Soichiro Fujiki

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.

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.

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.

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

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.

Generation of adaptive splitbelt treadmill walking by a biped robot using nonlinear oscillators with phase resetting

In this paper, we investigate the locomotor behaviors of a biped robot on a splitbelt treadmill using a locomotion-control system composed of nonlinear oscillators with phase resetting. Our results show that the robot establishes stable walking on the treadmill at various speeds of the belts due to modulation of the rhythm and phase by phase resetting. In addition, the phase differences between the leg movements shifted from out of phase, and duty factors were autonomously modulated depending on the speed discrepancy between the belts occurring through dynamic interactions among the robots mechanical system, the oscillator control system, and the environment. Such shifts of phase differences between the leg movements and modulations of duty factors are observed during human splitbelt treadmill walking, and our results suggest that our dynamic model using the robot and oscillator control system reflects a certain essence of the ability to produce adaptive locomotor behaviors.

Experimental verification of hysteresis in gait transition of a quadruped robot driven by nonlinear oscillators with phase resetting

In this paper, we investigated the locomotion of a quadruped robot, whose legs are controlled by an oscillator network system. In our previous work, simulation studies revealed that a quadruped robot produces walk and trot patterns through dynamic interactions among the robots mechanical system, the oscillator network system, and the environment. These studies also showed that a walk-trot transition is induced by changing the walking speed. In addition, the gait-pattern transition exhibited a hysteresis similar to that observed in the locomotion of humans and animals. The aim of the present study is to verify such dynamic characteristics in the gait generation of quadrupedal locomotion in the real world by developing and evaluating a quadruped robot.

Cusp catastrophe embedded in gait transition of a quadruped robot driven by nonlinear oscillators with phase resetting

In this paper, we investigated the dynamic locomotion of a quadruped robot. This robot is controlled by a locomotion control system composed of nonlinear oscillators, which was constructed based on the physiological concept of central pattern generator and phase resetting. In our previous work, we revealed that the quadruped robot produces the walk and trot gaits depending on the locomotion speed through dynamic interactions among the robot mechanical system, the oscillator control system, and the environment. In addition, we showed that it generates the walk-trot transition with a hysteresis, similar to that observed in locomotion of quadrupeds. To further clarify the gait transition mechanism, the present study investigated the dependence of the gait transition not only on the locomotion speed, but also on the physical conditions, such as the body mass. Our simulation results show that the codimension-2 cusp bifurcation appears in the gait transition, which further elucidates the dynamic structure inherent in quadrupedal locomotion.

Measuring body sway of bipedally standing rat and quantitative evaluation of its postural control.

Human generates very slow (<;1 Hz) body sway during standing, and the behavior of this sway is known to be changed characteristically depending on the neural ataxia. In order to investigate the sway mechanism and mechanism of neural ataxia through this sway behavior, the present research proposes an experimental environment of rats under bipedal standing. By the experiment, we succeeded the measurement of six intact rats standing for over 200 seconds without postural supports. Moreover, by comparing measured center of pressure (COP) and that of system model with nonlinear PID control model which is proposed as human standing model, control parameters of rats were numerically evaluated. Evaluated control parameters of rats were close to those of human, i.e., control strategy was considered to be comparable between rats and human.

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.