phase of activity during a normalized step cycle. About half the rhythmic cells fired in phase with either the flexor (F) or extensor (E) motoneurons. The rest fired in the transitions between the two phases (F-->E and E-->F). Longitudinal distributions of the four types of interneurons along the spinal cord were in agreement with observations that revealed distinct but overlapping flexor and extensor centers for walking. Some cells triggered short-latency responses in the elbow flexor or extensor muscles and may be last-order interneurons. These observations suggest that there is a differential distribution of phase-specific interneurons in the central pattern generator of the mudpuppy spinal cord for walking.

Pattern generation for walking and searching movements of a stick insect leg. II. Control of motoneuronal activity.

In the stick insect, Cuniculina impigra, intracellular recordings from mesothoracic motoneurons that control flexion and extension of the tibia and depression and levation of the trochantero-femur were made while the leg performed walking-like movements on a treadband or stereotyped rhythmic searching movements. We were interested in how synaptic input and intrinsic properties contribute to form the activity pattern of motoneurons during rhythmic leg movements without sensory feedback from other legs. During searching and walking, motoneurons expressed a rhythmic bursting pattern that was formed by a depolarizing input followed by a hyperpolarizing input in the inter-burst interval. This basic pattern was similar in all fast, semi-fast, and slow motoneurons that were recorded. Hyperpolarizations were in synchrony with activity in the antagonistic motoneurons. De- and hyperpolarizations were associated with a decrease in input resistance. All motoneurons showed spike frequency adaptation when depolarized by current injection to a membrane potential similar to that observed during walking. In the hyperpolarizing phase of fast flexor motoneurons, the initial maximum hyperpolarization was followed by a sag in potential toward more depolarized values. Consistent with this observation, only fast flexor motoneurons developed a depolarizing sag potential when hyperpolarized by injection of constant negative current.

Specific characteristics of speed skating

Fourteen well-trained speed skaters performed all-out exercise tests during ice speed skating, low walking (walking-like movement in skating position), and dry skating (side to side deep sitting push-offs). These dry land training activities, widely used by speed skaters during the summer period, are compared to speed skating in relation to the concept of training specificity. Relevant physiological and biomechanical variables (derived from film and video analysis) were measured. The maximal oxygen uptake achieved in low walking (60.0 +/- 5.8 ml.kg-1.min-1) was not significantly different to that achieved during speed skating (62.1 +/- 6.9), but the maximal level attained in dry skating (48.4 +/- 5.5) was significantly less than both of these. The biomechanical differences measured are substantial. The forward directed push-off, the more dynamic movement pattern in hip and knee joints, and the use of plantar flexors during low walking are essentially different from speed skating. In dry skating, a more convulsive movement pattern due to the fixed push-off position compared to speed skating was found. The consequences of the typical skating position on the physiological responses is discussed. It is concluded that neither low walking nor dry skating can be considered as specific training activities for speed skaters.

Development and characteristics of airstepping in chronic spinal cats

Airstepping, walking-like movements of the hindlimbs, is a commonly observed behavior in chronic spinal animals when they are held vertically. The purpose of this study was to: describe the development of airstepping after spinalization and compare it to the onset of segmental reflexes, characterize the EMG pattern of muscle activity during spontaneous airstepping, and examine the effects of sensory perturbation on the characteristic pattern. Airstepping was analyzed during three conditions of tonic sensory perturbation which included: tail pinching, tape applied to one hindpaw, and immobilization of the ankle and knee in a plaster cast. Seven adult cats were spinalized at T-12, and bipolar electrode wires were surgically implanted in selected hindlimb muscles at the hip, knee, and ankle. Testing began within 48 hr of transection. Segmental reflexes and paw-shake responses were present in the first week; however, the earliest observed airstepping occurred during tail pinching at 2 weeks after surgery, and the average onset of spontaneous airstepping (without exteroceptive stimuli) was at 33 days. The average cycle period of spontaneous airstepping (691 msec) was comparable to the shortest periods reported for fictive rhythms and to treadmill walking between 1 and 2 m/sec. Intralimb coordination was characterized by flexor and extensor synergies typical of locomotion, while interlimb coordination was characterized by alternating cycles similar to that reported for treadmill walking and fictive locomotion. Neither intralimb nor interlimb patterns of coordination were altered by conditions of sensory perturbation, although cycle period and EMG recruitment level were variable. Many characteristics of airstepping are similar to those of treadmill and fictive locomotion.(ABSTRACT TRUNCATED AT 250 WORDS)