Central Pattern Generator Model Research Articles

Coupling of neurons favors the bursting behavior and the predominance of the tripod gait

In nature, it has been observed that the dominant locomotor pattern of hexapod insects is often the tripod gait. Our analysis of a Central Pattern Generator (CPG) of the insect movement gives reasons for this dominance: the mathematical CPG model presents the tripod pattern with bursting dynamics in a parametric region where an isolated neuron has a simpler behavior. That is, we show how the coupling of small networks of neurons makes the system to continue having bursting dynamics even when an isolated neuron would be spiking. Moreover, in parametric regions where a neuron shows chaotic dynamics, the CPG exhibits a chaotic synchronization phenomenon: the chaotic tripod gait. In other words, coupling loves bursting… and tripod gait. The hyperchaotic phenomenon is also present and we locate regions where up to four Lyapunov exponents are positive.

Coupling Relationships between the Brain and the Central Pattern Generator Based on a Fractional-Order Extended Hindmarsh-Rose Model.

The states of the central nervous system (CNS) can be classified into subcritical, critical, and supercritical states that endow the system with information capacity, transmission capabilities, and dynamic range. A further investigation of the relationship between the CNS and the central pattern generators (CPG) is warranted to provide insight into the mechanisms that govern the locomotion system. In this study, we established a fractional-order CPG model based on an extended Hindmarsh-Rose model with time delay. A CNS model was further established using a recurrent excitation-inhibition neuronal network. Coupling between these CNS and CPG models was then explored, demonstrating a potential means by which oscillations generated by a neural network respond to periodic stimuli. These simulations yielded two key sets of findings. First, frequency sliding was observed when the CPG was sent to the CNS in the subcritical, critical, and supercritical states with different external stimulus and fractional-order index values, indicating that frequency sliding regulates brain function on multiple spatiotemporal scales when the CPG and CNS are coupled together. The main frequency range for these simulations was observed in the gamma band. Second, with increasing external inputs the coherence index for the CNS decreases, demonstrating that strong external inputs introduce neuronal stochasticity. Neural network synchronization is then reduced, triggering irregular neuronal firing. Together these results provide novel insight into the potential mechanisms that may underlie the locomotion system.

Structure and Gait Design of a Lunar Exploration Hexapod Robot Based on Central Pattern Generator Model

To address the challenges of sinking, imbalance, and complex control systems faced by hexapod robots walking on lunar soil, this study develops an umbrella-shaped foot lunar exploration hexapod robot. The overall structure of the robot is designed to mimic the body structure of insects. By incorporating a four-bar linkage mechanism to replace the commonly used naked joints in traditional hexapod robots, the robot reduces the number of degrees of freedom and simplifies control complexity. Additionally, an extension mechanism is added to the robot’s foot, unfolding into an umbrella shape to provide a larger support area, effectively addressing the issue of foot sinking instability during walking. This study adopts and simplifies the Central Pattern Generator (CPG) model to generate stable periodic control signals for the robot’s legs. Precise control of the extension mechanism’s unfolding period is achieved through mapping functions. A joint simulation platform using Solid Works and Matlab is established to analyze the stability of the robot’s walking. Finally, walking experiments are conducted on the prototype, confirming the smooth walking of the lunar exploration hexapod robot. The results indicate that the designed lunar exploration hexapod robot has a reasonable structure, excellent stability in motion, and the CPG control scheme is feasible.

CPG-Fuzzy Heading Control for a Hexapod Robot with Arc-Shaped Blade Legs

Based on the central pattern generator (CPG) and fuzzy controller, this paper proposes a heading control method for the directional motion for a new type of blade legged hexapod robot (BLHR). First, the modified Hopf oscillator is used to construct the CPG model of BLHR based on the limit cycle. Second, the fuzzy controller is applied to adjust the support angles of legs to change the heading of BLHR, thereby correcting the error between the actual and desired heading angle in real-time. Finally, the feasibility and effectiveness of the proposed CPG-Fuzzy control method is verified in Gazebo simulations and real-world experiments. This is the first attempt to combine CPG and fuzzy control in the context of hexapod robot. In comparison to existing control methods, the proposed CPG-Fuzzy controller can implement heading control of BLHR with better performance and value of further investigation.

The learnable CPG model based on Wilson-Cowan oscillator

The central pattern generator (CPG) is a micro circuit in neural system and it can generate rhythmic signals to regulate locomotion. The researchers have investigated the features of the CPG, and they have paid more attentions to the the programmable characteristic. In this address, a new learnable CPG based on Wilson-Cowan oscillator is established. The sine signal, the complex signal, the chaotic signal and angles of compass-like robot are used as input to test the new programmable central pattern generator. The simulations present that the learnable CPG has the ability to learn different signals effectively. These results are the significant contribution to the research of the programmable CPG.

Multi-constraint spatial coupling for the body joint quadruped robot and the CPG control method on rough terrain

Quadruped robots have frequently appeared in various situations, including wilderness rescue, planetary exploration, and nuclear power facility maintenance. The quadruped robot with an active body joint has better environmental adaptability than one without body joints. However, it is difficult to guarantee the stability of the body joint quadruped robot when walking on rough terrain. Given the above issues, this paper proposed a gait control method for the body joint quadruped robot based on multi-constraint spatial coupling (MCSC) algorithm. The body workspace of the robot is divided into three subspaces, which are solved for different gaits, and then coupled to obtain the stable workspace of the body. A multi-layer central pattern generator model based on the Hopf oscillator is built to realize the generation and switching of walk and trot gaits. Then, combined with the MCSC area of the body, the reflex adjustment strategy on different terrains is established to adjust the body’s posture in real time and realize the robot’s stable locomotion. Finally, the robot prototype is developed to verify the effectiveness of the control method. The simulation and experiment results show that the proposed method can reduce the offset of the swing legs and the fluctuation of the body attitude angle. Furthermore, the quadruped robot is ensured to maintain stability by dynamically modifying its body posture. The relevant result can offer a helpful reference for the control of quadruped robots in complex environments.

The Bcm rule allows a spinal cord model to learn rhythmic movements.

Currently, it is accepted that animal locomotion is controlled by a central pattern generator in the spinal cord. Experiments and models show that rhythm generating neurons and genetically determined network properties could sustain oscillatory output activity suitable for locomotion. However, current central pattern generator models do not explain how a spinal cord circuitry, which has the same basic genetic plan across species, can adapt to control the different biomechanical properties and locomotion patterns existing in these species. Here we demonstrate that rhythmic and alternating movements in pendulum models can be learned by a monolayer spinal cord circuitry model using the Bienenstock-Cooper-Munro learning rule, which has been previously proposed to explain learning in the visual cortex. These results provide an alternative theory to central pattern generator models, because rhythm generating neurons and genetically defined connectivity are not required in our model. Though our results are not in contradiction to current models, as existing neural mechanism and structures, not used in our model, can be expected to facilitate the kind of learning demonstrated here. Therefore, our model could be used to augment existing models.

Memristive circuit-based model of central pattern generator to reproduce spinal neuronal activity in walking pattern.

Existing methods of neurorehabilitation include invasive or non-invasive stimulators that are usually simple digital generators with manually set parameters like pulse width, period, burst duration, and frequency of stimulation series. An obvious lack of adaptation capability of stimulators, as well as poor biocompatibility and high power consumption of prosthetic devices, highlights the need for medical usage of neuromorphic systems including memristive devices. The latter are electrical devices providing a wide range of complex synaptic functionality within a single element. In this study, we propose the memristive schematic capable of self-learning according to bio-plausible spike-timing-dependant plasticity to organize the electrical activity of the walking pattern generated by the central pattern generator.

Heteroclinic cycling and extinction in May–Leonard models with demographic stochasticity

May and Leonard (SIAM J Appl Math 29:243–253, 1975) introduced a three-species Lotka–Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each “cycle”, passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic Escherichia coli), in the immune system, in neural information processing models (“winnerless competition”), and in models of neural central pattern generators. Yet as May and Leonard observed “Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two.” Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard’s ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.

Central pattern generator network model for the alternating hind limb gait of rats based on the modified Van der Pol equation.

Herein, we employed a central pattern generator (CPG), a spinal cord neural network that regulates lower-limb gait during intra-spinal micro-stimulation (ISMS). Particularly, ISMS was used to determine the spatial distribution pattern of CPG sites in the spinal cord and the signal regulation pattern that induced the CPG network to produce coordinated actions. Based on the oscillation phenomenon of the single CPG neurons of Van der Pol (VDP) oscillators, a double-cell CPG neural network model was constructed to realise double lower limbs, six-joint modelling, the simulation of 12 neural circuits, the CPG loci characterising stimuli-inducing alternating movements and changes in polarity stimulation signals in rat hindlimbs, and leg-state change movements. The feasibility and effectiveness of the CPG neural network were verified by recording the electromyographic burst-release mode of the flexor and extensor muscles of the knee joints during CPG electrical stimulation. The results revealed that the output pattern of the CPG presented stable rhythm and coordination characteristics. The 12-neuron CPG model based on the improved VDP equation realised single-point control while significantly reducing the number of stimulation electrodes in the gait training of spinal cord injury patients. We believe that this study advances motor function recovery in rehabilitation medicine.

Biomechanical and Sensory Feedback Regularize the Behavior of Different Locomotor Central Pattern Generators.

This work presents an in-depth numerical investigation into a hypothesized two-layer central pattern generator (CPG) that controls mammalian walking and how different parameter choices might affect the stepping of a simulated neuromechanical model. Particular attention is paid to the functional role of features that have not received a great deal of attention in previous work: the weak cross-excitatory connectivity within the rhythm generator and the synapse strength between the two layers. Sensitivity evaluations of deafferented CPG models and the combined neuromechanical model are performed. Locomotion frequency is increased in two different ways for both models to investigate whether the model's stability can be predicted by trends in the CPG's phase response curves (PRCs). Our results show that the weak cross-excitatory connection can make the CPG more sensitive to perturbations and that increasing the synaptic strength between the two layers results in a trade-off between forced phase locking and the amount of phase delay that can exist between the two layers. Additionally, although the models exhibit these differences in behavior when disconnected from the biomechanical model, these differences seem to disappear with the full neuromechanical model and result in similar behavior despite a variety of parameter combinations. This indicates that the neural variables do not have to be fixed precisely for stable walking; the biomechanical entrainment and sensory feedback may cancel out the strengths of excitatory connectivity in the neural circuit and play a critical role in shaping locomotor behavior. Our results support the importance of including biomechanical models in the development of computational neuroscience models that control mammalian locomotion.

Trajectory tracking with external disturbance of bionic underwater robot based on CPG and robust model predictive control

Aiming at the 3-D trajectory tracking control problem of underwater bionic robots, a novel trajectory tracking control strategy based on robust model predictive control (RMPC) and central pattern generator (CPG) is designed for underwater bionic robots with external disturbances. Firstly, the overall mathematical model of the robot is established, and a discrete robust model predictive controller is designed for trajectory tracking control, and then its stability is proved. Secondly, according to the mechanical analysis of the pectoral fin and the caudal fin, the transformation functions of the pectoral fin and the caudal fin is designed, and the lower CPG motion controller and the upper RMPC trajectory tracking controller are combined to establish an RMPC-CPG controller. It not only improves the coordination and smoothness of the motion of the bionic robot during the trajectory tracking process, but also incorporates many constraints in the motion process into the rolling optimization, so that the control input meets the actual drive constraints and avoids the problem of drive oversaturation. Finally, the simulation experiment is designed to verify the tracking performance of the bionic underwater robot under external disturbance. Simulation results demonstrate the effectiveness of the controller and its robustness to external disturbances.

Thrust Improvement of a Biomimetic Robotic Fish by Using a Deformable Caudal Fin.

In nature, live fish has various deformable fins which are capable to promote the swimming speed, efficiency, stability, and thrust generation. However, this feature is rarely possessed by current man-made biomimetic robotic fishes. In this paper, a novel deformable caudal fin platform is proposed to improve thrust generation of biomimetic robotic fish. First, the design of the deformable caudal fin is given, which includes a servo motor, a gear-based transmission mechanism, fin bones, and silica membrane. Second, an improved Central Pattern Generator (CPG) model was developed to coordinately control the flapping of the tail and the deformation of the caudal fin. More specifically, three deformation patterns, i.e., conventional nondeformable mode, sinusoidal-based mode, instant mode, of the caudal fin are investigated. Third, extensive experiments are conducted to explore the effects of deformation of the caudal fin on the thrust generation of the biomimetic robotic fish. It was found that the instant mode of the caudal fin has the largest thrust, which sees a 27.5% improvement compared to the conventional nondeformable mode, followed by the sinusoidal-based mode, which also sees an 18.2% improvement. This work provides a novel way to design and control the deformation of the caudal fin, which sheds light on the development of high-performance biomimetic robotic fish.

Embedded Real-Time Implementation of Bio-Inspired Central Pattern Generator with Self-Repairing Function

Both robustness and self-repairing of the rhythmic behaviors generated by central pattern generators (CPGs) play significant roles in locomotion control. Although current CPG models have been established to mimic rhythmic outputs, the mechanisms by which the self-repairing capacities of CPG systems are formed are largely unknown. In this paper, a novel bio-inspired self-repairing CPG model (BiSRP-CPG) is proposed based on the tripartite synapse, which reveals the critical role of astrocytes in the dynamic coordination of CPGs. BiSRP-CPG is implemented on the parallel FPGA platform to simulate CPG systems on real physiological scale, in which a hardware implementation method without multiplier is utilized to break the limitation of FPGA hardware resources. The experimental results verified both the robustness and self-repairing capabilities of rhythm of BiSRP-CPG in the presence of stochastic synaptic inputs and “faulty” synapse. Under the synaptic failure rate of 20%, BiSRP-CPG suffered only 10.53% performance degradation, which was much lower than the 36.84% spike loss rate of CPG networks without astrocytes. This paper provides an insight into one of the possible self-repair mechanisms of brain rhythms which can be utilized to develop autonomously fault-tolerant electronic systems.

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.

Motion Intention Prediction and Joint Trajectories Generation Toward Lower Limb Prostheses Using EMG and IMU Signals

Powered intelligent lower limb prostheses have been gaining interest as they provide functionality for walking on different terrains. This study proposes a hierarchical planner for intelligent lower limb prostheses based on sensor fusion and a central pattern generator (CPG). Electromyographic (EMG) and inertial measurement unit (IMU) signals were recorded and fused in the feature and decision levels. The high-level planner consists of cascade classifiers with a gait phase dependence. A secondary classifier for each stand phase and swing phase was developed to recognize five gait patterns. The mid-level planner was designed as a walking frequency estimator based on the Newton method. The low-level planner incorporates the CPG models, achieving the planning of lower limb joint trajectories. The proposed layered planner can recognize the users’ walking intention and gait speed in real-time, ensuring coordination between the joints of both legs. Eight healthy subjects were recruited, and the average accuracy of motion pattern recognition reached 99.13% and 99.39% for the standing and swing phases, respectively. The relative root mean square error (RMSE) of the walking frequency estimate was 2.3% under approximately 3.5 m/s gait speed. The promising results indicate that this method effectively predicts the continuous joint angle for lower limb prostheses.

Bio-inspired navigation and exploration system for a hexapod robotic platform

This paper presents a biologically inspired system for guiding and controlling a virtual hexapod robot. Our navigation and exploration system is composed of subsystems that execute processes of path integration, action selection, actuator control and correction of the robot’s orientation. For the subsystem that serves the path integration function we modified an existing model of bio-inspired vector summation by adding the capability of performing online calculation. For the action selection subsystem that allows to switch between the behaviors of exploration, approaching a target and homing we modified an existing model of decision making for mediating social behaviors in mice. We added an additional circuit that projects a signal to the units representing each of the behaviors. In the case of the actuator control subsystem, the structure of a central pattern generator model that incorporates feedback and adaptation was used as the base for generating and transforming signals for the actuators. Finally, the orientation correction subsystem is a novel model that determines an error value from a desired and the current orientations. The proposed models were simulated as independent scripts and then implemented as ROS (Robot Operating System) nodes for controlling a robot simulation in Gazebo.

Locomotor Pattern and Force Generation Modulated by Ionic Channels: A Computational Study of Spinal Networks Underlying Locomotion.

Locomotion is a fundamental movement in vertebrates produced by spinal networks known as central pattern generators (CPG). During fictive locomotion cat lumbar motoneurons (MNs) exhibit changes in membrane properties, including hyperpolarization of voltage threshold, reduction of afterhyperpolarization and input resistance, and amplification of nonlinear membrane properties. Both modeling and electrophysiological studies suggest that these changes can be produced by upregulating voltage-gated sodium channel (VGSC), persistent sodium (NaP), or L-type calcium channel (LTCC) or downregulating delayed-rectifier potassium (K(DR)) or calcium-dependent potassium channel (KCa) in spinal MNs. Further studies implicate that these channel modulations increase motor output and facilitate MN recruitment. However, it remains unknown how the channel modulation of CPG networks or MN pools affects the rhythmic generation of locomotion and force production of skeletal muscle during locomotion. In order to investigate this issue, we built a two-level CPG model composed of excitatory interneuron pools (Exc-INs), coupled reciprocally with inhibitory interneuron pools (Inh-INs), and projected to the flexor-extensor MN pools innervating skeletal muscles. Each pool consisted of 100 neurons with membrane properties based on cat spinal neurons. VGSC, K(DR), NaP, KCa, LTCC, and H-current channels were included in the model. Simulation results showed that (1) upregulating VGSC, NaP, or LTCC or downregulating KCa in MNs increased discharge rate and recruitment of MNs, thus facilitating locomotor pattern formation, increased amplitude of electroneurogram (ENG) bursting, and enhanced force generation of skeletal muscles. (2) The same channel modulation in Exc-INs increased the firing frequency of the Exc-INs, facilitated rhythmic generation, and increased flexor-extensor durations of step cycles. (3) Contrarily, downregulation of NaP or LTCC in MNs or Exc-INs or both CPG (Exc-INs and Inh-INs) and MNs disrupted locomotor pattern and reduced or even blocked the ENG bursting of MNs and force generation of skeletal muscles. (4) Pharmacological experiments showed that bath application of 25 μM nimodipine or 2 μM riluzole completely blocked fictive locomotion in isolated rat spinal cord, consistent with simulation results. We concluded that upregulation of VGSC, NaP, or LTCC or downregulation of KCa facilitated rhythmic generation and force production during walking, with NaP and LTCC playing an essential role.

CPG-based generation strategy of variable rhythmic chewing movements for a dental testing chewing robot.

The rhythmic chewing movement pattern is dynamically reshaped to adapt to a variable chewing environment. The variance affects the wear performance of dental prostheses. This study was aimed to generate these variable rhythmic chewing movements for dental testing equipment. A six-axis parallel chewing robot DUT-2 was adopted as the dental testing equipment. Four variances were extracted from the rhythmic movement, including period, offset, amplitude, and mode. The relevant movement cases, including gradually accelerating movement, gradually increasing movement, gradually shrinking movement, and bilateral movement, were designed. Then, a central pattern generator (CPG) model based on morphed phase oscillators was proposed. According to the coupling feature of the rhythmic movements, the specific modulation method of the CPG model was provided for these movements. The simulated incisor trajectory was outputted by importing the driving amplitudes from the CPG model to the virtual prototype of the chewing robot. The bite force (considering two-body and three-body contacts) was analyzed by writing the driving amplitudes into the motion controller of the chewing robot's physical prototype. The relative errors of offset and amplitude in the z-direction were 4.14% and 0.74%, respectively. The transition was smooth around the turning point during the gradually increasing movement and bilateral movement. For two-body contact, the average relative error and bias of the maximum bite force were 4.15% and 1.08%, respectively. The food involvement decreased the accuracies to 13.18% and 2.50%, respectively. The CPG model supplies a bionic and explicit approach for generating the variable rhythmic chewing movements. The variable movements related to chewing preferences and food properties could be replicated. Besides, the high repeatability of the maximum bite force is beneficial for running the repetitive wear tests. Finally, the CPG model makes it possible to study the influence of the variance on wear performance.

A Novel Ergodic Discrete Difference Equation Model of Central Pattern Generator: Theoretical Analysis and Efficient Implementation

A novel ergodic discrete difference equation (DDE) oscillator and its theoretical analysis method are presented. Theoretical analyses reveal the oscillator is more suitable to build a central pattern generator (CPG) compared to a standard non-ergodic DDE oscillator. Further, it is shown the ergodic DDE CPG can generate rhythmic signals suitable for realizing fundamental gaits of a quadruped robot. Then a prototype of the ergodic DDE CPG is implemented by a field programmable gate array and experiments show it can realize the fundamental gaits of the quadruped robot. Further, it is shown the ergodic DDE CPG consumes much lower power and much fewer circuit elements compared to a typical conventional CPG implemented as a customized digital signal processor.