Locomotor kinematics and EMG activity during quadrupedal versus bipedal gait in the Japanese macaque.

Several qualitative features distinguish bipedal from quadrupedal locomotion in mammals. In this study we show quantitative differences between quadrupedal and bipedal gait in the Japanese monkey in terms of gait patterns, trunk/hindlimb kinematics, and electromyographic (EMG) activity, obtained from 3 macaques during treadmill walking. We predicted that as a consequence of an almost upright body axis, bipedal gait would show properties consistent with temporal and spatial optimization countering higher trunk/hindlimb loads and a less stable center of mass (CoM). A comparatively larger step width, an ~9% longer duty cycle, and ~20% increased relative duration of the double-support phase were all in line with such a strategy. Bipedal joint kinematics showed the strongest differences in proximal, and least in distal, hindlimb joint excursions compared with quadrupedal gait. Hindlimb joint coordination (cyclograms) revealed more periods of single-joint rotations during bipedal gait and predominance of proximal joints during single support. The CoM described a symmetrical, quasi-sinusoidal left/right path during bipedal gait, with an alternating shift toward the weight-supporting limb during stance. Trunk/hindlimb EMG activity was nonuniformally increased during bipedal gait, most prominently in proximal antigravity muscles during stance (up to 10-fold). Non-antigravity hindlimb EMG showed altered temporal profiles during liftoff or touchdown. Muscle coactivation was more, but muscle synergies less, frequent during bipedal gait. Together, these results show that behavioral and EMG properties of bipedal vs. quadrupedal gait are quantitatively distinct and suggest that the neural control of bipedal primate locomotion underwent specific adaptations to generate these particular behavioral features to counteract increased load and instability. NEW & NOTEWORTHY Bipedal locomotion imposes particular biomechanical constraints on motor control. In a within-species comparative study, we investigated joint kinematics and electromyographic characteristics of bipedal vs. quadrupedal treadmill locomotion in Japanese macaques. Because these features represent (to a large extent) emergent properties of the underlying neural control, they provide a comparative, behavioral, and neurophysiological framework for understanding the neural system dedicated to bipedal locomotion in this nonhuman primate, which constitutes a critical animal model for human bipedalism.

Evaluation of the Phase-Dependent Rhythm Control of Human Walking Using Phase Response Curves.

Humans and animals control their walking rhythms to maintain motion in a variable environment. The neural mechanism for controlling rhythm has been investigated in many studies using mechanical and electrical stimulation. However, quantitative evaluation of rhythm variation in response to perturbation at various timings has rarely been investigated. Such a characteristic of rhythm is described by the phase response curve (PRC). Dynamical simulations of human skeletal models with changing walking rhythms (phase reset) described a relation between the effective phase reset on stability and PRC, and phase reset around touch-down was shown to improve stability. A PRC of human walking was estimated by pulling the swing leg, but such perturbations hardly influenced the stance leg, so the relation between the PRC and walking events was difficult to discuss. This research thus examines human response to variations in floor velocity. Such perturbation yields another problem, in that the swing leg is indirectly (and weakly) perturbed, so the precision of PRC decreases. To solve this problem, this research adopts the weighted spike-triggered average (WSTA) method. In the WSTA method, a sequential pulsed perturbation is used for stimulation. This is in contrast with the conventional impulse method, which applies an intermittent impulsive perturbation. The WSTA method can be used to analyze responses to a large number of perturbations for each sequence. In the experiment, perturbations are applied to walking subjects by rapidly accelerating and decelerating a treadmill belt, and measured data are analyzed by the WSTA and impulse methods. The PRC obtained by the WSTA method had clear and stable waveforms with a higher temporal resolution than those obtained by the impulse method. By investigation of the rhythm transition for each phase of walking using the obtained PRC, a rhythm change that extends the touch-down and mid-single support phases is found to occur.

Validating the feedback control of intersegmental coordination by fluctuation analysis of disturbed walking.

A walking motion is established by feedforward control for rhythmic locomotion and feedback control for adapting to environmental variations. To identify the control variables that underlie feedback control, uncontrolled manifold (UCM) analysis has been proposed and adopted for analyzing various movements. UCM analysis searches the controlled variables by comparing the fluctuation size of segmental groups related and unrelated to the movement of candidate variables, based on the assumption that a small fluctuation size indicates a relationship with the feedback control. The present study was based on UCM analysis and evaluated fluctuation size to determine the control mechanism for walking. While walking, the subjects were subjected to floor disturbances at two different frequencies, and the fluctuation sizes of the segmental groups related to characteristic variables were calculated and compared. The characteristic variables evaluated were the motion of the center of mass, limb axis, and head, and the intersegmental coordination of segmental groups with simultaneous coupled movements. Results showed that the fluctuations in intersegmental coordination were almost equally small for any segment, while fluctuations in the other variables were large in certain segments. Moreover, a comparison of the fluctuation sizes among the evaluated variables showed that the fluctuation size for intersegmental coordination was the smallest. These results indicate a possible relationship between intersegmental coordination and the control of walking.

Contributions of phase resetting and interlimb coordination to the adaptive control of hindlimb obstacle avoidance during locomotion in rats: a simulation study.

Obstacle avoidance during locomotion is essential for safe, smooth locomotion. Physiological studies regarding muscle synergy have shown that the combination of a small number of basic patterns produces the large part of muscle activities during locomotion and the addition of another pattern explains muscle activities for obstacle avoidance. Furthermore, central pattern generators in the spinal cord are thought to manage the timing to produce such basic patterns. In the present study, we investigated sensory-motor coordination for obstacle avoidance by the hindlimbs of the rat using a neuromusculoskeletal model. We constructed the musculoskeletal part of the model based on empirical anatomical data of the rat and the nervous system model based on the aforementioned physiological findings of central pattern generators and muscle synergy. To verify the dynamic simulation by the constructed model, we compared the simulation results with kinematic and electromyographic data measured during actual locomotion in rats. In addition, we incorporated sensory regulation models based on physiological evidence of phase resetting and interlimb coordination and examined their functional roles in stepping over an obstacle during locomotion. Our results show that the phase regulation based on interlimb coordination contributes to stepping over a higher obstacle and that based on phase resetting contributes to quick recovery after stepping over the obstacle. These results suggest the importance of sensory regulation in generating successful obstacle avoidance during locomotion.

A powered simple walking model explains the decline in propulsive force and hip flexion torque compensation in human gait.

Excessive hip flexion torque to prioritize leg swings in the elderly is likely to be a factor that reduces their propulsive force and gait stability, but the mechanism is not clear. To understand the mechanism, we investigated how propulsive force, hip flexion torque, and margin of stability (MoS) change when only the hip spring stiffness is increased without changing the walking speed in the simple walking model, and verified whether the relationship holds in human walking. The results showed that at walking speeds between 0.50 and 1.75 m/s, increasing hip spring stiffness increased hip flexion torque and decreased the propulsive force and MoS in both the model and human walking. Furthermore, it was found that the increase in hip flexion torque was explained by the increase in spring stiffness, and the decreases in the propulsive force and MoS were explained by the increase in step frequency associated with the increase in spring stiffness. Therefore, the increase in hip flexion torque likely decreased the propulsive force and MoS, and this mechanism was explained by the intervening hip spring stiffness. Our findings may help in the control design of walking assistance devices, and in improving our understanding of elderly walking strategies.

Maneuverable and Efficient Locomotion of a Myriapod Robot with Variable Body-Axis Flexibility via Instability and Bifurcation.

Legged robots have remarkable terrestrial mobility, but are susceptible to falling and leg malfunction during locomotion. The use of a large number of legs, as in centipedes, can overcome these problems, but it makes the body long and leads to many legs being constrained to contact with the ground to support the long body, which impedes maneuverability. A mechanism for maneuverable locomotion using a large number legs is thus desirable. However, controlling a long body with a large number of legs requires huge computational and energy costs. Inspired by agile locomotion in biological systems, this study proposes a control strategy for maneuverable and efficient locomotion of a myriapod robot based on dynamic instability. Specifically, our previous study made the body axis of a 12-legged robot flexible and showed that changing the body-axis flexibility produces pitchfork bifurcation. The bifurcation not only induces the dynamic instability of a straight walk but also a transition to a curved walk, whose curvature is controllable by the body-axis flexibility. This study incorporated a variable stiffness mechanism into the body axis and developed a simple control strategy based on the bifurcation characteristics. With this strategy, maneuverable and autonomous locomotion was achieved, as demonstrated by multiple robot experiments. Our approach does not directly control the movement of the body axis; instead, it controls body-axis flexibility, which significantly reduces computational and energy costs. This study provides a new design principle for maneuverable and efficient locomotion of myriapod robots.

Fore-Aft Asymmetry Improves the Stability of Trotting in the Transverse Plane: A Modeling Study.

Quadrupedal mammals have fore-aft asymmetry in their body structure, which affects their walking and running dynamics. However, the effects of asymmetry, particularly in the transverse plane, remain largely unclear. In this study, we examined the effects of fore-aft asymmetry on quadrupedal trotting in the transverse plane from a dynamic viewpoint using a simple model, which consists of two rigid bodies connected by a torsional joint with a torsional spring and four spring legs. Specifically, we introduced fore-aft asymmetry into the model by changing the physical parameters between the fore and hind parts of the model based on dogs, which have a short neck, and horses, which have a long neck. We numerically searched the periodic solutions for trotting and investigated the obtained solutions and their stability. We found that three types of periodic solutions with different foot patterns appeared that depended on the asymmetry. Additionally, the asymmetry improved gait stability. Our findings improve our understanding of gait dynamics in quadrupeds with fore-aft asymmetry.

Three Characteristics of Cheetah Galloping Improve Running Performance Through Spinal Movement: A Modeling Study.

Cheetahs are the fastest land animal. Their galloping shows three characteristics: small vertical movement of their center of mass, small whole-body pitching movement, and large spine bending movement. We hypothesize that these characteristics lead to enhanced gait performance in cheetahs, including higher gait speed. In this study, we used a simple model with a spine joint and torsional spring, which emulate the body flexibility, to verify our hypothesis from a dynamic perspective. Specifically, we numerically searched periodic solutions and evaluated what extent each solution shows the three characteristics. We then evaluated the gait performance and found that the solutions with the characteristics achieve high performances. This result supports our hypothesis. Furthermore, we revealed the mechanism for the high performances through the dynamics of the spine movement. These findings extend the current understanding of the dynamic mechanisms underlying high-speed locomotion in cheetahs.

Contribution of Phase Resetting to Statistical Persistence in Stride Intervals: A Modeling Study.

Stride intervals in human walking fluctuate from one stride to the next, exhibiting statistical persistence. This statistical property is changed by aging, neural disorders, and experimental interventions. It has been hypothesized that the central nervous system is responsible for the statistical persistence. Human walking is a complex phenomenon generated through the dynamic interactions between the central nervous system and the biomechanical system. It has also been hypothesized that the statistical persistence emerges through the dynamic interactions during walking. In particular, a previous study integrated a biomechanical model composed of seven rigid links with a central pattern generator (CPG) model, which incorporated a phase resetting mechanism as sensory feedback as well as feedforward, trajectory tracking, and intermittent feedback controllers, and suggested that phase resetting contributes to the statistical persistence in stride intervals. However, the essential mechanisms remain largely unclear due to the complexity of the neuromechanical model. In this study, we reproduced the statistical persistence in stride intervals using a simplified neuromechanical model composed of a simple compass-type biomechanical model and a simple CPG model that incorporates only phase resetting and a feedforward controller. A lack of phase resetting induced a loss of statistical persistence, as observed for aging, neural disorders, and experimental interventions. These mechanisms were clarified based on the phase response characteristics of our model. These findings provide useful insight into the mechanisms responsible for the statistical persistence of stride intervals in human walking.

Center of Mass Offset Enhances the Selection of Transverse Gallop in High-Speed Running by Horses: A Modeling Study.

Horses use the transverse gallop in high-speed running. However, different animals use different gaits, and the gait preference of horses remains largely unclear. Horses have fore-aft asymmetry in their body structure and their center of mass (CoM) is anteriorly located far from the center of the body. Since such a CoM offset affects the running dynamics, we hypothesize that the CoM offset of horses is important in gait selection. In order to verify our hypothesis and clarify the gait selection mechanisms by horses from a dynamic viewpoint, we developed a simple model with CoM offset and investigated its effects on running. Specifically, we numerically obtained periodic solutions and classified these solutions into six types of gaits, including the transverse gallop, based on the footfall pattern. Our results show that the transverse gallop is optimal when the CoM offset is located at the position estimated in horses. Our findings provide useful insight into the gait selection mechanisms in high-speed running of horses.

Contribution of Afferent Feedback to Adaptive Hindlimb Walking in Cats: A Neuromusculoskeletal Modeling Study.

Mammalian locomotion is generated by central pattern generators (CPGs) in the spinal cord, which produce alternating flexor and extensor activities controlling the locomotor movements of each limb. Afferent feedback signals from the limbs are integrated by the CPGs to provide adaptive control of locomotion. Responses of CPG-generated neural activity to afferent feedback stimulation have been previously studied during fictive locomotion in immobilized cats. Yet, locomotion in awake, behaving animals involves dynamic interactions between central neuronal circuits, afferent feedback, musculoskeletal system, and environment. To study these complex interactions, we developed a model simulating interactions between a half-center CPG and the musculoskeletal system of a cat hindlimb. Then, we analyzed the role of afferent feedback in the locomotor adaptation from a dynamic viewpoint using the methods of dynamical systems theory and nullcline analysis. Our model reproduced limb movements during regular cat walking as well as adaptive changes of these movements when the foot steps into a hole. The model generates important insights into the mechanism for adaptive locomotion resulting from dynamic interactions between the CPG-based neural circuits, the musculoskeletal system, and the environment.

Forward dynamic simulation of bipedal walking in the Japanese macaque: investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate.

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.

Generation of Direct-, Retrograde-, and Source-Wave Gaits in Multi-Legged Locomotion in a Decentralized Manner via Embodied Sensorimotor Interaction.

Multi-legged animals show several types of ipsilateral interlimb coordination. Millipedes use a direct-wave gait, in which the swing leg movements propagate from posterior to anterior. In contrast, centipedes use a retrograde-wave gait, in which the swing leg movements propagate from anterior to posterior. Interestingly, when millipedes walk in a specific way, both direct and retrograde waves of the swing leg movements appear with the waves' source, which we call the source-wave gait. However, the gait generation mechanism is still unclear because of the complex nature of the interaction between neural control and dynamic body systems. The present study used a simple model to understand the mechanism better, primarily how local sensory feedback affects multi-legged locomotion. The model comprises a multi-legged body and its locomotion control system using biologically inspired oscillators with local sensory feedback, phase resetting. Each oscillator controls each leg independently. Our simulation produced the above three types of animal gaits. These gaits are not predesigned but emerge through the interaction between the neural control and dynamic body systems through sensory feedback (embodied sensorimotor interaction) in a decentralized manner. The analytical description of these gaits' solution and stability clarifies the embodied sensorimotor interaction's functional roles in the interlimb coordination.

Fast and Slow Adaptations of Interlimb Coordination via Reflex and Learning During Split-Belt Treadmill Walking of a Quadruped Robot.

Interlimb coordination plays an important role in adaptive locomotion of humans and animals. This has been investigated using a split-belt treadmill, which imposes different speeds on the two sides of the body. Two types of adaptation have been identified, namely fast and slow adaptations. Fast adaptation induces asymmetric interlimb coordination soon after a change of the treadmill speed condition from same speed for both belts to different speeds. In contrast, slow adaptation slowly reduces the asymmetry after fast adaptation. It has been suggested that these adaptations are primarily achieved by the spinal reflex and cerebellar learning. However, these adaptation mechanisms remain unclear due to the complicated dynamics of locomotion. In our previous work, we developed a locomotion control system for a biped robot based on the spinal reflex and cerebellar learning. We reproduced the fast and slow adaptations observed in humans during split-belt treadmill walking of the biped robot and clarified the adaptation mechanisms from a dynamic viewpoint by focusing on the changes in the relative positions between the center of mass and foot stance induced by reflex and learning. In this study, we modified the control system for application to a quadruped robot. We demonstrate that even though the basic gait pattern of our robot is different from that of general quadrupeds (due to limitations of the robot experiment), fast and slow adaptations that are similar to those of quadrupeds appear during split-belt treadmill walking of the quadruped robot. Furthermore, we clarify these adaptation mechanisms from a dynamic viewpoint, as done in our previous work. These results will increase the understanding of how fast and slow adaptations are generated in quadrupedal locomotion on a split-belt treadmill through body dynamics and sensorimotor integration via the spinal reflex and cerebellar learning and help the development of control strategies for adaptive locomotion of quadruped robots.

Quantitative evaluation of posture control in rats with inferior olive lesions.

Impairment of inferior olivary neurons (IONs) affects whole-body movements and results in abnormal gait and posture. Because IONs are activated by unpredicted motion rather than regular body movements, the postural dysfunction caused by ION lesions is expected to involve factors other than simple loss of feedback control. In this study, we measured the postural movements of rats with pharmacological ION lesions (IO rats) trained to stand on their hindlimbs. The coordination of body segments as well as the distribution and frequency characteristics of center of mass (COM) motion were analyzed. We determined that the lesion altered the peak properties of the power spectrum density of the COM, whereas changes in coordination and COM distribution were minor. To investigate how the observed properties reflected changes in the control system, we constructed a mathematical model of the standing rats and quantitatively identified the control system. We found an increase in linear proportional control and a decrease in differential and nonlinear control in IO rats compared with intact rats. The dystonia-like changes in body stiffness explain the nature of the linear proportional and differential control, and a disorder in the internal model is one possible cause of the decrease in nonlinear control.

Dynamical determinants enabling two different types of flight in cheetah gallop to enhance speed through spine movement.

Cheetahs use a galloping gait in their fastest speed range. It has been reported that cheetahs achieve high-speed galloping by performing two types of flight through spine movement (gathered and extended). However, the dynamic factors that enable cheetahs to incorporate two types of flight while galloping remain unclear. To elucidate this issue from a dynamical viewpoint, we developed a simple analytical model. We derived possible periodic solutions with two different flight types (like cheetah galloping), and others with only one flight type (unlike cheetah galloping). The periodic solutions provided two criteria to determine the flight type, related to the position and magnitude of ground reaction forces entering the body. The periodic solutions and criteria were verified using measured cheetah data, and provided a dynamical mechanism by which galloping with two flight types enhances speed. These findings extend current understanding of the dynamical mechanisms underlying high-speed locomotion in cheetahs.

Variant and invariant patterns embedded in human locomotion through whole body kinematic coordination.

Step length, cadence and joint flexion all increase in response to increases in gradient and walking speed. However, the tuning strategy leading to these changes has not been elucidated. One characteristic of joint variation that occurs during walking is the close relationship among the joints. This property reduces the number of degrees of freedom and seems to be a key issue in discussing the tuning strategy. This correlation has been analyzed for the lower limbs, but the relation between the trunk and lower body is generally ignored. Two questions about posture during walking are discussed in this paper: (1) whether there is a low-dimensional restriction that determines walking posture, which depends not just on the lower limbs but on the whole body, including the trunk and (2) whether some simple rules appear in different walking conditions. To investigate the correlation, singular value decomposition was applied to a measured walking pattern. This showed that the whole movement can be described by a closed loop on a two-dimensional plane in joint space. Furthermore, by investigating the effect of the walking condition on the decomposed patterns, the position and the tilt of the constraint plane was found to change significantly, while the loop pattern on the constraint plane was shown to be robust. This result indicates that humans select only certain kinematic characteristics for adapting to various walking conditions.

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.

Body torsional flexibility effects on stability during trotting and pacing based on a simple analytical model.

Quadruped animals use not only their legs but also their trunks during walking and running. Although many previous studies have investigated the flexion, extension, and lateral bending of the trunk, few studies have investigated the body torsion, and its dynamic effects on locomotion thus remain unclear. In this study, we investigated the effects of body torsion on gait stability during trotting and pacing. Specifically, we constructed a simple model consisting of two rigid bodies connected via a torsional joint that has a torsional spring and four leg springs. We then derived periodic solutions for trotting and pacing and evaluated the stabilities of these motion types using a Poincaré map. We found that the moments of inertia of the bodies and the spring constant ratio of the torsional spring and the leg springs determine the stability of these periodic solutions. We then determined the stability conditions for these parameters and elucidated the relevant mechanisms. In addition, we clarified the importance of the body torsion to the gait stability by comparison with a rigid model. Finally, we analyzed the biological relevance of our findings and provided a design principle for development of quadruped robots.

Fractal mechanism of basin of attraction in passive dynamic walking.

Passive dynamic walking is a model that walks down a shallow slope without any control or input. This model has been widely used to investigate how humans walk with low energy consumption and provides design principles for energy-efficient biped robots. However, the basin of attraction is very small and thin and has a fractal-like complicated shape, which makes producing stable walking difficult. In our previous study, we used the simplest walking model and investigated the fractal-like basin of attraction based on dynamical systems theory by focusing on the hybrid dynamics of the model composed of the continuous dynamics with saddle hyperbolicity and the discontinuous dynamics caused by the impact upon foot contact. We clarified that the fractal-like basin of attraction is generated through iterative stretching and bending deformations of the domain of the Poincaré map by sequential inverse images. However, whether the fractal-like basin of attraction is actually fractal, i.e., whether infinitely many self-similar patterns are embedded in the basin of attraction, is dependent on the slope angle, and the mechanism remains unclear. In the present study, we improved our previous analysis in order to clarify this mechanism. In particular, we newly focused on the range of the Poincaré map and specified the regions that are stretched and bent by the sequential inverse images of the Poincaré map. Through the analysis of the specified regions, we clarified the conditions and mechanism required for the basin of attraction to be fractal.