Central Pattern Generator Model Research Articles

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.

Simulation of Spinal Muscle Control in Human Gait Using OpenSim

This paper presents a neuro-musculoskeletal simulation approach to human gait based on an original model of central pattern generator and the muscle synergy approach. The controller, shown here, aims at simplifying movement control by reducing the number of parameters to optimize. The model of the simplified motor coordination chain was built, from the midbrain through spinal neurons to the muscles allowing of simulating some neural and muscular values of gait, hard to obtain otherwise. The work also includes a bio-inspired reflex-based balance controller designed from knowledge of spinal gait. The used anatomic musculoskeletal model has been implemented in OpenSim platform. Time simulations show the ability of the platform to be able to produce different gait patterns including nominal and disturbed. Both gaits are controlled by the same bio-inspired closed-loop CPG- and reflex-based circuitries. After 2 second standing phase, the model was able to walk for about 5 meters with 10 steps. 2 steps were disrupted in the second simulation.

The walking and running control of a human musculoskeletal model using a low-power consumption hardware central pattern generator model

Applying a control system with low energy consumption and low load of motion control to robots, similar to living organisms, is considered to be one of the most important issues in robot development. We have been studying systems that use pulse-type hardware neural networks to control robotic motion with a small number of control signals, as is the case in living organisms. In particular, it has been mimicking the function of the central pattern generator localized in the spinal cord of living organisms to generate motion patterns. In the present article, a new biomimetic control system using pulse-type hardware neural networks for biped gait control is reported.

Using System Identification and Central Pattern Generators to Create Synthetic Gait Data

One way to accelerate fall prevention research is through the generation of synthetic gait data. The objective of this paper is to explore a proof-of-concept method using a central pattern generator (CPG) and system identification techniques to generate synthetic human gait data. The two neuron CPG model used in this paper actuated a single point mass that represented the height of the human hip. This continuous model was converted into a discrete system with four state variables – hip height, descending drive, and two CPG inhibition variables. To capture the step-to-step variation in the experimental dataset, we performed linear and nonlinear system identification on the discrete system. Compared to the experimental dataset, the linear model yielded a 12% error, while the nonlinear method yielded an 11% error, indicating that this system with the data used was predominantly linear. Using the identified linear model, we generated synthetic data by repeatedly applying the linear model to the current step's state to generate the next step's state. The resulting synthetic data had some similarity to the experimental data but clearly did not fully replicate the experimental signal properties, indicating that the methods used here have promise but are currently insufficient.

Towards more biologically plausible central-pattern-generator models.

Central pattern generators (CPGs) are relatively small neural networks that play a fundamental role in the control of animal locomotion. In this paper we define a method for the systematic design of CPG models able to exhibit biologically plausible gait transitions by implementing short-term synaptic plasticity mechanisms. As a case study, we focus on a simple CPG for quadruped locomotion. By applying the proposed method, three of four standard quadruped gaits were correctly reproduced by the obtained CPG model, not only in terms of the alternating sequence of the limbs but also in terms of frequency, duty cycle, and phase lags.

Simulation of a Central Pattern Generator Using Memristive Devices

The central pattern generator (CPG) is one of the key elements of the nervous system of Vertebrates, determining the motor, breathing, swallowing, etc. cyclic motor patterns of a living organism, which require constant maintenance and prompt (or immediate) recovery in the case of injury. In this context, the construction of neuroprosthetic systems requires the development of electronic analogs (the corresponding CPGs). It is proposed to use memristive devices as adaptive elements with continuous tunable characteristics in these systems, because they exhibit a property, similar to bio-synaptic plasticity. The CPG model is developed, which yields an output activity, similar to that of biological objects. The requirements for the temporal characteristics of tunable elements for their successful use as artificial synapses are also specified. Memristive devices of a new type are fabricated according to the Langmuir–Schaefer technique using benzothieno[3,2-b] [1]-benzothiophene (BTBT) dimer as an active layer. BTBT-based devices make it possible to switch the conductivity at low voltages and currents, which is important in the development of energy-efficient neuroprosthetic systems, and the characteristic switching times are about several hundred milliseconds, which indicates that they can be used as analogs of synapses upon instrumental realization of the CPG.

Central Pattern Generator Model Design and Gait Control Research of Amphibious Robotic Fish

Central Pattern Generator (CPG) has the characteristics of strong adaptability and various output forms, which is suitable for amphibious robotic fish whose environment may change at any time. According to the bionic prototype, the Hopf oscillators on ipsilateral and contralateral side were coupled to form a CPG network topology model, which was used to control the steering gear and realize the waveform propulsion of the fins. In MATLAB, parameters such as amplitude and frequency were set for the model to obtain the motion characteristics under five actual gaits. The output curve is consistent with the theory and the conversion flow field is smooth, which proves the correctness of the CPG model and can be used as the target of subsequent simulation. Finally, through ADAMS and MATLAB co-simulation, the output swing angle curve of the controlled object (steering gear) is obtained, which accords with the abovementioned control goal. This guaranteed the effectiveness of CPG model control. Moreover, the centroid and torque of the steering gear changes in the gait process of crawling and steering are especially analyzed, these changes indicate that the steering gear does not lose too much power during the rigid contact between the fin and the ground and prove the practical feasibility of the theory.

A spiking central pattern generator for the control of a simulated lamprey robot running on SpiNNaker and Loihi neuromorphic boards

Central pattern generator (CPG) models have long been used to investigate both the neural mechanisms that underlie animal locomotion, as well as for robotic research. In this work we propose a spiking central pattern generator (SCPG) neural network and its implementation on neuromorphic hardware as a means to control a simulated lamprey model. To construct our SCPG model, we employ the naturally emerging dynamical systems that arise through the use of recurrent neural populations in the neural engineering framework (NEF). We define the mathematical formulation behind our model, which consists of a system of coupled abstract oscillators modulated by high-level signals, capable of producing a variety of output gaits. We show that with this mathematical formulation of the CPG model, the model can be turned into a spiking neural network (SNN) that can be easily simulated with Nengo, an SNN simulator. The SCPG model is then used to produce the swimming gaits of a simulated lamprey robot model in various scenarios. We show that by modifying the input to the network, which can be provided by sensory information, the robot can be controlled dynamically in direction and pace. The proposed methodology can be generalized to other types of CPGs suitable for both engineering applications and scientific research. We test our system on two neuromorphic platforms, SpiNNaker and Loihi. Finally, we show that this category of spiking algorithms displays a promising potential to exploit the theoretical advantages of neuromorphic hardware in terms of energy efficiency and computational speed.

A new biological central pattern generator model and its relationship with the motor units.

The central pattern generator (CPG) is a key neural-circuit component of the locomotion control system. Recently, numerous molecular and genetic approaches have been proposed for investigating the CPG mechanisms. The rhythm in the CPG locomotor circuits comes from the activity in the ipsilateral excitatory neurons whose output is controlled by inter-neuron inhibitory connections. Conventional models for simulating the CPG mechanism are complex Hodgkin-Huxley-type models. Inspired by biological investigations and the continuous-time Matsuoka model, we propose new integral-order and fractional-order CPG models, which consider time delays and synaptic interfaces. The phase diagrams exhibit limit cycles and periodic solutions, in agreement with the CPG biological characteristics. As well, the fractional-order model shows state transitions with order variations. In addition, we investigate the relationship between the CPG and the motor units through the construction of integral-order and fractional-order coupling models. Simulations of these coupling models show that the states generated by the three motor units are in accordance with the experimentally-obtained states in previous studies. The proposed models reveal that the CPG can regulate limb locomotion patterns through connection weights and synaptic interfaces. Moreover, in comparison to the integral-order models, the fractional-order ones appear to be more effective, and hence more suitable for describing the dynamics of the CPG biological system.

An optimality principle for locomotor central pattern generators

Two types of neural circuits contribute to legged locomotion: central pattern generators (CPGs) that produce rhythmic motor commands (even in the absence of feedback, termed “fictive locomotion”), and reflex circuits driven by sensory feedback. Each circuit alone serves a clear purpose, and the two together are understood to cooperate during normal locomotion. The difficulty is in explaining their relative balance objectively within a control model, as there are infinite combinations that could produce the same nominal motor pattern. Here we propose that optimization in the presence of uncertainty can explain how the circuits should best be combined for locomotion. The key is to re-interpret the CPG in the context of state estimator-based control: an internal model of the limbs that predicts their state, using sensory feedback to optimally balance competing effects of environmental and sensory uncertainties. We demonstrate use of optimally predicted state to drive a simple model of bipedal, dynamic walking, which thus yields minimal energetic cost of transport and best stability. The internal model may be implemented with neural circuitry compatible with classic CPG models, except with neural parameters determined by optimal estimation principles. Fictive locomotion also emerges, but as a side effect of estimator dynamics rather than an explicit internal rhythm. Uncertainty could be key to shaping CPG behavior and governing optimal use of feedback.

Humanoid adaptive locomotion control through a bioinspired CPG-based controller

AbstractTo achieve adaptive gait planning of humanoid robots, a hierarchical central pattern generator (H-CPG) model with a basic rhythmic signal generation layer and a pattern formation layer is proposed to modulate the center of mass (CoM) and the online foot trajectory. The entrainment property of the CPG is exploited for adaptive walking in the absence of a priori knowledge of walking conditions, and the sensory feedback is applied to modulate the generated trajectories online to improve walking adaptability and stability. The developed control strategy is verified using a humanoid robot on sloped terrain and shows good performance.

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.

Characterization of interval variability in the sequential activity of a central pattern generator model

Central pattern generators (CPG) are neural circuits that generate robust sequences of coordinated neural activity to control motor rhythms. We have recently revealed the presence of dynamical invariants in the relationships between specific intervals that build the CPG sequence and the instantaneous period of the rhythm in the pyloric CPG of crustacean. In this paper, we analyze the variability of the intervals comprising the rhythm in a model of a mollusk feeding CPG. We measured the cycle-by-cycle time intervals of the CPG rhythm under distinct single neuron stimulation. We characterized interval variability and report dynamical invariants found only for specific time intervals building the sequence of the feeding CPG. Together with our previous findings, the results reported in this paper indicate that dynamical invariants can be a universal feature of any sequence generating circuit.

Design and Locomotion Control of a Dactylopteridae-Inspired Biomimetic Underwater Vehicle With Hybrid Propulsion

This article presents the design and implementation of an innovative biomimetic underwater vehicle (BUV) and its locomotion controller. Through mimicking a dactylopteridae, the hybrid propulsion BUV is designed with two symmetrical bio-inspired long-fins and a double-joint fishtail. The mechatronic design of the dactylopteridae-inspired BUV with the pectoral long-fins and a double-joint fishtail is first provided. The two flexible long-fins compose the median and/or paired fin (MPF) propulsion, while the fishtail acts as the body and/or caudal fin (BCF) propulsion. Through the coordination of BCF and MPF propulsion modes, the BUV obtains excellent low-speed locomotion stability and also keeps high maneuverability. Moreover, the locomotion control methods based on central pattern generators (CPGs) model and fuzzy adaptive proportion integral differential (PID) are proposed for this BUV. In the end, the experimental results of the multimode motion and closed-loop motion control demonstrate the feasibility and effectiveness of the mechanism and the locomotion control system. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation behind this article is the design of a novel biomimetic underwater vehicle (BUV) that possesses low-speed locomotion stability and fast swimming ability, which is suitable for carrying relevant sensors to complete water quality monitoring, biological observation, underwater equipment inspection, underwater structure detection, and other marine tasks. Currently, BUVs are usually designed as only one propulsion mode by caudal fin or paired fins, which makes it difficult to have the advantages of both modes. In order to further study the problem, we designed a dactylopteridae-inspired BUV with the bilateral pectoral long-fins (providing low-speed locomotion stability) and a double-joint fishtail (providing fast swimming ability). A hybrid-driven motion control framework is presented for the BUV based on a central pattern generators (CPGs) model and fuzzy adaptive proportion integral differential (PID). A series of experiments suggests that the mechanism and the locomotion control system are practical and valid. Hopefully, our mechanism and control framework can provide valuable theoretical and technical support guidance to the practicing marine engineer for the codesign of propulsion mode and control.

Rhythm motion control in bio‐inspired fishtail based on central pattern generator

The elastic oscillation structure based on central pattern generators (CPGs), which can produce rhythmic motions, is discussed. First, Hopf CPG, the typical CPG model, being a signal generator for the elastic oscillation structure, is analysed via the theory of differential equations. Next, the well-posedness results of a coupling system composed by the CPG and an elastic beam are proved by means of the linear operator semi-group theory. Then, the numerical results using the finite difference method indicate that the coupled system can obtain a variety of periodic motion behaviours by choosing the internal parameters of the CPG network. Finally, the dynamic simulation of complex system motion is investigated using COMSOL Multiphysics.

Reproducing Five Motor Behaviors in a Salamander Robot With Virtual Muscles and a Distributed CPG Controller Regulated by Drive Signals and Proprioceptive Feedback.

Diverse locomotor behaviors emerge from the interactions between the spinal central pattern generator (CPG), descending brain signals and sensory feedback. Salamander motor behaviors include swimming, struggling, forward underwater stepping, and forward and backward terrestrial stepping. Electromyographic and kinematic recordings of the trunk show that each of these five behaviors is characterized by specific patterns of muscle activation and body curvature. Electrophysiological recordings in isolated spinal cords show even more diverse patterns of activity. Using numerical modeling and robotics, we explored the mechanisms through which descending brain signals and proprioceptive feedback could take advantage of the flexibility of the spinal CPG to generate different motor patterns. Adapting a previous CPG model based on abstract oscillators, we propose a model that reproduces the features of spinal cord recordings: the diversity of motor patterns, the correlation between phase lags and cycle frequencies, and the spontaneous switches between slow and fast rhythms. The five salamander behaviors were reproduced by connecting the CPG model to a mechanical simulation of the salamander with virtual muscles and local proprioceptive feedback. The main results were validated on a robot. A distributed controller was used to obtain the fast control loops necessary for implementing the virtual muscles. The distributed control is demonstrated in an experiment where the robot splits into multiple functional parts. The five salamander behaviors were emulated by regulating the CPG with two descending drives. Reproducing the kinematics of backward stepping and struggling however required stronger muscle contractions. The passive oscillations observed in the salamander's tail during forward underwater stepping could be reproduced using a third descending drive of zero to the tail oscillators. This reduced the drag on the body in our hydrodynamic simulation. We explored the effect of local proprioceptive feedback during swimming and forward terrestrial stepping. We found that feedback could replace or reduce the need for different drives in both cases. It also reduced the variability of intersegmental phase lags toward values appropriate for locomotion. Our work suggests that different motor behaviors do not require different CPG circuits: a single circuit can produce various behaviors when modulated by descending drive and sensory feedback.