Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator

Abnormal activity in the brainstem affects gait in a neuromusculoskeletal model

BACKGROUND

The ability to start and stop locomotion in response to different situations is an essential survival strategy in mammals. Mammalian locomotion is controlled by central pattern generators in the spinal cord, which are modulated by higher centers, particularly by the stimulation of the midbrain locomotor region. The midbrain locomotor region consists of the pedunculopontine nucleus and cuneiform nucleus, each having different roles in animals. Optogenetic activation of the cuneiform nucleus increases locomotion activities, whereas that of pedunculopontine nucleus decreases them. In neurological disorders such as Parkinson's disease, patients exhibit disturbed locomotion controls, including freezing of gait, which is defined as "a brief, episodic absence or marked reduction in the forward progression of the feet despite the intention to walk." However, the details and pathophysiological mechanisms of freezing of gait remain unclear.

METHODS

In this study, we aimed to elucidate the mechanisms underlying freezing of gait using a two-dimensional neuromusculoskeletal model fixed on the sagittal plane. This model consisted of a body with seven links and 18 muscles as well as a neural system including the brainstem and spinal cord. We developed a normal condition model and then derived a model of abnormal brainstem activity by modifying the parameters of the pedunculopontine nucleus and cuneiform nucleus during the initial 3 s of walking.

RESULTS

The normal models walked successfully following internal parameter optimization using standard genetic algorithms. In an abnormal model, 156 freezing of gait events were detected among 40,000 parameter sets using a freezing of gait-identifying algorithm. Hierarchical cluster analysis identified four clusters of parameters, based on the intensities of the pedunculopontine nucleus and cuneiform nucleus activity, differentiated in physiological movement types during freezing of gait events that were similar to the clinical classification types of freezing of gait.

CONCLUSIONS

Our results indicate that pedunculopontine nucleus and cuneiform nucleus activities could be linked with freezing of gait and that different modifications of those activities could generate observed freezing of gait subtypes. Our models can provide insights relevant for understanding the pathophysiological mechanisms of freezing of gait and are expected to assist in the classification of freezing of gait subtypes.

Active Arm Swing During Running Improves Rotational Stability of the Upper Body and Metabolic Energy Efficiency

PURPOSE

The kinematic benefits of arm swing during running for upper body stability have been previously investigated, while its role in metabolic energy efficiency remains controversial. To address this, this study aimed to test the hypothesis that active arm swing during running reduces both torso angular motion around the longitudinal axis and metabolic energy consumption.

METHODS

We employed forward dynamics musculoskeletal running simulations with different arm conditions to investigate the hypothesis. Full-body musculoskeletal running models, incorporating 150 muscles, were developed using artificial neural network-based running controllers. Three arm conditions were simulated using the running models and controllers: active arm swing, passive arm swing, and fixed arms.

RESULTS

Our results revealed that the active arm swing model demonstrated the lowest total metabolic energy consumption per traveling distance. The costs of transport were 5.52, 5.73, and 5.82 J/kg-m for active, passive, and fixed arm models, respectively. Interestingly, while metabolic energy consumption in the upper limb muscles was higher during active arm swing, the total energy consumption was lower. Additionally, the longitudinal rotation of the torso was minimal in the active arm swing condition.

CONCLUSION

These findings support our hypothesis, demonstrating that active arm swing during running reduces the angular motion of the torso and the metabolic energy consumption. This study provides evidence that arm swing during running is performed actively as an energy-saving mechanism. These results contribute to understanding of running biomechanics and may have implications for performance optimization in sports and rehabilitation settings.

Multibody dynamics-based musculoskeletal modeling for gait analysis: a systematic review

Beyond qualitative assessment, gait analysis involves the quantitative evaluation of various parameters such as joint kinematics, spatiotemporal metrics, external forces, and muscle activation patterns and forces. Utilizing multibody dynamics-based musculoskeletal (MSK) modeling provides a time and cost-effective non-invasive tool for the prediction of internal joint and muscle forces. Recent advancements in the development of biofidelic MSK models have facilitated their integration into clinical decision-making processes, including quantitative diagnostics, functional assessment of prosthesis and implants, and devising data-driven gait rehabilitation protocols. Through an extensive search and meta-analysis of over 116 studies, this PRISMA-based systematic review provides a comprehensive overview of different existing multibody MSK modeling platforms, including generic templates, methods for personalization to individual subjects, and the solutions used to address statically indeterminate problems. Additionally, it summarizes post-processing techniques and the practical applications of MSK modeling tools. In the field of biomechanics, MSK modeling provides an indispensable tool for simulating and understanding human movement dynamics. However, limitations which remain elusive include the absence of MSK modeling templates based on female anatomy underscores the need for further advancements in this area.

Bifurcation analysis of a two-neuron central pattern generator model for both oscillatory and convergent neuronal activities

The neural oscillator model proposed by Matsuoka is a piecewise affine system that exhibits distinctive periodic solutions. Although such typical oscillation patterns have been widely studied, little is understood about the dynamics of convergence to certain fixed points and bifurcations between the periodic orbits and fixed points in this model. We performed fixed point analysis on a two-neuron version of the Matsuoka oscillator model, the result of which explains the mechanism of oscillation and the discontinuity-induced bifurcations such as subcritical/supercritical Hopf-like, homoclinic-like and grazing bifurcations. Furthermore, it provided theoretical predictions concerning a logarithmic oscillation-period scaling law and noise-induced oscillations observed around those bifurcations. These results are expected to underpin further investigations into oscillatory and transient neuronal activities concerning central pattern generators.

Sensory feedback and central neuronal interactions in mouse locomotion

Locomotion is a complex process involving specific interactions between the central neural controller and the mechanical components of the system. The basic rhythmic activity generated by locomotor circuits in the spinal cord defines rhythmic limb movements and their central coordination. The operation of these circuits is modulated by sensory feedback from the limbs providing information about the state of the limbs and the body. However, the specific role and contribution of central interactions and sensory feedback in the control of locomotor gait and posture remain poorly understood. We use biomechanical data on quadrupedal locomotion in mice and recent findings on the organization of neural interactions within the spinal locomotor circuitry to create and analyse a tractable mathematical model of mouse locomotion. The model includes a simplified mechanical model of the mouse body with four limbs and a central controller composed of four rhythm generators, each operating as a state machine controlling the state of one limb. Feedback signals characterize the load and extension of each limb as well as postural stability (balance). We systematically investigate and compare several model versions and compare their behaviour to existing experimental data on mouse locomotion. Our results highlight the specific roles of sensory feedback and some central propriospinal interactions between circuits controlling fore and hind limbs for speed-dependent gait expression. Our models suggest that postural imbalance feedback may be critically involved in the control of swing-to-stance transitions in each limb and the stabilization of walking direction.

Delayed center of mass feedback in elderly humans leads to greater muscle co-contraction and altered balance strategy under perturbed balance: A predictive musculoskeletal simulation study

Falls are one of the leading causes of non-disease death and injury in the elderly, often due to delayed sensory neural feedback essential for balance. This delay, challenging to measure or manipulate in human studies, necessitates exploration through neuromusculoskeletal modeling to reveal its intricate effects on balance. In this study, we developed a novel three-way muscle feedback control approach, including muscle length feedback, muscle force feedback, and enter of mass feedback, for balancing and investigated specifically the effects of center of mass feedback delay on elderly people's balance strategies. We conducted simulations of cyclic perturbed balance at different magnitudes ranging from 0 to 80 mm and with three center of mass feedback delays (100, 150 & 200 ms). The results reveal two key points: 1) Longer center of mass feedback delays resulted in increased muscle activations and co-contraction, 2) Prolonged center of mass feedback delays led to noticeable shifts in balance strategies during perturbed standing. Under low-amplitude perturbations, the ankle strategy was predominantly used, while higher amplitude disturbances saw more frequent employment of hip and knee strategies. Additionally, prolonged center of mass delays altered balance strategies across different phases of perturbation, with a noticeable increase in overall ankle strategy usage. These findings underline the adverse effects of prolonged feedback delays on an individual's stability, necessitating greater muscle co-contraction and balance strategy adjustment to maintain balance under perturbation. Our findings advocate for the development of training programs tailored to enhance balance reactions and mitigate muscle feedback delays within clinical or rehabilitation settings for fall prevention in elderly people.

Investigating the roles of reflexes and central pattern generators in the control and modulation of human locomotion using a physiologically plausible neuromechanical model

Objective.Studying the neural components regulating movement in human locomotion is obstructed by the inability to perform invasive experimental recording in the human neural circuits. Neuromechanical simulations can provide insights by modeling the locomotor circuits. Past neuromechanical models proposed control of locomotion either driven by central pattern generators (CPGs) with simple sensory commands or by a purely reflex-based network regulated by state-machine mechanisms, which activate and deactivate reflexes depending on the detected gait cycle phases. However, the physiological interpretation of these state machines remains unclear. Here, we present a physiologically plausible model to investigate spinal control and modulation of human locomotion.Approach.We propose a bio-inspired controller composed of two coupled CPGs that produce the rhythm and pattern, and a reflex-based network simulating low-level reflex pathways and Renshaw cells. This reflex network is based on leaky-integration neurons, and the whole system does not rely on changing reflex gains according to the gait cycle state. The musculoskeletal model is composed of a skeletal structure and nine muscles per leg generating movement in sagittal plane.Main results.Optimizing the open parameters for effort minimization and stability, human kinematics and muscle activation naturally emerged. Furthermore, when CPGs were not activated, periodic motion could not be achieved through optimization, suggesting the necessity of this component to generate rhythmic behavior without a state machine mechanism regulating reflex activation. The controller could reproduce ranges of speeds from 0.3 to 1.9 m s-1. The results showed that the net influence of feedback on motoneurons (MNs) during perturbed locomotion is predominantly inhibitory and that the CPGs provide the timing of MNs' activation by exciting or inhibiting muscles in specific gait phases.Significance.The proposed bio-inspired controller could contribute to our understanding of locomotor circuits of the intact spinal cord and could be used to study neuromotor disorders.

Sensory Feedback and Central Neuronal Interactions in Mouse Locomotion

Locomotion is a complex process involving specific interactions between the central neural controller and the mechanical components of the system. The basic rhythmic activity generated by locomotor circuits in the spinal cord defines rhythmic limb movements and their central coordination. The operation of these circuits is modulated by sensory feedback from the limbs providing information about the state of the limbs and the body. However, the specific role and contribution of central interactions and sensory feedback in the control of locomotor gait and posture remain poorly understood. We use biomechanical data on quadrupedal locomotion in mice and recent findings on the organization of neural interactions within the spinal locomotor circuitry to create and analyze a tractable mathematical model of mouse locomotion. The model includes a simplified mechanical model of the mouse body with four limbs and a central controller composed of four rhythm generators, each operating as a state machine controlling the state of one limb. Feedback signals characterize the load and extension of each limb as well as postural stability (balance). We systematically investigate and compare several model versions and compare their behavior to existing experimental data on mouse locomotion. Our results highlight the specific roles of sensory feedback and some central propriospinal interactions between circuits controlling fore and hind limbs for speed-dependent gait expression. Our models suggest that postural imbalance feedback may be critically involved in the control of swing-to-stance transitions in each limb and the stabilization of walking direction.

Methods for integrating postural control into biomechanical human simulations: a systematic review

Understanding of the human body's internal processes to maintain balance is fundamental to simulate postural control behaviour. The body uses multiple sensory systems' information to obtain a reliable estimate about the current body state. This information is used to control the reactive behaviour to maintain balance. To predict a certain motion behaviour with knowledge of the muscle forces, forward dynamic simulations of biomechanical human models can be utilized. We aim to use predictive postural control simulations to give therapy recommendations to patients suffering from postural disorders in the future. It is important to know which types of modelling approaches already exist to apply such predictive forward dynamic simulations. Current literature provides different models that aim to simulate human postural control. We conducted a systematic literature research to identify the different approaches of postural control models. The different approaches are discussed regarding their applied biomechanical models, sensory representation, sensory integration, and control methods in standing and gait simulations. We searched on Scopus, Web of Science and PubMed using a search string, scanned 1253 records, and found 102 studies to be eligible for inclusion. The included studies use different ways for sensory representation and integration, although underlying neural processes still remain unclear. We found that for postural control optimal control methods like linear quadratic regulators and model predictive control methods are used less, when models' level of details is increasing, and nonlinearities become more important. Considering musculoskeletal models, reflex-based and PD controllers are mainly applied and show promising results, as they aim to create human-like motion behaviour considering physiological processes.

Acquisition of bipedal locomotion in a neuromusculoskeletal model with unilateral transtibial amputation

Adaptive locomotion is an essential behavior for animals to survive. The central pattern generator in the spinal cord is responsible for the basic rhythm of locomotion through sensory feedback coordination, resulting in energy-efficient locomotor patterns. Individuals with symmetrical body proportions exhibit an energy-efficient symmetrical gait on flat ground. In contrast, individuals with lower limb amputation, who have morphologically asymmetrical body proportions, exhibit asymmetrical gait patterns. However, it remains unclear how the nervous system adjusts the control of the lower limbs. Thus, in this study, we investigated how individuals with unilateral transtibial amputation control their left and right lower limbs during locomotion using a two-dimensional neuromusculoskeletal model. The model included a musculoskeletal model with 7 segments and 18 muscles, as well as a neural model with a central pattern generator and sensory feedback systems. Specifically, we examined whether individuals with unilateral transtibial amputation acquire prosthetic gait through a symmetric or asymmetric feedback control for the left and right lower limbs. After acquiring locomotion, the metabolic costs of transport and the symmetry of the spatiotemporal gait factors were evaluated. Regarding the metabolic costs of transportation, the symmetric control model showed values approximately twice those of the asymmetric control model, whereas both scenarios showed asymmetry of spatiotemporal gait patterns. Our results suggest that individuals with unilateral transtibial amputation can reacquire locomotion by modifying sensory feedback parameters. In particular, the model reacquired reasonable locomotion for activities of daily living by re-searching asymmetric feedback parameters for each lower limb. These results could provide insight into effective gait assessment and rehabilitation methods to reacquire locomotion in individuals with unilateral transtibial amputation.

Producing non-steady-state gaits (starting, stopping, and turning) in a biologically realistic quadrupedal simulation

Multibody dynamic analysis (MDA) has become part of the standard toolkit used to reconstruct the biomechanics of extinct animals. However, its use is currently almost exclusively limited to steady state activities such as walking and running at constant velocity. If we want to reconstruct the full range of activities that a given morphology can achieve then we must be able to reconstruct non-steady-state activities such as starting, stopping, and turning. In this paper we demonstrate how we can borrow techniques from the robotics literature to produce gait controllers that allow us to generate non-steady-state gaits in a biologically realistic quadrupedal simulation of a chimpanzee. We use a novel proportional-derivative (PD) reach controller that can accommodate both the non-linear contraction dynamics of Hill-type muscles and the large numbers of both single-joint and two-joint muscles to allow us to define the trajectory of the distal limb segment. With defined autopodial trajectories we can then use tegotae style locomotor controllers that use decentralized reaction force feedback to control the trajectory speed in order to produce quadrupedal gait. This combination of controllers can generate starting, stopping, and turning kinematics, something that we believe has never before been achieved in a simulation that uses both physiologically realistic muscles and a high level of anatomical fidelity. The gait quality is currently relatively low compared to the more commonly used feedforward control methods, but this can almost certainly be improved in future by using more biologically based foot trajectories and increasing the complexity of the underlying model and controllers. Understanding these more complex gaits is essential, particularly in fields such as paleoanthropology where the transition from an ancestral hominoid with a diversified repertoire to a bipedal hominin is of such fundamental importance, and this approach illustrates one possible avenue for further research in this area.

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.

EMG-driven control in lower limb prostheses: a topic-based systematic review

BACKGROUND

The inability of users to directly and intuitively control their state-of-the-art commercial prosthesis contributes to a low device acceptance rate. Since Electromyography (EMG)-based control has the potential to address those inabilities, research has flourished on investigating its incorporation in microprocessor-controlled lower limb prostheses (MLLPs). However, despite the proposed benefits of doing so, there is no clear explanation regarding the absence of a commercial product, in contrast to their upper limb counterparts.

OBJECTIVE AND METHODOLOGIES

This manuscript aims to provide a comparative overview of EMG-driven control methods for MLLPs, to identify their prospects and limitations, and to formulate suggestions on future research and development. This is done by systematically reviewing academical studies on EMG MLLPs. In particular, this review is structured by considering four major topics: (1) type of neuro-control, which discusses methods that allow the nervous system to control prosthetic devices through the muscles; (2) type of EMG-driven controllers, which defines the different classes of EMG controllers proposed in the literature; (3) type of neural input and processing, which describes how EMG-driven controllers are implemented; (4) type of performance assessment, which reports the performance of the current state of the art controllers.

RESULTS AND CONCLUSIONS

The obtained results show that the lack of quantitative and standardized measures hinders the possibility to analytically compare the performances of different EMG-driven controllers. In relation to this issue, the real efficacy of EMG-driven controllers for MLLPs have yet to be validated. Nevertheless, in anticipation of the development of a standardized approach for validating EMG MLLPs, the literature suggests that combining multiple neuro-controller types has the potential to develop a more seamless and reliable EMG-driven control. This solution has the promise to retain the high performance of the currently employed non-EMG-driven controllers for rhythmic activities such as walking, whilst improving the performance of volitional activities such as task switching or non-repetitive movements. Although EMG-driven controllers suffer from many drawbacks, such as high sensitivity to noise, recent progress in invasive neural interfaces for prosthetic control (bionics) will allow to build a more reliable connection between the user and the MLLPs. Therefore, advancements in powered MLLPs with integrated EMG-driven control have the potential to strongly reduce the effects of psychosomatic conditions and musculoskeletal degenerative pathologies that are currently affecting lower limb amputees.

Optimization of immune receptor-related hypersensitive cell death response assay using agrobacterium-mediated transient expression in tobacco plants

BACKGROUND

The study of the regulatory mechanisms of evolutionarily conserved Nucleotide-binding leucine-rich repeat (NLR) resistance (R) proteins in animals and plants is of increasing importance due to understanding basic immunity and the value of various crop engineering applications of NLR immune receptors. The importance of temperature is also emerging when applying NLR to crops responding to global climate change. In particular, studies of pathogen effector recognition and autoimmune activity of NLRs in plants can quickly and easily determine their function in tobacco using agro-mediated transient assay. However, there are conditions that should not be overlooked in these cell death-related assays in tobacco.

RESULTS

Environmental conditions play an important role in the immune response of plants. The system used in this study was to establish conditions for optimal hypertensive response (HR) cell death analysis by using the paired NLR RPS4/RRS1 autoimmune and AvrRps4 effector recognition system. The most suitable greenhouse temperature for growing plants was fixed at 22 °C. In this study, RPS4/RRS1-mediated autoimmune activity, RPS4 TIR domain-dependent cell death, and RPS4/RRS1-mediated HR cell death upon AvrRps4 perception significantly inhibited under conditions of 65% humidity. The HR is strongly activated when the humidity is below 10%. Besides, the leaf position of tobacco is important for HR cell death. Position #4 of the leaf from the top in 4-5 weeks old tobacco plants showed the most effective HR cell death.

CONCLUSIONS

As whole genome sequencing (WGS) or resistance gene enrichment sequencing (RenSeq) of various crops continues, different types of NLRs and their functions will be studied. At this time, if we optimize the conditions for evaluating NLR-mediated HR cell death, it will help to more accurately identify the function of NLRs. In addition, it will be possible to contribute to crop development in response to global climate change through NLR engineering.

Adapting Footfall Rhythmicity to Auditory Perturbations Affects Resilience of Locomotor Behavior: A Proof-of-Concept Study

For humans, the ability to effectively adapt footfall rhythm to perturbations is critical for stable locomotion. However, only limited information exists regarding how dynamic stability changes when individuals modify their footfall rhythm. In this study, we recorded 3D kinematic activity from 20 participants (13 males, 18–30 years old) during walking on a treadmill while synchronizing with an auditory metronome sequence individualized to their baseline walking characteristics. The sequence then included unexpected temporal perturbations in the beat intervals with the subjects required to adapt their footfall rhythm accordingly. Building on a novel approach to quantify resilience of locomotor behavior, this study found that, in response to auditory perturbation, the mean center of mass (COM) recovery time across all participants who showed deviation from steady state (N = 15) was 7.4 (8.9) s. Importantly, recovery of footfall synchronization with the metronome beats after perturbation was achieved prior (+3.4 [95.0% CI +0.1, +9.5] s) to the recovery of COM kinematics. These results highlight the scale of temporal adaptation to perturbations and provide implications for understanding regulation of rhythm and balance. Thus, our study extends the sensorimotor synchronization paradigm to include analysis of COM recovery time toward improving our understanding of an individual’s resilience to perturbations and potentially also their fall risk.

Adaptive and Energy-Efficient Optimal Control in CPGs Through Tegotae-Based Feedback

To obtain biologically inspired robotic control, the architecture of central pattern generators (CPGs) has been extensively adopted to generate periodic patterns for locomotor control. This is attributed to the interesting properties of nonlinear oscillators. Although sensory feedback in CPGs is not necessary for the generation of patterns, it plays a central role in guaranteeing adaptivity to environmental conditions. Nonetheless, its inclusion significantly modifies the dynamics of the CPG architecture, which often leads to bifurcations. For instance, the force feedback can be exploited to derive information regarding the state of the system. In particular, the Tegotae approach can be adopted by coupling proprioceptive information with the state of the oscillation itself in the CPG model. This paper discusses this policy with respect to other types of feedback; it provides higher adaptivity and an optimal energy efficiency for reflex-like actuation. We believe this is the first attempt to analyse the optimal energy efficiency along with the adaptivity of the Tegotae approach.

Sensory modulation of gait characteristics in human locomotion: A neuromusculoskeletal modeling study

The central nervous system of humans and other animals modulates spinal cord activity to achieve several locomotion behaviors. Previous neuromechanical models investigated the modulation of human gait changing selected parameters belonging to CPGs (Central Pattern Generators) feedforward oscillatory structures or to feedback reflex circuits. CPG-based models could replicate slow and fast walking by changing only the oscillation’s properties. On the other hand, reflex-based models could achieve different behaviors through optimizations of large dimensional parameter spaces. However, they could not effectively identify individual key reflex parameters responsible for gait characteristics’ modulation. This study investigates which reflex parameters modulate the gait characteristics through neuromechanical simulations. A recently developed reflex-based model is used to perform optimizations with different target behaviors on speed, step length, and step duration to analyze the correlation between reflex parameters and their influence on these gait characteristics. We identified nine key parameters that may affect the target speed ranging from slow to fast walking (0.48 and 1.71 m/s) as well as a large range of step lengths (0.43 and 0.88 m) and step duration (0.51, 0.98 s). The findings show that specific reflexes during stance significantly affect step length regulation, mainly given by positive force feedback of the ankle plantarflexors’ group. On the other hand, stretch reflexes active during swing of iliopsoas and gluteus maximus regulate all the gait characteristics under analysis. Additionally, the results show that the hamstrings’ group’s stretch reflex during the landing phase is responsible for modulating the step length and step duration. Additional validation studies in simulations demonstrated that the modulation of identified reflexes is sufficient to regulate the investigated gait characteristics. Thus, this study provides an overview of possible reflexes involved in modulating speed, step length, and step duration of human gaits.

This study investigates the possible reflex parameters that the central nervous system could use to modulate human locomotion. Specifically, we target the modulation of three gait characteristics: speed, step length, and step duration. We utilize human locomotion simulations with a previously developed reflex-based model and perform multiple optimizations ranging targeting low to high values of the three gait characteristics investigated. From the data acquired in optimizations, we investigate which reflex parameter correlates most with the gait characteristics changes. We identified nine key reflex parameters affecting gait modulation, performed validation experiments, and verified that the optimization of key reflex parameters alone could generate modulation in the studied locomotion behaviors. Kinematics, ground reaction forces, and muscle activity obtained in simulations show similarities with past experimental studies on gait modulation. Therefore, the identified parameters could potentially be used by the nervous system to regulate locomotion behaviors in a task-dependent manner. Other circuits not modeled in this study could play a crucial role in gait modulation, and further investigations should be done in the co-optimization of feedforward and feedback circuits.

Tegotae-Based Control Produces Adaptive Inter- and Intra-limb Coordination in Bipedal Walking

Despite the appealing concept of central pattern generator (CPG)-based control for bipedal walking robots, there is currently no systematic methodology for designing a CPG-based controller. To remedy this oversight, we attempted to apply the Tegotae approach, a Japanese concept describing how well a perceived reaction, i.e., sensory information, matches an expectation, i.e., an intended motor command, in designing localised controllers in the CPG-based bipedal walking model. To this end, we developed a Tegotae function that quantifies the Tegotae concept. This function allowed incorporating decentralised controllers into the proposed bipedal walking model systematically. We designed a two-dimensional bipedal walking model using Tegotae functions and subsequently implemented it in simulations to validate the proposed design scheme. We found that our model can walk on both flat and uneven terrains and confirmed that the application of the Tegotae functions in all joint controllers results in excellent adaptability to environmental changes.

Forward dynamic simulation of Japanese macaque bipedal locomotion demonstrates better energetic economy in a virtualised plantigrade posture

A plantigrade foot with a large robust calcaneus is regarded as a distinctive morphological feature of the human foot; it is presumably the result of adaptation for habitual bipedal locomotion. The foot of the Japanese macaque, on the other hand, does not have such a feature, which hampers it from making foot-ground contact at the heel during bipedal locomotion. Understanding how this morphological difference functionally affects the generation of bipedal locomotion is crucial for elucidating the evolution of human bipedalism. In this study, we constructed a forward dynamic simulation of bipedal locomotion in the Japanese macaque based on a neuromusculoskeletal model to evaluate how virtual manipulation of the foot structure from digitigrade to plantigrade affects the kinematics, dynamics, and energetics of bipedal locomotion in a nonhuman primate whose musculoskeletal anatomy is not adapted to bipedalism. The normal bipedal locomotion generated was in good agreement with that of actual Japanese macaques. If, as in human walking, the foot morphology was altered to allow heel contact, the vertical ground reaction force profile became double-peaked and the cost of transport decreased. These results suggest that evolutionary changes in the foot structure were important for the acquisition of human-like efficient bipedal locomotion.

Contribution of Phase Resetting to Adaptive Rhythm Control in Human Walking Based on the Phase Response Curves of a Neuromusculoskeletal Model

Humans walk adaptively in varying environments by manipulating their complicated and redundant musculoskeletal system. Although the central pattern generators in the spinal cord are largely responsible for adaptive walking through sensory-motor coordination, it remains unclear what neural mechanisms determine walking adaptability. It has been reported that locomotor rhythm and phase are regulated by the production of phase shift and rhythm resetting (phase resetting) for periodic motor commands in response to sensory feedback and perturbation. While the phase resetting has been suggested to make a large contribution to adaptive walking, it has only been investigated based on fictive locomotion in decerebrate cats, and thus it remains unclear if human motor control has such a rhythm regulation mechanism during walking. In our previous work, we incorporated a phase resetting mechanism into a motor control model and demonstrated that it improves the stability and robustness of walking through forward dynamic simulations of a human musculoskeletal model. However, this did not necessarily verify that phase resetting plays a role in human motor control. In our other previous work, we used kinematic measurements of human walking to identify the phase response curve (PRC), which explains phase-dependent responses of a limit cycle oscillator to a perturbation. This revealed how human walking rhythm is regulated by perturbations. In this study, we integrated these two approaches using a physical model and identification of the PRC to examine the hypothesis that phase resetting plays a role in the control of walking rhythm in humans. More specifically, we calculated the PRC using our neuromusculoskeletal model in the same way as our previous human experiment. In particular, we compared the PRCs calculated from two different models with and without phase resetting while referring to the PRC for humans. As a result, although the PRC for the model without phase resetting did not show any characteristic shape, the PRC for the model with phase resetting showed a characteristic phase-dependent shape with trends similar to those of the PRC for humans. These results support our hypothesis and will improve our understanding of adaptive rhythm control in human walking.

Phase resetting and intermittent control at the edge of stability in a simple biped model generates 1/f-like gait cycle variability

The 1/f-like gait cycle variability, characterized by temporal changes in stride-time intervals during steady-state human walking, is a well-documented gait characteristic. Such gait fractality is apparent in healthy young adults, but tends to disappear in the elderly and patients with neurological diseases. However, mechanisms that give rise to gait fractality have yet to be fully clarified. We aimed to provide novel insights into neuro-mechanical mechanisms of gait fractality, based on a numerical simulation model of biped walking. A previously developed heel-toe footed, seven-rigid-link biped model with human-like body parameters in the sagittal plane was implemented and expanded. It has been shown that the gait model, stabilized rigidly by means of impedance control with large values of proportional (P) and derivative (D) gains for a linear feedback controller, is destabilized only in a low-dimensional eigenspace, as P and D decrease below and even far below critical values. Such low-dimensional linear instability can be compensated by impulsive, phase-dependent actions of nonlinear controllers (phase resetting and intermittent controllers), leading to the flexible walking with joint impedance in the model being as small as that in humans. Here, we added white noise to the model to examine P-value-dependent stochastic dynamics of the model for small D-values. The simulation results demonstrated that introduction of the nonlinear controllers in the model determined the fractal features of gait for a wide range of the P-values, provided that the model operates near the edge of stability. In other words, neither the model stabilized only by pure impedance control even at the edge of linear stability, nor the model stabilized by specific nonlinear controllers, but with P-values far inside the stability region, could induce gait fractality. Although only limited types of controllers were examined, we suggest that the impulsive nonlinear controllers and criticality could be major mechanisms for the genesis of gait fractality.

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.

Variant and Invariant Spatiotemporal Structures in Kinematic Coordination to Regulate Speed During Walking and Running

Humans walk, run, and change their speed in accordance with circumstances. These gaits are rhythmic motions generated by multi-articulated movements, which have specific spatiotemporal patterns. The kinematic characteristics depend on the gait and speed. In this study, we focused on the kinematic coordination of locomotor behavior to clarify the underlying mechanism for the effect of speed on the spatiotemporal kinematic patterns for each gait. In particular, we used seven elevation angles for the whole-body motion and separated the measured data into different phases depending on the foot-contact condition, that is, single-stance phase, double-stance phase, and flight phase, which have different physical constraints during locomotion. We extracted the spatiotemporal kinematic coordination patterns with singular value decomposition and investigated the effect of speed on the coordination patterns. Our results showed that most of the whole-body motion could be explained by only two sets of temporal and spatial coordination patterns in each phase. Furthermore, the temporal coordination patterns were invariant for different speeds, while the spatial coordination patterns varied. These findings will improve our understanding of human adaptation mechanisms to tune locomotor behavior for changing speed.

A Pathological Condition Affects Motor Modules in a Bipedal Locomotion Model

Bipedal locomotion is a basic motor activity that requires simultaneous control of multiple muscles. Physiological experiments suggest that the nervous system controls bipedal locomotion efficiently by using motor modules of synergistic muscle activations. If these modules were merged, abnormal locomotion patterns would be realized as observed in patients with neural impairments such as chronic stroke. However, sub-acute patients have been reported not to show such merged motor modules. Therefore, in this study, we examined what conditions in the nervous system merges motor modules. we built a two-dimensional bipedal locomotion model that included a musculoskeletal model with 7 segments and 18 muscles, a neural system with a hierarchical central pattern generator (CPG), and various feedback inputs from reflex organs. The CPG generated synergistic muscle activations comprising 5 motor modules to produce locomotion phases. Our model succeeded to acquire stable locomotion by using the motor modules and reflexes. Next, we examined how a pathological condition altered motor modules. Specifically, we weakened neural inputs to muscles on one leg to simulate a stroke condition. Immediately after the simulated stroke, the model did not walk. Then, internal parameters were modified to recover stable locomotion. We refitted either (a) reflex parameters or (b) CPG parameters to compensate the locomotion by adapting (a) reflexes or (b) the controller. Stable locomotion was recovered in both conditions. However the motor modules were merged only in (b). These results suggest that light or sub-acute stroke patients, who can compensate stable locomotion by just adapting reflexes, would not show merge of motor modules, whereas severe or chronic patients, who needed to adapt the controller for compensation, would show the merge, as consistent with experimental findings.

CPG-Based Gait Generation of the Curved-Leg Hexapod Robot with Smooth Gait Transition

This paper presents a novel CPG-based gait generation of the curved-leg hexapod robot that can enable smooth gait transitions between multi-mode gaits. First, the locomotion of the curved leg and instability during the gait transitions are analyzed. Then, a modified Hopf oscillator is applied in the CPG control, which can realize multiple gaits by adjusting a simple parameter. In addition, a smooth gait switching method is also proposed via smooth gait transition functions and gait planning. Tripod gait, quadruped gait, and wave gait are planned for the hexapod robot to achieve quick and stable gait transitions smoothly and continuously. MATLAB and ADAMS simulations and corresponding practical experiments are conducted. The results show that the proposed method can achieve smooth and continuous mutual gait transitions, which proves the effectiveness of the proposed CPG-based hexapod robot control.

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

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.

Visual and Vestibular Inputs Affect Muscle Synergies Responsible for Body Extension and Stabilization in Sit-to-Stand Motion

The sit-to-stand motion is a common movement in daily life and understanding the mechanism of the sit-to-stand motion is important. Our previous study shows that four muscle synergies can characterize the sit-to-stand motion, and they have specific roles, such as upper body flexion, rising from a chair, body extension, and posture stabilization. The time-varying weight of these synergies are changed to achieve adaptive movement. However, the relationship between sensory input and the activation of the muscle synergies is not completely understood. In this paper, we aim to clarify how vestibular and visual inputs affect the muscle synergy in sit-to-stand motion. To address this, we conducted experiments as follows. Muscle activity, body kinematics, and ground reaction force were measured for the sit-to-stand motion under three different conditions: control, visual-disturbance, and vestibular-disturbance conditions. Under the control condition, the participants stood without any intervention. Under the visual-disturbance condition, the participants wore convex lens glasses and performed the sit-to-stand motion in a dark room. Under the vestibular-disturbance condition, a caloric test was performed. Muscle synergies were calculated for these three conditions using non-negative matrix factorization. We examined whether the same four muscle synergies were employed under each condition, and the changes in the time-varying coefficients were determined. These experiments were conducted on seven healthy, young participants. It was found that four muscle synergies could explain the muscle activity in the sit-to-stand motion under the three conditions. However, there were significant differences in the time-varying weight coefficients. When the visual input was disturbed, a larger amplitude was found for the muscle synergy that activated mostly in the final posture stabilization phase of the sit-to-stand motion. Under vestibular-disturbance condition, a longer activation was observed for the synergies that extended the entire body and led to posture stabilization. The results implied that during human sit-to-stand motion, visual input has less contribution to alter or correct activation of muscle synergies until the last phase. On the other hand, duration of muscle synergies after the buttocks leave are prolonged in order to adapt to the unstable condition in which sense of verticality is decreased under vestibular-disturbance.

Adaptive hindlimb split-belt treadmill walking in rats by controlling basic muscle activation patterns via phase resetting

To investigate the adaptive locomotion mechanism in animals, a split-belt treadmill has been used, which has two parallel belts to produce left–right symmetric and asymmetric environments for walking. Spinal cats walking on the treadmill have suggested the contribution of the spinal cord and associated peripheral nervous system to the adaptive locomotion. Physiological studies have shown that phase resetting of locomotor commands involving a phase shift occurs depending on the types of sensory nerves and stimulation timing, and that muscle activation patterns during walking are represented by a linear combination of a few numbers of basic temporal patterns despite the complexity of the activation patterns. Our working hypothesis was that resetting the onset timings of basic temporal patterns based on the sensory information from the leg, especially extension of hip flexors, contributes to adaptive locomotion on the split-belt treadmill. Our hypothesis was examined by conducting forward dynamic simulations using a neuromusculoskeletal model of a rat walking on a split-belt treadmill with its hindlimbs and by comparing the simulated motions with the measured motions of rats.

The Benefit of Combining Neuronal Feedback and Feed-Forward Control for Robustness in Step Down Perturbations of Simulated Human Walking Depends on the Muscle Function

It is often assumed that the spinal control of human locomotion combines feed-forward central pattern generation with sensory feedback via muscle reflexes. However, the actual contribution of each component to the generation and stabilization of gait is not well understood, as direct experimental evidence for either is difficult to obtain. We here investigate the relative contribution of the two components to gait stability in a simulation model of human walking. Specifically, we hypothesize that a simple linear combination of feedback and feed-forward control at the level of the spinal cord improves the reaction to unexpected step down perturbations. In previous work, we found preliminary evidence supporting this hypothesis when studying a very reduced model of rebounding behaviors. In the present work, we investigate if the evidence extends to a more realistic model of human walking. We revisit a model that has previously been published and relies on spinal feedback control to generate walking. We extend the control of this model with a feed-forward muscle activation pattern. The feed-forward pattern is recorded from the unperturbed feedback control output. We find that the improvement in the robustness of the walking model with respect to step down perturbations depends on the ratio between the two strategies and on the muscle to which they are applied. The results suggest that combining feed-forward and feedback control is not guaranteed to improve locomotion, as the beneficial effects are dependent on the muscle and its function during walking.

Walking with perturbations: a guide for biped humans and robots

This paper provides an update on the neural control of bipedal walking in relation to bioinspired models and robots. It is argued that most current models or robots are based on the construct of a symmetrical central pattern generator (CPG). However, new evidence suggests that CPG functioning is basically asymmetrical with its flexor half linked more tightly to the rhythm generator. The stability of bipedal gait, which is an important problem for robots and biological systems, is also addressed. While it is not possible to determine how biological biped systems guarantee stability, robot solutions can be useful to propose new hypotheses for biology. In the second part of this review, the focus is on gait perturbations, which is an important topic in robotics in view of the frequent falls of robots when faced with perturbations. From the human physiology it is known that the initial reaction often consists of a brief interruption followed by an adequate response. For instance, the successful recovery from a trip is achieved using some basic reactions (termed elevating and lowering strategies), that depend on the phase of the step cycle of the trip occurrence. Reactions to stepping unexpectedly in a hole depend on comparing expected and real feedback. Implementation of these ideas in models and robotics starts to emerge, with the most advanced robots being able to learn how to fall safely and how to deal with complicated disturbances such as provided by walking on a split-belt.

Bio-inspired controller achieving forward speed modulation with a 3D bipedal walker

Despite all the effort devoted to generating locomotion algorithms for bipedal walkers, robots are still far from reaching the impressive human walking capabilities, for instance regarding robustness and energy consumption. In this paper, we have developed a bio-inspired torque-based controller supporting the emergence of a new generation of robust and energy-efficient walkers. It recruits virtual muscles driven by reflexes and a central pattern generator, and thus requires no computationally intensive inverse kinematics or dynamics modeling. This controller is capable of generating energy-efficient and human-like gaits (both regarding kinematics and dynamics) across a large range of forward speeds, in a 3D environment. After a single off-line optimization process, the forward speed can be continuously commanded within this range by changing high-level parameters, as linear or quadratic functions of the target speed. Sharp speed transitions can then be achieved with no additional tuning, resulting in immediate adaptations of the step length and frequency. In this paper, we particularly embodied this controller on a simulated version of COMAN, a 95 cm tall humanoid robot. We reached forward speed modulations between 0.4 and 0.9 m/s. This covers normal human walking speeds once scaled to the robot size. Finally, the walker demonstrated significant robustness against a large spectrum of unpredicted perturbations: facing external pushes or walking on altered environments, such as stairs, slopes, and irregular ground.

Adaptive Control Strategies for Interlimb Coordination in Legged Robots: A Review

Walking animals produce adaptive interlimb coordination during locomotion in accordance with their situation. Interlimb coordination is generated through the dynamic interactions of the neural system, the musculoskeletal system, and the environment, although the underlying mechanisms remain unclear. Recently, investigations of the adaptation mechanisms of living beings have attracted attention, and bio-inspired control systems based on neurophysiological findings regarding sensorimotor interactions are being developed for legged robots. In this review, we introduce adaptive interlimb coordination for legged robots induced by various factors (locomotion speed, environmental situation, body properties, and task). In addition, we show characteristic properties of adaptive interlimb coordination, such as gait hysteresis and different time-scale adaptations. We also discuss the underlying mechanisms and control strategies to achieve adaptive interlimb coordination and the design principle for the control system of legged robots.

Dynamically and Biologically Inspired Legged Locomotion: A Review

[abstFig src='/00290003/01.jpg' width='300' text='Passive dynamic walking: RW03 and Jenkka III' ] Legged locomotion, such as walking, running, turning, and jumping depends strongly on the dynamics and the biological characteristics of the body involved. Gait patterns and energy efficiency, for instance, are known to be greatly affected, not only by travel speed and ground contact conditions but also by body structure such as joint stiffness and coordination, and foot sole shape. To understand legged locomotion principles, we must elucidate how the body’s dynamic and biological characteristics affect locomotion. Efforts should also be made to incorporate these characteristics inventively in order to improve locomotion performance with regard to robustness, adaptability, and efficiency, which realize more refined legged locomotion. For this special issue, we invited our readers to submit papers with approaches to achieving legged locomotion based on dynamic and biological characteristics and studies investigating the effects of these characteristics. In this paper, we review studies on dynamically and biologically inspired legged locomotion.

Evaluation of a Neuromechanical Walking Control Model Using Disturbance Experiments

Neuromechanical simulations have been used to study the spinal control of human locomotion which involves complex mechanical dynamics. So far, most neuromechanical simulation studies have focused on demonstrating the capability of a proposed control model in generating normal walking. As many of these models with competing control hypotheses can generate human-like normal walking behaviors, a more in-depth evaluation is required. Here, we conduct the more in-depth evaluation on a spinal-reflex-based control model using five representative gait disturbances, ranging from electrical stimulation to mechanical perturbation at individual leg joints and at the whole body. The immediate changes in muscle activations of the model are compared to those of humans across different gait phases and disturbance magnitudes. Remarkably similar response trends for the majority of investigated muscles and experimental conditions reinforce the plausibility of the reflex circuits of the model. However, the model's responses lack in amplitude for two experiments with whole body disturbances suggesting that in these cases the proposed reflex circuits need to be amplified by additional control structures such as location-specific cutaneous reflexes. A model that captures these selective amplifications would be able to explain both steady and reactive spinal control of human locomotion. Neuromechanical simulations that investigate hypothesized control models are complementary to gait experiments in better understanding the control of human locomotion.

Modular neuromuscular control of human locomotion by central pattern generator

The central pattern generators (CPG) in the spinal cord are thought to be responsible for producing the rhythmic motor patterns during rhythmic activities. For locomotor tasks, this involves much complexity, due to a redundant system of muscle actuators with a large number of highly nonlinear muscles. This study proposes a reduced neural control strategy for the CPG, based on modular organization of the co-active muscles, i.e., muscle synergies. Four synergies were extracted from the EMG data of the major leg muscles of two subjects, during two gait trials each, using non-negative matrix factorization algorithm. A Matsuoka׳s four-neuron CPG model with mutual inhibition, was utilized to generate the rhythmic activation patterns of the muscle synergies, using the hip flexion angle and foot contact force information from the sensory afferents as inputs. The model parameters were tuned using the experimental data of one gait trial, which resulted in a good fitting accuracy (RMSEs between 0.0491 and 0.1399) between the simulation and experimental synergy activations. The model׳s performance was then assessed by comparing its predictions for the activation patterns of the individual leg muscles during locomotion with the relevant EMG data. Results indicated that the characteristic features of the complex activation patterns of the muscles were well reproduced by the model for different gait trials and subjects. In general, the CPG- and muscle synergy-based model was promising in view of its simple architecture, yet extensive potentials for neuromuscular control, e.g., resolving redundancies, distributed and fast control, and modulation of locomotion by simple control signals.

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.

Humans and animals tune their walking rhythms when motion is disturbed, such that they hesitate before making the transition from stance to swing phase. The effectiveness of rhythm control for stability has also been shown, and thus the elucidation of rhythm responses is important to understanding human strategies for walking control. In this research, how and when humans change their walking rhythm in response to disturbance is analyzed over the complete walking cycle. Phase response of human walking has previously been estimated by pulling the swing leg. The problem with this perturbation is that it hardly disturbs the stance leg, so here we apply the perturbation by changing floor velocity. However, perturbation from the floor yields another problem in that it weakly influences the swing leg, decreasing the precision of the PRC. The present research tackles this problem by introducing a new method for identifying rhythm characteristics by use of high-frequency perturbation, which allows us to obtain results with clear temporal resolution. We found that the human walking rhythm changes by lengthening the touch-down and mid-single support phases. These phase responses are compared with neural mechanisms for rhythm control, and relevance to the cutaneous and proprioceptive originated responses is shown.

Neuromusculoskeletal models based on the muscle synergy hypothesis for the investigation of adaptive motor control in locomotion via sensory-motor coordination

Humans and animals walk adaptively in diverse situations by skillfully manipulating their complicated and redundant musculoskeletal systems. From an analysis of measured electromyographic (EMG) data, it appears that despite complicated spatiotemporal properties, muscle activation patterns can be explained by a low dimensional spatiotemporal structure. More specifically, they can be accounted for by the combination of a small number of basic activation patterns. The basic patterns and distribution weights indicate temporal and spatial structures, respectively, and the weights show the muscle sets that are activated synchronously. In addition, various locomotor behaviors have similar low dimensional structures and major differences appear in the basic patterns. These analysis results suggest that neural systems use muscle group combinations to solve motor control redundancy problems (muscle synergy hypothesis) and manipulate those basic patterns to create various locomotor functions. However, it remains unclear how the neural system controls such muscle groups and basic patterns through neuromechanical interactions in order to achieve adaptive locomotor behavior. This paper reviews simulation studies that explored adaptive motor control in locomotion via sensory-motor coordination using neuromusculoskeletal models based on the muscle synergy hypothesis. Herein, the neural mechanism in motor control related to the muscle synergy for adaptive locomotion and a potential muscle synergy analysis method including neuromusculoskeletal modeling for motor impairments and rehabilitation are discussed.

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.

Visually guided gait modifications for stepping over an obstacle: a bio-inspired approach

There is an increasing interest in conceiving robotic systems that are able to move and act in an unstructured and not predefined environment, for which autonomy and adaptability are crucial features. In nature, animals are autonomous biological systems, which often serve as bio-inspiration models, not only for their physical and mechanical properties, but also their control structures that enable adaptability and autonomy-for which learning is (at least) partially responsible. This work proposes a system which seeks to enable a quadruped robot to online learn to detect and to avoid stumbling on an obstacle in its path. The detection relies in a forward internal model that estimates the robot's perceptive information by exploring the locomotion repetitive nature. The system adapts the locomotion in order to place the robot optimally before attempting to step over the obstacle, avoiding any stumbling. Locomotion adaptation is achieved by changing control parameters of a central pattern generator (CPG)-based locomotion controller. The mechanism learns the necessary alterations to the stride length in order to adapt the locomotion by changing the required CPG parameter. Both learning tasks occur online and together define a sensorimotor map, which enables the robot to learn to step over the obstacle in its path. Simulation results show the feasibility of the proposed approach.

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.

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.

From spinal central pattern generators to cortical network: integrated BCI for walking rehabilitation

Success in locomotor rehabilitation programs can be improved with the use of brain-computer interfaces (BCIs). Although a wealth of research has demonstrated that locomotion is largely controlled by spinal mechanisms, the brain is of utmost importance in monitoring locomotor patterns and therefore contains information regarding central pattern generation functioning. In addition, there is also a tight coordination between the upper and lower limbs, which can also be useful in controlling locomotion. The current paper critically investigates different approaches that are applicable to this field: the use of electroencephalogram (EEG), upper limb electromyogram (EMG), or a hybrid of the two neurophysiological signals to control assistive exoskeletons used in locomotion based on programmable central pattern generators (PCPGs) or dynamic recurrent neural networks (DRNNs). Plantar surface tactile stimulation devices combined with virtual reality may provide the sensation of walking while in a supine position for use of training brain signals generated during locomotion. These methods may exploit mechanisms of brain plasticity and assist in the neurorehabilitation of gait in a variety of clinical conditions, including stroke, spinal trauma, multiple sclerosis, and cerebral palsy.