Nozomi Tomita

A stability-based mechanism for hysteresis in the walk-trot transition in quadruped locomotion.

Quadrupeds vary their gaits in accordance with their locomotion speed. Such gait transitions exhibit hysteresis. However, the underlying mechanism for this hysteresis remains largely unclear. It has been suggested that gaits correspond to attractors in their dynamics and that gait transitions are non-equilibrium phase transitions that are accompanied by a loss in stability. In the present study, we used a robotic platform to investigate the dynamic stability of gaits and to clarify the hysteresis mechanism in the walk–trot transition of quadrupeds. Specifically, we used a quadruped robot as the body mechanical model and an oscillator network for the nervous system model to emulate dynamic locomotion of a quadruped. Experiments using this robot revealed that dynamic interactions among the robot mechanical system, the oscillator network, and the environment generate walk and trot gaits depending on the locomotion speed. In addition, a walk–trot transition that exhibited hysteresis was observed when the locomotion speed was changed. We evaluated the gait changes of the robot by measuring the locomotion of dogs. Furthermore, we investigated the stability structure during the gait transition of the robot by constructing a potential function from the return map of the relative phase of the legs and clarified the physical characteristics inherent to the gait transition in terms of the dynamics.

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.

Adaptation mechanism of interlimb coordination in human split-belt treadmill walking through learning of foot contact timing: a robotics study

Human walking behaviour adaptation strategies have previously been examined using split-belt treadmills, which have two parallel independently controlled belts. In such human split-belt treadmill walking, two types of adaptations have been identified: early and late. Early-type adaptations appear as rapid changes in interlimb and intralimb coordination activities when the belt speeds of the treadmill change between tied (same speed for both belts) and split-belt (different speeds for each belt) configurations. By contrast, late-type adaptations occur after the early-type adaptations as a gradual change and only involve interlimb coordination. Furthermore, interlimb coordination shows after-effects that are related to these adaptations. It has been suggested that these adaptations are governed primarily by the spinal cord and cerebellum, but the underlying mechanism remains unclear. Because various physiological findings suggest that foot contact timing is crucial to adaptive locomotion, this paper reports on the development of a two-layered control model for walking composed of spinal and cerebellar models, and on its use as the focus of our control model. The spinal model generates rhythmic motor commands using an oscillator network based on a central pattern generator and modulates the commands formulated in immediate response to foot contact, while the cerebellar model modifies motor commands through learning based on error information related to differences between the predicted and actual foot contact timings of each leg. We investigated adaptive behaviour and its mechanism by split-belt treadmill walking experiments using both computer simulations and an experimental bipedal robot. Our results showed that the robot exhibited rapid changes in interlimb and intralimb coordination that were similar to the early-type adaptations observed in humans. In addition, despite the lack of direct interlimb coordination control, gradual changes and after-effects in the interlimb coordination appeared in a manner that was similar to the late-type adaptations and after-effects observed in humans. The adaptation results of the robot were then evaluated in comparison with human split-belt treadmill walking, and the adaptation mechanism was clarified from a dynamic viewpoint.

Adaptive splitbelt treadmill walking of a biped robot using nonlinear oscillators with phase resetting

To investigate the adaptability of a biped robot controlled by nonlinear oscillators with phase resetting based on central pattern generators, we examined the walking behavior of a biped robot on a splitbelt treadmill that has two parallel belts controlled independently. In an experiment, we demonstrated the dynamic interactions among the robot mechanical system, the oscillator control system, and the environment. The robot produced stable walking on the splitbelt treadmill at various belt speeds without changing the control strategy and parameters, despite a large discrepancy between the belt speeds. This is due to modulation of the locomotor rhythm and its phase through the phase resetting mechanism, which induces the relative phase between leg movements to shift from antiphase, and causes the duty factors to be autonomously modulated depending on the speed discrepancy between the belts. Such shifts of the relative phase and modulations of the duty factors are observed during human splitbelt treadmill walking. Clarifying the mechanisms producing such adaptive splitbelt treadmill walking will lead to a better understanding of the phase resetting mechanism in the generation of adaptive locomotion in biological systems and consequently to a guiding principle for designing control systems for legged robots.

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.

Smooth enlargement of human standing sway by instability due to weak reaction floor and noise

Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predicted to exhibit bifurcation. The presence of stability-dependent transition enables dynamic reaction that depends on the stability of the environment, and can explain the change in sway characteristics that accompanies some neurological disorders. This research analyses the characteristics of a system model that induces transition, and discusses whether human standing reflects such a mechanism. In mathematical analysis of system models, (intermittent control-like) nonlinear control with integral control is shown to exhibit Hopf bifurcation. Moreover, from the analytical solution of the system model with noise, noise is shown to work to smooth the enlargement of sway around the bifurcation point. This solution is compared with measured human standing sway on floors with different stabilities. By quantitatively comparing the control parameters between human observation and model prediction, enlargement of sway is shown to appear as predicted by the model analysis.

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.

Dynamical analysis of human standing model with cyclic motion

Human standing is characterized by large body sway, which cannot be explained by linear control. In past researches, sway has been considered as an uncontrolled biological noise. In contrast, we consider the sway to be a cyclic motion generated by continuous proportional-integral-derivative (PID) control with weak nonlinearlity. Through mathematical analysis of nonliner PID control, cyclic motion is shown to be generated by a stability-gain dependent Hopf bifurcation, and biological noise is shown to help the smooth transition between stationary stable state and cyclic state. The relevance of the proposed sway generation mechanism is verified through human experiment on floors with different stability. As a result, the existence of Hopf bifurcation, i.e., apparent expansion of sway with small decrease of control parameters, realized by the destabilization of floor, is observed.

Kinematic analysis of low dimensional structure in walking and running

Humans walk and run at various speeds by coordinating their whole-body movements skillfully, where they regulate the movements in accordance with the speed. However, it remains unclear what kinds of locomotion parameters they regulate and how to regulate the parameters. In the present study, to clarify the human strategy for regulating the whole-body movements in accordance with the speed, we measured human joint angles on sagittal plane during walking and running and analyzed the measured data by extracting low dimensional structure of the joint movements using singular value decomposition. Our results suggest a formation mechanism of human gaits, which contributes to elucidating the adaptation mechanism of human locomotion.

Hindlimb splitbelt treadmill walking of a rat based on a neuromusculoskeletal model

In this study, we conducted computer simulation of splitbelt treadmill walking by the hindlimbs of a rat based on a neuromusculoskeletal model. We developed the skeletal model based on anatomical data and constructed the nervous system model for locomotion based on the physiological findings of muscle synergy, central pattern generator, and sensory regulation by phase resetting. Our simulation results show that even in asymmetric environment due to the speed discrepancy between the left and right belts of a splitbelt treadmill, the rat model produced stable walking. The sensory regulation model contributed to generation of adaptive splitbelt treadmill walking while inducing the modulation of locomotion parameters, such as relative phase between the legs and duty factors, as observed in splitbelt treadmill walking of humans and animals. This helps understanding of the adaptation mechanism in locomotion through dynamic interactions among the nervous system, the musculoskeletal system, and the environment.