Tetsuro Funato

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.

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.

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.

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.

Sensory regulation of stance-to-swing transition in generation of adaptive human walking: A simulation study

In this paper, we investigated sensory mechanisms to regulate the transition from the stance to swing phases in the generation of adaptive human bipedal walking based on a neuromusculoskeletal model. We examined the contributions of the sensory information from the force-sensitive afferents in the ankle extensor muscle and from the position-sensitive afferents from the hip, inspired by a neuro-mechanical simulation for the stepping of the hind legs of cats. Our simulation results showed that the sensory signals related to the force in the ankle extensor muscle make a larger contribution than sensory signals related to the joint angle at the hip to produce robust walking against disturbances, as observed in the simulation results of cat locomotion. This suggests that such a sensorimotor mechanism is a general property and is also embedded in the neuro-control system of human bipedal walking.

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.

Motion Control of Dense Robot Colony Using Thermodynamics

In the last decades the theory of the complex dynamical systems has come to maturation providing a lot of important results in the field of many applied sciences. Also robotics has taken advantages from this new approach in what the behavior-based paradigm is particularly suitable to devise specific sensing activity since sensors usually provide information about the environment in a form which depends on the physics of the interaction. It is not required to be immediately converted into some symbolic representation but, on the contrary, it can be maintained at some physical level as a metaphor of the events observed in the environment. The close connection between the motor schema with its companion perceptual schema seems suggesting the presence of a substratum which underlies both perception and action activities, driving the flow of information accordingly. In the paper we consider a colony of robots immersed in a well-specified thermodinamical substratum where enthalpy and heat flux are devised to go vern the diffusion/ merging behavior of a swarm.

A system model that focuses on kinematic synergy for understanding human control structure

Human locomotion is a complex system generated by redundant actuators and its interaction with environment. Human manages the redundant body with dexterity for adapting to various environments. Analytical studies have revealed that multiple joints and muscles move simultaneously as if the motion is constraint in low-dimensional structures. These low-dimensional structures, called synergy, should reflect the human control strategy. Neural mechanism that probably contributes on the formation of synergy has been indicated and behavioral evidence that shows the contribution of synergy on neural control has been shown. However, behavioral approaches could not distinguish the active (neural) control and reaction from environment, thus it was difficult to discuss the control characteristic of synergy. The present research proposed a system model based on physiological knowledge about kinematic synergy, and performed a dynamical simulation on flat and slope floors. Based on the resultant motion on different environment, the effect of reaction from environment on walking posture, and the contribution of three kinematic synergies on walking control were revealed.

Human gait control suggested by the evaluation of the fluctuation of synergy

A high correlation among the motion of joints and muscles is observed when human walking. A group of the correlated motion is called synergy and the contribution of synergy on the locomotion control has been discussed. This research consider the motion pattern obtained by the singular value decomposition of joint motion as synergy, and consider the mode control using synergy for human locomotion. Several current researches evaluate the fluctuation of motion and search the variable with low fluctuation as control variable (UCM analysis), thus the evaluation of fluctuation will reveal whether synergy is control variable or not. Then we calculate the fluctuation of the whole motion and several principal motion such as COM, head and hip, and compare them with the fluctuation of synergy. As the result, the fluctuation of the synergy is shown to be relatively small, thus human locomotion is possible to be controlled using synergy.