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

Functional Roles of Phase Resetting in the Gait Transition of a Biped Robot From Quadrupedal to Bipedal Locomotion

Although physiological studies have shown evidence of phase resetting during fictive locomotion, the functional roles of phase resetting in actual locomotion remain largely unclear. In this paper, we have constructed a control system for a biped robot based on physiological findings and investigated the functional roles of phase resetting in the gait transition from quadrupedal to bipedal locomotion by numerical simulations and experiments. So far, although many studies have investigated methods to achieve stable locomotor behaviors for various gait patterns of legged robots, their transitions have not been thoroughly examined. Especially, the gait transition from quadrupedal to bipedal requires drastic changes in the robot posture and the reduction of the number of supporting limbs, and therefore, the stability greatly changes during the transition. Thus, this transition poses a challenging task. We constructed a locomotion control system using an oscillator network model based on a two-layer hierarchical network model of a central pattern generator while incorporating the phase resetting mechanism and created robot motions for the gait transition based on the physiological concept of synergies. Our results, which demonstrate that phase resetting increases the robustness in gait transition, will contribute to the understanding of the phase resetting mechanism in biological systems and lead to a guiding principle to design control systems for legged robots

Hysteresis in the metachronal-tripod gait transition of insects: A modeling study

Locomotion in biological systems involves various gaits, and hysteresis appears when the gaits change in accordance with the locomotion speed. That is, the gaits vary at different locomotion speeds depending on the direction of speed change. Although hysteresis is a typical characteristic of nonlinear dynamic systems, the underlying mechanism for the hysteresis in gait transitions remains largely unclear. In this study, we construct a neuromechanical model of an insect and investigate the dynamic characteristics of its gait and gait transition. The simulation results show that our insect model produces metachronal and tripod gaits depending on the locomotion speed through dynamic interactions among the body mechanical system, the nervous system, and the environment in a self-organized manner. They also show that it undergoes the metachronal-tripod gait transition with hysteresis by changing the locomotion speed. We examined the hysteresis mechanism in the metachronal-tripod gait transition of insects 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

Phase-dependent response to afferent stimulation during fictive locomotion: a computational modeling study

Central pattern generators (CPGs) in the spinal cord generate rhythmic neural activity and control locomotion in vertebrates. These CPGs operate under the control of sensory feedback that affects the generated locomotor pattern and adapt it to the animal's biomechanics and environment. Studies of the effects of afferent stimulation on fictive locomotion in immobilized cats have shown that brief stimulation of peripheral nerves can reset the ongoing locomotor rhythm. Depending on the phase of stimulation and the stimulated nerve, the applied stimulation can either shorten or prolong the current locomotor phase and the locomotor cycle. Here, we used a mathematical model of a half-center CPG to investigate the phase-dependent effects of brief stimulation applied to CPG on the CPG-generated locomotor oscillations. The CPG in the model consisted of two half-centers mutually inhibiting each other. The rhythmic activity in each half-center was based on a slowly inactivating, persistent sodium current. Brief stimulation was applied to CPG half-centers in different phases of the locomotor cycle to produce phase-dependent changes in CPG activity. The model reproduced several results from experiments on the effect of afferent stimulation of fictive locomotion in cats. The mechanisms of locomotor rhythm resetting under different conditions were analyzed using dynamic systems theory methods

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

Advanced turning maneuver of a multi-legged robot using pitchfork bifurcation

Legged robots have excellent terrestrial mobility for traversing diverse environments and thus have the potential to be deployed in a wide variety of scenarios. However, they are susceptible to falling and leg malfunction during locomotion. Although the use of a large number of legs can overcome these problems, 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. To improve the locomotion maneuverability of such robots, the present study focuses on dynamic instability, which induces rapid and large movement changes, and uses a 12-legged robot with a flexible body axis. Our previous work found that the straight walk of the robot becomes unstable through Hopf bifurcation when the body axis flexibility is changed, which induces body undulations. Furthermore, we developed a simple controller based on the Hopf bifurcation and showed that the instability facilitates the turning of the robot. In this study, we newly found that the straight walk becomes unstable through pitchfork bifurcation when the body-axis flexibility is changed in a way different from that in our previous work. In addition, the pitchfork bifurcation induces a transition into a curved walk, whose curvature can be controlled by the body-axis flexibility. We developed a simple controller based on the pitchfork-bifurcation characteristics and demonstrated that the robot can perform a turning maneuver superior to that with the previous controller. This study provides a novel design principle for maneuverable locomotion of many-legged robots using intrinsic dynamic properties

Neuromusculoskeletal model that walks and runs across a speed range with a few motor control parameter changes based on the muscle synergy hypothesis

脳神経による⼈間の歩⾏と⾛⾏の制御様式を数理モデルで解明 --歩くと走るはどの程度違うのか--. 京都大学プレスリリース. 2019-01-24.Humans walk and run, as well as change their gait speed, through the control of their complicated and redundant musculoskeletal system. These gaits exhibit different locomotor behaviors, such as a double-stance phase in walking and flight phase in running. The complex and redundant nature of the musculoskeletal system and the wide variation in locomotion characteristics lead us to imagine that the motor control strategies for these gaits, which remain unclear, are extremely complex and differ from one another. It has been previously proposed that muscle activations may be generated by linearly combining a small set of basic pulses produced by central pattern generators (muscle synergy hypothesis). This control scheme is simple and thought to be shared between walking and running at different speeds. Demonstrating that this control scheme can generate walking and running and change the speed is critical, as bipedal locomotion is dynamically challenging. Here, we provide such a demonstration by using a motor control model with 69 parameters developed based on the muscle synergy hypothesis. Specifically, we show that it produces both walking and running of a human musculoskeletal model by changing only seven key motor control parameters. Furthermore, we show that the model can walk and run at different speeds by changing only the same seven parameters based on the desired speed. These findings will improve our understanding of human motor control in locomotion and provide guiding principles for the control design of wearable exoskeletons and prostheses

Advantage of straight walk instability in turning maneuver of multilegged locomotion: a robotics approach.

ムカデはなぜあれほど機敏に動けるのだろうか?－多足ロボットを用いた実験的検証－. 京都大学プレスリリース. 2016-07-22.Multilegged locomotion improves the mobility of terrestrial animals and artifacts. Using many legs has advantages, such as the ability to avoid falling and to tolerate leg malfunction. However, many intrinsic degrees of freedom make the motion planning and control difficult, and many contact legs can impede the maneuverability during locomotion. The underlying mechanism for generating agile locomotion using many legs remains unclear from biological and engineering viewpoints. The present study used a centipede-like multilegged robot composed of six body segments and twelve legs. The body segments are passively connected through yaw joints with torsional springs. The dynamic stability of the robot walking in a straight line changes through a supercritical Hopf bifurcation due to the body axis flexibility. We focused on a quick turning task of the robot and quantitatively investigated the relationship between stability and maneuverability in multilegged locomotion by using a simple control strategy. Our experimental results show that the straight walk instability does help the turning maneuver. We discuss the importance and relevance of our findings for biological systems and propose a design principle for a simple control scheme to create maneuverable locomotion of multilegged robots