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The "infinitesimal phase response curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences in general and neuroscience in particular. We make the observation that the PRC with respect to a coordinate v actually depends on the choice of other coordinates. As a consequence, a complete delay embedding reconstruction of the dynamics using v which would allow phase to be computed still does not allow the v PRC to be computed. We give a coordinate-free definition of the PRC making this observation obvious. This leads to an experimental protocol: first collect an appropriate ensemble of measurements by intermittently controlling neuron voltage. Then, for any suitable current carrier dynamic postulated, we show how the ensemble can be used to compute the voltage PRC with that current carrier. The approach extends to many oscillators measured and controlled through a subset of their coordinates. [ABSTRACT FROM AUTHOR]

Movement is one of the essential characteristics of living beings. Despite the diversity of animal species and the apparent differences, standard features exist between their movement systems that follow a particular pattern. The movements can mainly be divided into discrete and rhythmic categories controlled by the central nervous system. Scientists usually consider these two types of motion separately in the control system and use different methods and resources to produce and model them. Proposing a unified and comprehensive model for generating and controlling rhythmic and discrete movement with the same control system is more valuable, albeit challenging. This is essential because such a model would address a fundamental problem in the field of motor control, offering a holistic solution to understanding how living beings generate and control movement. A unified model could revolutionize various fields, including robotics, rehabilitation, and neuroscience, by providing a versatile framework applicable to various applications. In this study, we employed the Hodgkin-Huxley (HH) equations in our computational model; their suitability lies in their ability to capture the intricate dynamics of neural oscillations and the behavior of neural networks, making them an ideal choice for our investigation. Our comprehensive analysis of the model, factors influencing motion, and oscillation revealed crucial insights. We found that supraspinal input and motor neuron feedback, as the key motor control parameters, play pivotal roles in generating and controlling rhythmic and discrete movements. These findings contribute to our understanding of how the nervous system orchestrates both types of motion within a single framework. Developing a neuromechanical model capable of creating rhythmic and discrete movements holds promising implications. This research can potentially advance fields such as robotics, biomechanics, and rehabilitation by providing a unified framework for motor control. Moreover, understanding the switching mechanism between rhythmic and discrete states could lead to innovative strategies for designing more versatile and adaptive robotic systems and improving rehabilitation protocols for individuals with motor impairments. [ABSTRACT FROM AUTHOR]

The study on neuromorphic oscillation behaviors and their oscillators have been considered as one of the most straightforward approaches to mimic some biological neurons via the configured nonlinear memristive equivalent circuits. Also, neuromorphic oscillation is one classical oscillation phenomenon, both the frequency response and zero-pole analysis could be clearly regarded as a complete description of the sinusoidal oscillation behavior for a nonlinear circuit. As one of the most classical memristors, Chua corsage memristor (CCM) is so famous to exhibit chaotic oscillation and neuromorphic dynamics due to its locally active and edge of chaos. However, the parasitic phenomena in the practical circuits are unique and tiny but existed as one of the inherent characteristics, which could lead to some unexpected results. Even a pretty small perturbation may heavily affect the quality of the entire system. In this paper, one modified CCM with the parasitic parameter (named $g_{p}$ ) is proposed. Then, some unique and unusual phenomena are captured and analyzed. Moreover, the analysis on the distributions for the locally-active domains (LADs) and edge of chaos are presented. Furthermore, one small-signal equivalent circuit with a positive capacitance is introduced, as well as its impedance and admittance functions. Also, both types of neuromorphic oscillators are captured and observed via external inductor and capacitor, respectively. Finally, the applications in neural networks are explored, which herald the proposed model could be more suitable to transmit the mental, physical fatigue, memory load and closer to simulating the actual neuromorphic systems.

Neural oscillators, which are a mathematical model of a central pattern generator, have been used to investigate human gait and control mobile robots. A typical neural oscillator uses two neurons that mutually inhibit each other’s activity. The exact orbitally-stable conditions of the neural activity of neural oscillators without external signals have been reported. However, the behavior of neural oscillators with external signals is unclear because their neural activity depends on the external signals, which have many types. In this study, for simplicity, external signals were regarded as a sinusoidal wave with a period Tex and an amplitude Aex. The connectivity aij, ratio for time constants τz/τx, and fatigue coefficient b were changed for neurons i and j, while Tex and Aex were changed for external signals. The orbit-stability of the output signals from a neuron was decided based on the transient time (≦ 3 s) and the duration (≧ 30 s). The period Tout and the amplitude Aout of the output signals were evaluated. Tout had discrete values of Tex, 2Tex, or 0.5Tex or was non-orbitally-stable (value of 0). When Aex was greater than or equal to ui, the neural oscillator became synchronized. For a small Tex, some combinations of τz/τx and aij values led to instability. For a large Tex, some combinations of b and aij values led to instability. In contrast to Tout, the amplitude Aout of the output signal showed continuous changes depending on τz/τx, b, and aij. The amplitude Aout could be expressed as the sum of ui and Aex. Aout was not significantly affected by τz/τx but decreased with decreasing b.

We celebrate the 60th anniversary of Biological Cybernetics. It has also been 30 years since "Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment" was published in Biological Cybernetics (Taga et al. in Biol Cybern 65(3):147–159, 1991). I would like to look back on the creation of this paper and discuss its subsequent development and future perspectives. [ABSTRACT FROM AUTHOR]

In this paper, construction of a newly designed snake robot is suggested along with the algorithm for generation of different rhythmic motions. The proposed robot system has modular structures with extendable length. It is subdivided into body, neck, head and tail modules. Each body module has two rotary motors to generate pitch and yaw motions of the snake robot. A linear actuator is also installed inside each body module in order to change the length of robot. The neck module in the robot is provided with two rotary motors to make the spherical motion of head module. Neural oscillator based central pattern generators (CPG) are used to produce rhythmic patterns for various snake robot movements, for example, serpentine, side-winding, two-step-concertina and four-step-concertina motions are generated in the snake robot using the proposed CPG algorithm. For serpentine motion, the body of robot is bent to form the planar sinusoidal waveform using whole body modules on the ground. To generate side-winding motion, the robot body is bent in such a way that it makes two dimensional sinusoidal waveform and only a few points of its body make contacts with the ground. By using the CPG algorithm, these contact points are propagated from tail to head, and the robot is ultimately moved along one side. In concertina motion, the body is sequentially pushed forward in steps from tail to head using the proposed algorithm. Finally several experiments are conducted on a laboratory floor in order to confirm the authenticity of robot design and CPG algorithm so that the comparison between different motions can be achieved. [ABSTRACT FROM AUTHOR]

The prediction of the joint angle position, especially during tremor bursts, can be useful for detecting, tracking, and forecasting tremors. Thus, this research proposes a new model for predicting the wrist joint position during rhythmic bursts and inter-burst intervals. Since a tremor is an approximately rhythmic and roughly sinusoidal movement, neural oscillators have been selected to underlie the proposed model. Two neural oscillators were adopted. Electromyogram (EMG) signals were recorded from the extensor carpi radialis and flexor carpi radialis muscles concurrent with the joint angle signals of a stroke subject in an arm constant-posture. The output frequency of each oscillator was equal to the frequency corresponding to the maximum value of power spectrum related to the rhythmic wrist joint angle signals which had been recorded during a postural tremor. The phase shift between the outputs of the two oscillators was equal to the phase shift between the muscle activation of the wrist flexor and extensor muscles. The difference between the two oscillators′ output signals was considered the main pattern. Along with a proportional compensator, an adaptive neural controller has adjusted the amplitude of the main pattern in such a way so as to minimize the wrist joint prediction error during a stroke patient′s tremor burst and a healthy subject′s generated artificial tremor. In regard to the range of wrist joint movement during the observed rhythmic motions, a calculated prediction error is deemed acceptable.

For the crawl stroke in swimming, it is important that the stroke made by the upper limbs and the flutter kick made by the lower limbs are well coordinated in order to enhance swimming performance. However, the training method to acquire the appropriate flutter kick timing has not been sufficiently established. In the present study, a biofeedback training system for swimmers to acquire appropriate kick timing was proposed. In this system, the most difficult and important part is the estimation of the appropriate kick timing. Therefore, the objective of this study was to develop a kick timing estimation algorithm in the crawl stroke for biofeedback training system using neural oscillators. First, a CPG network which outputs the kick estimation timing according to the input was constructed. In order to synchronize the roll angle in the CPG network with the actual one measured by a sensor, a special algorithm to change the cycle of the oscillation for the CPG network was introduced. Validation for the output of sinusoidal input accompanying sudden change in cycle was examined. It was found that the output signal for the roll tracked the input signal well, despite the sudden change in cycle. Validation for the actual input obtained in the experiment was next examined. It was found that the output from the CPG network was sufficiently consistent with the experimental values, suggesting sufficient performance of the proposed estimation algorithm.

The involvement of glial cells in the regulation of physiological functions is being increasingly recognized, yet their role in plasticity of neural oscillators has remained largely elusive. An excellent model system to address the latter function is the pacemaker nucleus of the weakly electric fish, Apteronotus leptorhynchus. This brainstem oscillator drives the fish's electric organ discharge in a one-to-one fashion, with median frequencies of 880 Hz in males and 740 Hz in females. Morphometric analysis of the pacemaker nucleus has shown that astrocytes outnumber mature neurons seven-fold, and oscillator neurons even 200-fold. A similar dominance of astrocytes occurs among the adult-born cells that differentiate into glia and neurons. The astrocytes form a dense meshwork of cells interconnected by gap junctions. The degree of association of astrocytic fibers with the neural oscillator cells, and the gap-junction coupling between individual astrocytes, exhibit a sexual dimorphism, which parallels the sexual dimorphisms in the output frequency of the pacemaker nucleus, and ultimately in the electric organ discharge of the fish. It is hypothesized that the dynamics in astroglial structure mediate differences in the capacity to buffer potassium, which increases during the generation of action potentials. These differences, in turn, affect the excitability of the neural oscillator cells, and thus the output frequency of the pacemaker nucleus. Comparison of the pacemaker nucleus with other brain oscillators suggests that modulation of the output activity is one of the chief functions of the interaction of glia with the neural oscillator cells.

The objective of this study was to propose a CPG network which can generate the swimming motion of the crawl stroke. First, the CPG network for legs performing a flutter kick was constructed by connecting the neural oscillators for the leg joints. The flutter kick motion was successfully generated by the proposed CPG network. The propulsion by the generated flutter kick motion was confirmed by the simulation of the swimming movement. Next, the CPG network for both the arms and legs were constructed, in which the neural oscillator for the arms initiated the trigger signal to start the prescribed stroke motion. By changing the intrinsic cycle of the neural oscillators for the legs, both six- and two-beat crawls could be realized. It was also found that a stable region with respect to the relationship between the intrinsic cycles of the neural oscillators for the arms and legs certainly existed for the six-beat crawl, although the intrinsic cycles of the arms were three times longer than those of the legs in this case. The propulsion by the generated swimming motion was confirmed by the simulation of the swimming movement both for the six- and two-beat crawls. Finally, the roll angle of the swimmer was fed back into the CPG network in order to restore the balance in the roll direction. Restoring the balance in the roll direction was successfully realized by the proposed feedback algorithm. The resultant motion showed a complicated behavior, such as skipping strokes.

This study proposes a neural oscillator-based brain–computer interface (BCI) that controls a bipedal neuromusculoskeletal (NMS) model by inputting electroencephalogram (EEG) signals. In this BCI system, while the bipedal NMS system realizes bipedal locomotion through internal entrainment among neural oscillators and a musculoskeletal system, the locomotion of the system is controlled via external entrainment of the neural oscillators to the external input of EEG signals. As the first step in developing the neural oscillator-based BCI controlling a bipedal NMS model, exploratory numerical simulations were conducted to investigate the behavior of the proposed BCI when sinusoidal waves and alpha waves were inputted. The following tendencies were observed: (a) inputting sinusoidal waves with small amplitudes and high frequencies did not affect the natural walking behavior of the bipedal NMS model that was generated by including only offset values in the external input, (b) inputting sinusoidal waves with small amplitudes and low frequencies disturbed and decelerated the walking behavior, (c) inputting sinusoidal waves with large amplitudes accelerated the walking behavior, (d) inputting sinusoidal waves with large amplitudes and a particular frequency changed walking behavior to running behavior, (e) changing the external input of alpha waves between an eyes-open condition and an eyes-closed condition successfully changed the walking behavior. The eyes-open condition led to faster walking compared with the eyes-closed condition.

Taxis behaviour in Drosophila larva is thought to consist of distinct control mechanisms triggering specific actions. Here, we support a simpler hypothesis: that taxis results from direct sensory modulation of continuous lateral oscillations of the anterior body, sparing the need for ‘action selection’. Our analysis of larvae motion reveals a rhythmic, continuous lateral oscillation of the anterior body, encompassing all head-sweeps, small or large, without breaking the oscillatory rhythm. Further, we show that an agent-model that embeds this hypothesis reproduces a surprising number of taxis signatures observed in larvae. Also, by coupling the sensory input to a neural oscillator in continuous time, we show that the mechanism is robust and biologically plausible. The mechanism provides a simple architecture for combining information across modalities, and explaining how learnt associations modulate taxis. We discuss the results in the light of larval neural circuitry and make testable predictions.

This study proposes a neural oscillator-based brain-computer interface (BCI) that controls a bipedal neuromusculoskeletal (NMS) model by inputting electroencephalogram (EEG) signals. In this BCI system, while the bipedal NMS system realizes bipedal locomotion through internal entrainment among neural oscillators and a musculoskeletal system, the locomotion of the system is controlled via external entrainment of the neural oscillators to the external input of EEG signals. As the first step in developing the neural oscillator-based BCI controlling a bipedal NMS model, exploratory numerical simulations were conducted to investigate the behavior of the proposed BCI when sinusoidal waves and alpha waves were inputted. The following tendencies were observed: (a) inputting sinusoidal waves with small amplitudes and high frequencies did not affect the natural walking behavior of the bipedal NMS model that was generated by including only offset values in the external input, (b) inputting sinusoidal waves with small amplitudes and low frequencies disturbed and decelerated the walking behavior, (c) inputting sinusoidal waves with large amplitudes accelerated the walking behavior, (d) inputting sinusoidal waves with large amplitudes and a particular frequency changed walking behavior to running behavior, (e) changing the external input of alpha waves between an eyes-open condition and an eyes-closed condition successfully changed the walking behavior. The eyes-open condition led to faster walking compared with the eyes-closed condition. [ABSTRACT FROM AUTHOR]

This paper proposes the control system for 3-D locomotion of a humanoid biped robot based on a biological approach. The muscular system in the human body and the neural oscillator for generating locomotion signals are adapted in this paper. We extend the neuro-locomotion system for modeling a multiple neuron system, where motoric neurons represent the muscular system and sensoric neurons represent the sensor system inside the human body. The output signals from coupled neurons representing the angle joint level are controlled by gain neurons that represent the energy burst for driving the joint in each motor. The direction and the length of step in robot locomotion can be adjusted by command neurons. In order to form the locomotion pattern, we apply multiobjective evolutionary computation to solve the multiobjective problem when optimizing synapse weights between the motoric neurons. We use recurrent neural network (RNN) for the stabilization system required for supporting locomotion. RNN generates a dynamic weight synapse value between the sensoric neuron and the motoric neuron. The effectiveness of our system is demonstrated in open dynamic engine computer simulation and in a real robot application that has 12 degrees of freedom (DoFs) in legs and four DoFs in hands. [ABSTRACT FROM PUBLISHER]

The prediction of the joint angle position, especially during tremor bursts, can be useful for detecting, tracking, and forecasting tremors. Thus, this research proposes a new model for predicting the wrist joint position during rhythmic bursts and inter-burst intervals. Since a tremor is an approximately rhythmic and roughly sinusoidal movement, neural oscillators have been selected to underlie the proposed model. Two neural oscillators were adopted. Electromyogram (EMG) signals were recorded from the extensor carpi radialis and flexor carpi radialis muscles concurrent with the joint angle signals of a stroke subject in an arm constant-posture. The output frequency of each oscillator was equal to the frequency corresponding to the maximum value of power spectrum related to the rhythmic wrist joint angle signals which had been recorded during a postural tremor. The phase shift between the outputs of the two oscillators was equal to the phase shift between the muscle activation of the wrist flexor and extensor muscles. The difference between the two oscillators' output signals was considered the main pattern. Along with a proportional compensator, an adaptive neural controller has adjusted the amplitude of the main pattern in such a way so as to minimize the wrist joint prediction error during a stroke patient's tremor burst and a healthy subject's generated artificial tremor. In regard to the range of wrist joint movement during the observed rhythmic motions, a calculated prediction error is deemed acceptable. [ABSTRACT FROM AUTHOR]

This paper contributes to the understanding and implementation of different types of locomotion in a snake-like robot by using a proposed unified neural oscillator model as central pattern generator (CPG). A neural oscillator network is suggested so that several rhythmic movements can be generated in order to mimic the actual snake movements on land. The unified coupled neural oscillators in the network provide the desired orientation and displacement for the snake-like robot and they are applied to the different types of snake locomotion by just altering some of the parameters proposed in the paper. The design of snake-like robot, consisting of a series of wheeled links (links with active wheels) connected with each other using the passive prismatic and revolute joints, is also suggested in the paper. The passive prismatic joints facilitate the change of lengths of wheel-less links and in this way the robot can be elongated as well as shortened. In this paper the serpentine, rectilinear, and concertina types of actual snake locomotion are realized, through simulation studies, by using the unified neural oscillator model proposed for the snake-like robots. [ABSTRACT FROM AUTHOR]

Purpose - This paper aims to use the Matsuoka's neural oscillators as the basic units of central pattern generator (CPG), and to offer a new CPG architecture consisting of a dual neural CPG of circular three links responsible for oscillator phase adjustment, to which an external neural oscillator is added, which is responsible for oscillator amplitude adjustment, to control foot depth to balance itself when treading on an obstacle. Design/methodology/approach - It is equipped with a triaxial accelerometer and a triaxial gyroscope to obtain a real-time robot attitude, and to disintegrate the foot tilt in each direction as feedback signals to CPG to restore the robot' horizontal attitude on an uneven terrain. The CPG controller is a distributed control method, with each foot controller consisting of a group of reciprocally coupling neural oscillators and sensors to generate different locomotion by different coupling patterns. Findings - The experiment results indicated that the gait design method succeeded in enabling a steady hexapod walking on a rugged terrain, the mode of response is such that adjustments can only be made when the tilt occurs. Practical implications - The overall control mechanism uses individual foot tilts as the feedback signal input to the neural oscillators to change the amplitude and compare against the reference oscillators of fixed amplitude to generate the foot height reference signals that can balance the body, and then convert the control signals, through a trajectory generator, to foot trajectories from which the actual rotation angle of servo motors can be obtained through inverse kinematics to achieve the effect of restoring the balance when traveling. Originality/value - The controller design based on the bionic CPG model has the ability to restore its balance when its body tilts. In addition to the model's ability to control locomotion, from the response waveforms of this experiment, it can also be noticed that it can control the foot depth to balance itself when treading on an obstacle, and it can adapt to a changing environment. When the obstacle is removed, the robot can quickly regain its balance. [ABSTRACT FROM AUTHOR]

Prior to developing the wearable walking assistant robot that supports walking for hemiplegia patients, a neural oscillator, a type of CPG (central pattern generation), was applied to 2-DOF double pendulum, which can replace the leg of a robot. The walking pattern generation method was proposed using the gait pattern of the non-affected side of hemiplegia patients. Because it is difficult for hemiplegia patients to distinguish the intended action signal of the patient wearing a robot on their affected side, we had to utilize a limited amount of information to get the maximum effect. We needed an effective solution for robot control in an outside environment where many unknown disturbances exist. In order to deal with these two problems, we used a nonlinear oscillator with a double pendulum as a test bed to explore the possibility of producing a robot walking pattern. [ABSTRACT FROM AUTHOR]

Sexually dimorphic behaviors develop under the influence of sex steroids, which induce reversible changes in the underlying neural network of the brain. However, little is known about the proteins that mediate these activational effects of sex steroids. Here, we used a proteomics approach for large-scale identification of proteins involved in the development of a sexually dimorphic behavior, the electric organ discharge of brown ghost knifefish, Apteronotus leptorhynchus. In this weakly electric fish, the discharge frequency is controlled by the medullary pacemaker nucleus and is higher in males than in females. After lowering the discharge frequency by chronic administration of -estradiol, 2-dimensional difference gel electrophoresis revealed 62 proteins spots in tissue samples from the pacemaker nucleus that exhibited significant changes in abundance of >1.5-fold. The 20 identified protein spots indicated, among others, a potential involvement of astrocytes in the establishment of the behavioral dimorphism. Indeed, immunohistochemical analysis demonstrated higher expression of the astrocytic marker protein GFAP and increased gapjunction coupling between astrocytes in females compared with males. We hypothesize that changes in the size of the glial syncytium, glial coupling, and/or number of glia-specific potassium channels lead to alterations in the firing frequency of the pacemaker nucleus via a mechanism mediating the uptake of extracellular potassium ions from the extracellular space. [ABSTRACT FROM AUTHOR]

Since neural oscillator based control methods can generate rhythmic motion without information on system dynamics, they can be a promising alternative to traditional motion planning based control approaches. However, for field application, they still need to be robust against unexpected forces or changes in environments so as to be able to generate "natural motion" like most biological systems. In this study a biologically inspired control algorithm that combines neural oscillators and virtual force is proposed. This work gives the condition with respect to parameters tuning to stably activate the neural oscillators. This is helpful to achieve motion adaptability to environmental changes keeping the motion repeatability. He efficacy and efficiency of the proposed methods are tested in the control of a planar three-linkage robotic arm. It is shown that the proposed controller generates a given circular path stably and repeatedly, even with unexpected contact with a wall. The adaptivity of motion control is also tested in control of a robotic arm with redundant degrees of freedom. The proposed control algorithm works throughout the simulations and experiments. [ABSTRACT FROM AUTHOR]

Biologically inspired snake robots have been widely studied for their various motion patterns. Most research has focused on the design of a controller for a given motion pattern. However, relatively limited work appears to have been done on the design of a controller for self-adaptive locomotion. In this brief, we add sensory inputs to a control system in order to investigate collision avoidance in a snake robot using a neural controller based on central pattern generator. From an analysis of the steering mechanism during serpentine locomotion, we derive a mathematical model of the joint configuration and the steering angle. In a neural oscillator network, steering control can be achieved via the proposed amplitude modulation method by modulating the neural oscillation parameters. A head-navigated motion pattern is employed to allow the range sensors to accurately detect obstacles for collision avoidance. Through the head-navigated locomotion, the head of the snake robot can be controlled to keep the orientation the same as the motion direction. The proposed control method is experimentally verified by application to the SR-I snake robot. [ABSTRACT FROM AUTHOR]

In most of our daily motion tasks, the coordination between limbs is very crucial for successful execution of the tasks. In this paper, coordination among oscillators controlling in Cartesian space is studied to control bipedal walking. In our method, phase adjustment among oscillators is considered as one of the key issues to achieve coordination. A new phase adjustment method is proposed. With this method, an oscillator is able to coordinate other oscillators and maintain a desired phase relationship. This property is important for the walking control especially when external perturbations are given. To simplify the relationship between oscillators in a central pattern generator (CPG), a hierarchical CPG structure is adopted, where a main oscillator will be used to adjust other oscillators. In the simulation, the walking motion controlled by the CPG controller converges to a stable pattern even with external perturbations. We have implemented the controller in both the simulation model and real hardware robot. [ABSTRACT FROM PUBLISHER]

We derive a formula that relates the spike-triggered covariance (STC) to the phase resetting curve (PRC) of a neural oscillator. We use this to show how changes in the shape of the PRC alter the sensitivity of the neuron to different stimulus features, which are the eigenvectors of the STC. We compute the PRC and STC for some biophysical models. We compare the STCs and their spectral properties for a two-parameter family of PRCs. Surprisingly, the skew of the PRC has a larger effect on the spectrum and shape of the STC than does the bimodality of the PRC (which plays a large role in synchronization properties). Finally, we relate the STC directly to the spike-triggered average and apply this theory to an olfactory bulb mitral cell recording. [ABSTRACT FROM AUTHOR]

We explore patterns in the spike timing of neurons receiving periodic inputs, with an emphasis on stable characteristics which are realized in both models and in-vitro whole-cell recordings. We report on whole-cell recordings of pyramidal CA1 cells from rat hippocampus and entorhinal cortex and compare this data to model simulations. Cells were injected with a constant current to induce a steady firing rate and then a modest rhythm was added which altered the spike times and their corresponding phases relative to the rhythm. For both experiment and theory the relationship between consecutive spike phases is characterized by a probability distribution with peaks concentrated near a one-dimensional firing map. As is well-known, stable fixed points of this map correspond to the neuron phase-locking to the rhythm. We show that the interaction between noise and sufficiently steep maps can also cause a new kind of spike-time organization, in which consecutive spike time pairs organize into discrete clusters, with transitions between these clusters proceeding in a fixed sequence. This structure is not just a vestige of the noise-free dynamics. This slow dynamics and temporal organization in the relationship between consecutive spike phases is not evident in either the neuron's voltage traces or single phase or interspike interval histograms. Furthermore, the consecutive spike relationship is also evident in consecutive ISIs, and hence this ordering can be observed without detailed knowledge of the rhythm (e.g. without concurrent LFP recordings). [ABSTRACT FROM AUTHOR]

Despite recent major advances in computational power and control algorithms, the stable and robust control of a bipedal robot is still a challenging issue due to the complexity and high nonlinearity of robot dynamics. To address the issue an efficient and powerful alternative based on a biologically inspired control framework employing neural oscillators is proposed and tested. In a numerical test the virtual force controller combined with the neural oscillator of a humanoid robot generated rhythmic control signals and stable bipedal locomotion when coupled with proper impedance components. The entrainment nature inherent to neural oscillators also achieved stable and robust walking even in the presence of unexpected disturbances, in that the centre of mass (COM) was successfully kept in phase with the zero moment point (ZMP) input trajectory. The efficiency of the proposed control scheme is discussed alongside simulation results. [ABSTRACT FROM AUTHOR]

Abstract: Postural responses are usually investigated as reflexes. Several trials are averaged, and trial-to-trial variations are interpreted as noise. Several studies providing single-trial data plots revealed oscillations that may be cancelled out in averaged time series. Variations between single trials may also be interpreted as a consequence of changed dynamic properties of the neural circuitries. Therefore, we propose a Matsuoka oscillator model to describe single-trial postural responses to external perturbations. The applicability of the model was demonstrated by a comparison between simulations and experimental electromyographic (EMG) data. Vertical force perturbations of durations 0.4s and 0.2s were applied via a handle to 10 subjects. Handle force was used as model input, and EMG data from the external oblique muscles was compared with simulation output. Model coefficients were optimized by a least-squares algorithm. The optimization produced a good similarity between simulation and experimental data with determination coefficients of and greater. Furthermore, as a model validation, the model coefficients were used to predict other perturbation trials with similarities between predictions and respective EMG data of about , which was in the range of trial-to-trial EMG variability. The observed oscillations are assumed to originate from the central nervous system with changes in the neural circuitries between trials. Hence, the oscillations in single trial responses which are usually regarded as noise might be generated by the dynamics of a neural oscillator. [Copyright &y& Elsevier]

Abstract: A new synchronization-based trajectory generation method is proposed for a robotic suit that is designed to assist walking by supporting the hip joints. Neural oscillators are connected to each hip joint of the robotic suit to synchronize the suit’s movement with the human user’s movement (outer synchronization). At the same time, mutual inhibition is incorporated between the neural oscillators on the left and right hip joints of the suit to help maintain a human-gait-like anti-phase relationship (inner inhibition). We developed a two-degree-of-freedom robotic suit, which consists of two actuators located where the human hip joints are. Each actuator has a built-in torque sensor, which measures the mutual joint torque generated if any difference arises between the movement of a user and that of the suit. The mutual joint torque serves as input to neural oscillators, which control each actuator of the robotic suit through outer synchronization with the mutual joint torque and inner inhibition. The inhibitory weight, used to adjust the inhibitory strength between neural oscillators, is designed in a series of simulations. We conducted walking experiments to show the validity of our proposal for walking assistance of the robotic suit with mutual inhibition between neural oscillators. [Copyright &y& Elsevier]

Detrusor-sphincter dyssynergia (DSD) is a condition in which the urethral outlet actively contracts during a detrusor contraction. This is most often caused by isolated and complete suprasacral spinal cord lesions and can be manifested by external urethral sphincter (EUS) or bladder neck/proximal urethral smooth muscle contraction, or both, reflexly generated against a hyperreflexive detrusor contraction. The resultant generation of high intravesical pressures, if left untreated, can cause damage to the bladder itself and result in ureteral reflux, hydronephrosis, and renal failure. Current therapies solve some problems but do not address the underlying pathology. Thus, understanding the pathophysiology underlying EUS DSD remains a priority in the urologic care of patients with suprasacral transverse spinal myelopathies. This review examines data and concepts from animals and humans to elucidate the pathophysiology of EUS DSD. [ABSTRACT FROM AUTHOR]

Inspired by the temporal correlation theory of brain functions, researchers have presented a number of neural oscillator networks to implement visual scene segmentation problems. Recently, it is shown that many biological neural networks are typical small-world networks. In this paper, we propose and investigate two small-world models derived from the well-known LEGION (locally excitatory and globally inhibitory oscillator network) model. To form a small-world network, we add a proper proportion of unidirectional shortcuts (random long-range connections) to the original LEGION model. With local connections and shortcuts, the neural oscillators can not only communicate with neighbors but also exchange phase information with remote partners. Model 1 introduces excitatory shortcuts to enhance the synchronization within an oscillator group representing the same object. Model 2 goes further to replace the global inhibitor with a sparse set of inhibitory shortcuts. Simulation results indicate that the proposed small-world models could achieve synchronization faster than the original LEGION model and are more likely to bind disconnected image regions belonging together. In addition, we argue that these two models are more biologically plausible. [ABSTRACT FROM AUTHOR]

Abstract: This paper explores the possibility to adopt neural oscillators for pathological tremor attenuation. The objective is to suppress the tremor of a single joint of upper limb via functional electrical stimulation (FES). A biologically inspired neural oscillator is developed, which generates the anti-tremor rhythmic stimulation patterns to stimulate a pair of antagonist muscles. Surface electromyographic (EMG) signal is used to entrain the neural oscillator reciprocally and shape the stimulation pattern adaptively. The neural oscillator serves as an adaptive feedforward controller, which is combined with a feedback regulator. Simulation study is performed on musculoskeletal models of wrist joint and elbow joint separately, and some promising results are presented. [ABSTRACT FROM AUTHOR]

Distributed synchronization is known to occur at several scales in the brain, and has been suggested as playing a key functional role in perceptual grouping. State-of-the-art visual grouping algorithms, however, seem to give comparatively little attention to neural synchronization analogies. Based on the framework of concurrent synchronization of dynamical systems. simple networks of neural oscillators coupled with diffusive connections are proposed to solve visual grouping problems. The key idea is to embed the desired grouping properties in the choice of the diffusive couplings, so that synchronization of oscillators within each group indicates perceptual grouping of the underlying stimulative atoms, while desynchronization between groups corresponds to group segregation. Compared with state-of-the-art approaches, the same algorithm is shown to achieve promising results on several classical visual grouping problems, including point clustering, contour integration, and image segmentation. [ABSTRACT FROM AUTHOR]

This paper studies the mechanisms of ionic channels in neurons of lamprey central pattern generator (CPG), such as the N-methyl-D-aspartate (NMDA) receptor channel and the calcium-dependent potassium channel etc. The CPG properties on oscillation attributed to the ionic mechanisms are exploited. The conditions for oscillation, divergence, convergence and the guidelines on selection of the parameters are established. The effects of key parameters on CPG frequency and duty cycle are investigated. Mathematical analysis and simulation study is performed to verify these results. This study will potentially enhance the effective application of biological CPG model into engineering practice such as robotics. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the intrinsic relationship between energy consumption and neural information coding in local neural networks of the cerebral cortex is studied. The energy functions of a variety of membrane potential are obtained under some conditions of mutual coupling at both the supra-threshold and the sub-threshold states in a neural population. These energy functions can accurately reproduce excitatory postsynaptic potentials (EPSP), inhibitory postsynaptic potentials (IPSP), as well as an action potential, found in the experiments of neuro-electrophysiology. Recently, it has been proved that signal transmission and neuronal energetic demands are tightly coupled to information coding in the cerebral cortex in functional magnetic resonance imaging (fMRI) experiments. Therefore, the analytic results obtained in this paper show that the principle of energy coding is quite fundamental and is beneficial to the study of the important scientific problem as how the brain performs coding at the level of local neural networks. [Copyright &y& Elsevier]

Central Pattern Generator (CPG) is used in bipedal locomotion control to provide the basic rhythm signal for actuators. Generally, the CPG is composed of many neural oscillators coupled together. In this paper, the coordination between neural oscillators in CPG is studied to achieve robust rhythm motions. By using the entrainment property of the neural oscillator, we develop a method which uses the difference between oscillator's output and desired output to adjust the inner states of neural oscillators. In the simulation, a CPG structure with coordination between neural oscillators is used to control a 2D bipedal robot. The robot can walk continuously when several external forces are applied on the robot during walking. The method is also implemented on our humanoid robot NUSBIP-III ASLAN for the test of walking forward. With the coordination between neural oscillators, the CPG generated rhythmic and robust control signals which enable the robot to walk forward stably. [ABSTRACT FROM AUTHOR]

Abstract: We intend to apply Matsuoka neural oscillator into humanoid chewing robots to generate rhythmic actuation of central pattern generator (CPG) and adapt it for voluntary actuation due to sensory feedback. In this paper a single Matsuoka oscillator of two neurons is used for two phase-locked muscles (e.g. masseter and digastric muscles) or for a single robotic joint. To help design and tune the oscillator we have developed three graphical user interfaces (GUI) with aid of which the simulation, parameters’ influence and adaptation of the oscillator can be analysed and for specific pattern of muscle activities the oscillator can be selected. Discussions are made in relation to the experimentally confirmed EMG (electromyography) of muscle activities for various foods. A case study involving a jaw, driven by a couple of opening and closing muscles that are commanded by motoneurons is presented. The force of the muscles is described in nonlinear Hill model while the motoneuron for muscle activities is modelled in the oscillator. Simulations are performed to show the oscillator’s ability in generating and adapting its rhythmic outputs with respect to the chewing without food (i.e, EMG only for rhythmic muscle activities), with foods (i.e., EMG for rhythmic and additional muscle activities) and with crushable foods (to see how quickly the oscillator to reduce its force commands in order not to damage the teeth). Our work is also meaningful for brain-based control of assistive or rehabilitative devices and EMG-driven neuromusculoskeletal models. [Copyright &y& Elsevier]

We propose a new neural oscillator model to attain rhythmic movements of robotic arms that features enhanced entrainment property. It is known that neural oscillator networks could produce rhythmic commands efficiently and robustly under the changing task environment. However, when a quasi-periodic or non-periodic signal is inputted into the neural oscillator, even the most widely used Matsuoka’s neural oscillator (MNO) may not be entrained to the signal. Therefore, most existing neural oscillator models are only applicable to a particular situation, and if they are coupled to the joints of robotic arms, they may not be capable of achieving human-like rhythmic movement. In this paper, we perform simulations of rotating a crank by a two-link planar arm whose joints are coupled to the proposed entrainment-enhanced neural oscillator (EENO). Specifically, we demonstrate the excellence of EENO and compare it with that of MNO by optimizing their parameters based on simulated annealing (SA). In addition, we show an impressive capability of self-adaptation of EENO that enables the planar arm to make adaptive changes from a circular motion into an elliptical motion. To the authors’ knowledge, this study seems to be the first attempt to enable the oscillator-coupled robotic arm to track a desired trajectory interacting with the environment. [ABSTRACT FROM AUTHOR]

Biologically inspired control approaches based on central pattern generators (CPGs) with neural oscillators have been drawing much attention for the purpose of generating rhythmic motion for biped robots with human-like locomotion. This article describes the design of a neural-oscillator-based gait-rhythm generator using a network of Matsuoka oscillators to generate a walking pattern for biped robots. This includes the proper consideration of the oscillator’s parameters, such as a time constant for the adaptation rate, coupling factors for mutual inhibitory connections, etc., to obtain a stable and desirable response from the network. The article examines the characteristics of a CPG network with six oscillators, and the effect of assigning symmetrical and asymmetrical coupling coefficients among oscillators within the network structure under different possible inhibitions and excitations. The kinematics and dynamics of a five-link biped robot have been modeled, and its joints are actuated through simulation by the torques output from the neural rhythm generator to generate the trajectories for hip, knee, and ankle joints. The parameters of the neural oscillators are tuned to achieve flexible trajectories. The CPG-based control strategy is implemented and tested through a simulation. [ABSTRACT FROM AUTHOR]

Abstract: An artificial bionic neural network to control fish-robot locomotion is presented. The fish-robot, which is inspired from “Gymnarchus niloticus”, is modeled as a multi-joint dynamic system with parallel connections and composed of several motors. The principle of the central pattern generators (CPGs) governing the locomotion of fish is analyzed. An artificial neural network which has many comparability with the biological CPGs is designed to control the fish-robot. Experimental results of startup, stop, forward swimming and backward swimming show its validity and efficiency. [Copyright &y& Elsevier]

Neural oscillator is derived from the central pattern generator (CPG) in the biological nervous system. It can generate motor patterns for the rhythmic movements. Neural oscillator is widely adopted in biomimic robot and humanoid robot for different types of rhythmic movement controls such as swimming and walking. Theoretical analysis about neural oscillator toward biomimic robot control is presented in this paper. The methods adopted here include stability theory, describing function, and piecewise linear analysis. Some important properties of the neural oscillator, such as the determination of frequency, oscillation, and stability, are exploited. Network property of multiple neural oscillators is also studied. The insightful results will strengthen the foundation of the neural oscillator and enhance its efficient application for robotic control purpose. [ABSTRACT FROM AUTHOR]

Abstract: Recently, models of neural oscillators have been applied to many robots that perform various rhythmic movements. This paper describes a robot that performs a dish-spinning trick using a neural oscillator model. Two oscillators actuate a two-link manipulator to whirl a vertical rod on top of which a dish is hanged, while the angular position of the dish is fed back to the oscillators as input. Essentially, the controlled system has two different dynamic modes, i.e., a low-speed, large-radius whirl and a high-speed, small-radius one. A main difficulty in the control is that the oscillators must adapt to both the modes and change its mode from one to the other. Though there exists no direct interaction between the oscillators, the robot achieves the dish-spinning trick by making use of indirect interaction by way of the mechanical system. [Copyright &y& Elsevier]

Central pattern generator (CPG) is a neuronal circuit in the nervous system that can generate oscillatory patterns for the rhythmic movements. Its simplified format, neural oscillator, is wildly adopted in engineering application. This paper explores the CPG from an integral view that combines biology and engineering together. Biological CPG and simplified CPG are both studied. Computer simulation reveals the mechanism of CPG. Some properties, such as effect of tonic input and sensory feedback, stable oscillation, robustness, entrainment etc., are further studied. The promising results provide foundation for the potential engineering application in future. [ABSTRACT FROM AUTHOR]

The pattern-generator-based approach for legged robot control is inspired by biological neural mechanisms of locomotion, in which a special challenge is gait transition. In this paper we build a holosymmetric central pattern generator model and propose parameter-setting principles for a gait matrix capable of producing typical quadrupedal gaits, and based on them present an approach of directly replacing the gait matrix for gait transition, with a focus on three problems emerging during transition: breakpoint, phase-lock and oscillation-stop. Breakpoints are smoothed by remaining the current outputs during transition, similar to a zero-order holder. Breaking the phase-lock is accomplished by adding a perturbation to the state matrix at the transiting point. An oscillation-stop of less than one period can be ignored. With such treatments, it is proved that gait transitions between any two gaits on a quadrupedal robot can be achieved at arbitrary phase locations in a walk cycle, theoretically and experimentally in part. [ABSTRACT FROM AUTHOR]

Abstract: A neural oscillator model is applied to a giant swing control of an underactuated double pendulum. The oscillator receives the angle signal of the upper link and provides a relative angle of the lower link. The oscillator tunes itself to the natural dynamics of the pendulum increasing the swing amplitude, and finally the pendulum system enters the phase of giant swing. A most remarkable feature is that the transition from simple swing to giant swing can be made without changing the values of the parameters of the neural oscillator. [Copyright &y& Elsevier]

The present study investigates the coordination between two people oscillating handheld pendulums, with a special emphasis on the influence of the mechanical properties of the effector systems involved. The first part of the study is an experiment in which eight pairs of participants are asked to coordinate the oscillation of their pendulum with the other participant’s in an in-phase or antiphase fashion. Two types of pendulums, A and B, having different resonance frequencies (Freq A=0.98 Hz and Freq B=0.64 Hz), were used in different experimental combinations. Results confirm that the preferred frequencies produced by participants while manipulating each pendulum individually were close to the resonance frequencies of the pendulums. In their attempt to synchronize with one another, participants met at common frequencies that were influenced by the mechanical properties of the two pendulums involved. In agreement with previous studies, both the variability of the behavior and the shift in the intended relative phase were found to depend on the task-effector asymmetry, i.e., the difference between the mechanical properties of the effector systems involved. In the second part of the study, we propose a model to account for these results. The model consists of two cross-coupled neuro-mechanical units, each composed of a neural oscillator driving a wrist-pendulum system. Taken individually, each unit reproduced the natural tendency of the participants to freely oscillate a pendulum close to its resonance frequency. When cross-coupled through the vision of the pendulum of the other unit, the two units entrain each other and meet at a common frequency influenced by the mechanical properties of the two pendulums involved. The ability of the proposed model to address the other effects observed as a function of the different conditions of the pendulum and intended mode of coordination is discussed. [ABSTRACT FROM AUTHOR]