Central Pattern Generator Model Research Articles

Design and CPG-based control of biomimetic robotic fish

The authors propose the design and control of a biologically-inspired biomimetic robotic fish capable of three-dimensional locomotion. The mechanical configuration and the hardware system of the robotic fish are described. The control architecture of the robotic fish is constructed based on central pattern generator (CPG). A model for a system of coupled non-linear oscillators is established to construct CPG and has been successfully applied to the four-link robotic fish. The CPGs are modeled as non-linear oscillators for joints and inter-joint coordination is achieved by altering the connection weights between joints. Coordinated gait patterns of rhythmic movements for swimming can be produced by modulating simple control parameters in the CPG model. The CPG-based method shows elegant and smooth transitions between swimming gaits, and enhanced ability to cope with transient perturbations because of non-linear characteristic. A series of swimming tests are designed to give speed evaluation and turning maneuver analysis. The effectiveness of the proposed method is confirmed via simulation and some experimental results.

A NOVEL CPG WITH PROPRIOCEPTION AND ITS APPLICATION ON THE LOCOMOTION CONTROL OF QUADRUPED ROBOT

This paper proposes a novel central pattern generator (CPG) model with proprioceptive mechanism and the dynamic connectivity mechanism. It not only contains the sensory information of the environment but also contains the information of the actuators and automatically tunes the parameters of CPG corresponding to the actuators information and inner sensory information. The position of the joints linked directly with the output of CPG is introduced to the CPG to find its proprioceptive system, spontaneously making the robot realize the actuator working status, further changing the CPG output to fit the change and decrease the influence of the problematic joints or actuators on the robot being controlled. So the damage would be avoided and self-protection is implemented. Its application on the locomotion control of a quadruped robot demonstrates the effectiveness of the proposed approach.

Fractal dynamics of human gait: a reassessment of the 1996 data of Hausdorff et al.

We propose in this paper a reassessment of the original data of Hausdorff et al. (Hausdorff JM, Purdon PL, Peng C-K, Ladin Z, Wei JY, Goldberger AR. J Appl Physiol 80: 1448-1457, 1996). We confirm, using autoregressive fractionally integrated moving average modeling, the presence of genuine fractal correlations in stride interval series in self-paced conditions. In contrast with the conclusions of the authors, we show that correlations did not disappear in metronomic conditions. The series of stride intervals presented antipersistent correlations, and 1/f fluctuations were evidenced in the asynchronies to the metronome. We show that the super central pattern generator model (West B, Scafetta N. Phys Rev E Stat Nonlin Soft Matter Phys 67: 051917, 2003) allows accounting for the experimentally observed correlations in both self-paced and metronomic conditions, by the simple setting of the coupling strength parameter. We conclude that 1/f fluctuations in gait are not overridden by supraspinal influences when walking is paced by a metronome. The source of 1/f noise is still at work in this condition, but expressed differently under the influence of a continuous coupling process.

Multiple Rhythmic States in a Model of the Respiratory Central Pattern Generator

The three-phase respiratory pattern observed during normal breathing changes with alterations in metabolic or physiological conditions. A recent study using in situ perfused rat brain preparations demonstrated a reorganization of the respiratory pattern with sequential reduction of the brain stem respiratory network. Specifically, with removal of the pons, the normal three-phase pattern transformed to a two-phase inspiratory-expiratory pattern and, with more caudal transections, to one-phase, intrinsically generated inspiratory oscillations. A minimal neural network proposed to reproduce these transformations includes 1) a ringlike mutually inhibitory network composed of the postinspiratory, augmenting expiratory, and early-inspiratory neurons and 2) an excitatory preinspiratory neuron, with persistent sodium current (I(NaP))-dependent intrinsic bursting properties, that dynamically participates in the expiratory-inspiratory phase transition and inspiratory phase generation. We used activity-based single-neuron models and applied numerical simulations, bifurcation methods, and fast-slow decomposition to describe the behavior of this network in the functional states corresponding to the three-, two-, and one-phase oscillatory regimes, as well as to analyze the transitions between states and between respiratory phases within each state. We demonstrate that, although I(NaP) is not necessary for the generation of three- and two-phase oscillations, it contributes to control of the oscillation period in each state. We also show that the transitions between states can be produced by progressive changes of drives to particular neurons and proceed through intermediate regimes, featuring high-amplitude late-expiratory and biphasic-expiratory activities or ectopic burst generation. Our results provide important insights for understanding the state-dependent mechanisms for respiratory rhythm generation and control.

Control of oscillation periods and phase durations in half-center central pattern generators: a comparative mechanistic analysis

Central pattern generators (CPGs) consisting of interacting groups of neurons drive a variety of repetitive, rhythmic behaviors in invertebrates and vertebrates, such as arise in locomotion, respiration, mastication, scratching, and so on. These CPGs are able to generate rhythmic activity in the absence of afferent feedback or rhythmic inputs. However, functionally relevant CPGs must adaptively respond to changing demands, manifested as changes in oscillation period or in relative phase durations in response to variations in non-patterned inputs or drives. Although many half-center CPG models, composed of symmetric units linked by reciprocal inhibition yet varying in their intrinsic cellular properties, have been proposed, the precise oscillatory mechanisms operating in most biological CPGs remain unknown. Using numerical simulations and phase-plane analysis, we comparatively investigated how the intrinsic cellular features incorporated in different CPG models, such as subthreshold activation based on a slowly inactivating persistent sodium current, adaptation based on slowly activating calcium-dependent potassium current, or post-inhibitory rebound excitation, can contribute to the control of oscillation period and phase durations in response to changes in excitatory external drive to one or both half-centers. Our analysis shows that both the sensitivity of oscillation period to alterations of excitatory drive and the degree to which the duration of each phase can be separately controlled depend strongly on the intrinsic cellular mechanisms involved in rhythm generation and phase transitions. In particular, the CPG formed from units incorporating a slowly inactivating persistent sodium current shows the greatest range of oscillation periods and the greatest degree of independence in phase duration control by asymmetric inputs. These results are explained based on geometric analysis of the phase plane structures corresponding to the dynamics for each CPG type, which in particular helps pinpoint the roles of escape and release from synaptic inhibition in the effects we find.

Construction and Central Pattern Generator-Based Control of a Flipper-Actuated Turtle-Like Underwater Robot

This paper deals with the construction and control of a turtle-like underwater robot with four mechanical flippers. Each flipper consists of two joints generating a rowing motion by a combination of lead-lag and feathering motions. With cooperative movements of four flippers, the robot can propel and maneuver in any direction without rotation of its main body and execute complicated three-dimensional movements, including ascending, submerging, rolling and hovering. The control architecture is constructed based on a central pattern generator (CPG). A model for a system of coupled nonlinear oscillators is established to construct a CPG and has been successfully applied to the eight-joint turtle-like robot. The CPGs are modeled as nonlinear oscillators for joints and inter-joint coordination is achieved by altering the connection weights between joints. Rowing action can be produced by modulating the control parameters in the CPG model. The CPG-based method performs elegant and smooth transitions between swimming gaits, and enhanced adaptation to the transient perturbations due to nonlinear characteristics. The effectiveness of the proposed method is confirmed via simulations and experimental results.

Multivariable harmonic balance for central pattern generators

The central pattern generator (CPG) is a nonlinear oscillator formed by a group of neurons, providing a fundamental control mechanism underlying rhythmic movements in animal locomotion. We consider a class of CPGs modeled by a set of interconnected identical neurons. Based on the idea of multivariable harmonic balance, we show how the oscillation profile is related to the connectivity matrix that specifies the architecture and strengths of the interconnections. Specifically, the frequency, amplitudes, and phases are essentially encoded in terms of a pair of eigenvalue and eigenvector. This basic principle is used to estimate the oscillation profile of a given CPG model. Moreover, a systematic method is proposed for designing a CPG-based nonlinear oscillator that achieves a prescribed oscillation profile.

Central pattern generators for locomotion control in animals and robots: A review

The problem of controlling locomotion is an area in which neuroscience and robotics can fruitfully interact. In this article, I will review research carried out on locomotor central pattern generators (CPGs), i.e. neural circuits capable of producing coordinated patterns of high-dimensional rhythmic output signals while receiving only simple, low-dimensional, input signals. The review will first cover neurobiological observations concerning locomotor CPGs and their numerical modelling, with a special focus on vertebrates. It will then cover how CPG models implemented as neural networks or systems of coupled oscillators can be used in robotics for controlling the locomotion of articulated robots. The review also presents how robots can be used as scientific tools to obtain a better understanding of the functioning of biological CPGs. Finally, various methods for designing CPGs to control specific modes of locomotion will be briefly reviewed. In this process, I will discuss different types of CPG models, the pros and cons of using CPGs with robots, and the pros and cons of using robots as scientific tools. Open research topics both in biology and in robotics will also be discussed.

Learning to Move in Modular Robots using Central Pattern Generators and Online Optimization

This article addresses the problem of how modular robotics systems, i.e. systems composed of multiple modules that can be configured into different robotic structures, can learn to locomote. In particular, we tackle the problems of online learning, that is, learning while moving, and the problem of dealing with unknown arbitrary robotic structures. We propose a framework for learning locomotion controllers based on two components: a central pattern generator (CPG) and a gradient-free optimization algorithm referred to as Powell's method. The CPG is implemented as a system of coupled nonlinear oscillators in our YaMoR modular robotic system, with one oscillator per module. The nonlinear oscillators are coupled together across modules using Bluetooth communication to obtain specific gaits, i.e. synchronized patterns of oscillations among modules. Online learning involves running the Powell optimization algorithm in parallel with the CPG model, with the speed of locomotion being the criterion to be optimized. Interesting aspects of the optimization include the fact that it is carried out online, the robots do not require stopping or resetting and it is fast. We present results showing the interesting properties of this framework for a modular robotic system. In particular, our CPG model can readily be implemented in a distributed system, it is computationally cheap, it exhibits limit cycle behavior (temporary perturbations are rapidly forgotten), it produces smooth trajectories even when control parameters are abruptly changed and it is robust against imperfect communication among modules. We also present results of learning to move with three different robot structures. Interesting locomotion modes are obtained after running the optimization for less than 60 minutes.

Analysis of coupled van der Pol oscillators and implementation to a myriapod robot

According to the study of nervous system ethology, it is thought that a walk movement of an animal is controlled by Central Pattern Generator (CPG). There are a lot of studies to try the control of the leg type robot based on CPG principle. However, most of the studies consider two or four leg type robots, and there are not many studies performed for robots more than six legs. One of its factor is probably difficulty of constituting stable and periodic CPG in the case of many number of the legs. Therefore, this paper proposes the novel CPG model which is based on coupled van del Pol oscillators. And this paper reports the analysis of proposed coupled van del Pol oscillators model and the implementation result to an actual myriapod robot.

Controlling swimming and crawling in a fish robot using a central pattern generator

Online trajectory generation for robots with multiple degrees of freedom is still a difficult and unsolved problem, in particular for non-steady state locomotion, that is, when the robot has to move in a complex environment with continuous variations of the speed, direction, and type of locomotor behavior. In this article we address the problem of controlling the non-steady state swimming and crawling of a novel fish robot. For this, we have designed a control architecture based on a central pattern generator (CPG) implemented as a system of coupled nonlinear oscillators. The CPG, like its biological counterpart, can produce coordinated patterns of rhythmic activity while being modulated by simple control parameters. To test our controller, we designed BoxyBot, a simple fish robot with three actuated fins capable of swimming in water and crawling on firm ground. Using the CPG model, the robot is capable of performing and switching between a variety of different locomotor behaviors such as swimming forwards, swimming backwards, turning, rolling, moving upwards/downwards, and crawling. These behaviors are triggered and modulated by sensory input provided by light, water, and touch sensors. Results are presented demonstrating the agility of the robot and interesting properties of a CPG-based control approach such as stability of the rhythmic patterns due to limit cycle behavior, and the production of smooth trajectories despite abrupt changes of control parameters. The robot is currently used in a temporary 20-month long exhibition at the EPFL. We present the hardware setup that was designed for the exhibition, and the type of interactions with the control system that allow visitors to influence the behavior of the robot. The exhibition is useful to test the robustness of the robot for long term use, and to demonstrate the suitability of the CPG-based approach for interactive control with a human in the loop. This article is an extended version of an article presented at BioRob2006 the first IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics.

The Design of Central Pattern Generators Based on the Matsuoka Oscillator to Generate Rhythmic Human-Like Movement for Biped Robots

We propose a controller based on a central pattern generator (CPG) network of mutually coupled Matsuoka nonlinear neural oscillators to generate rhythmic human-like movement for biped robots. The parameters of mutually inhibited and coupled Matsuoka oscillators and the necessary interconnection coupling coefficients within the CPG network directly influence the generation of the required rhythmic signals related to targeted motion. Our objective is to analyze the mutually coupled neuron models of Matsuoka oscillators to realize an efficient CPG design that leads to have dynamic, stable, sustained rhythmic movement with robust gaits for bipedal robots. We discuss the design of a CPG model with new interconnection coupling links and its inhibitation coefficients for a CPG-based controller. The new design was studied through interaction between simulated interconnection coupling dynamics with six links and a musculoskeletal model with the 6 degrees of freedom (DOFs) of a biped robot. We used the weighted outputs of mutually inhibited oscillators as torques to actuate joints. We verified the effectiveness of our proposal through simulation and compared the results to those of Taga’s CPG model, confirming better, more efficient generation of stable rhythmic walking at different speeds and robustness in response to disturbances.

Numerical Simulations in Two CPG Models for Bipedal Locomotion

Pinto and Golubitsky proposed a new model for a central pattern generator (CPG) for arm/leg coordination in bipeds, the network arm. arm is derived from a CPG quadruped model (quad) by breaking the symmetry between fore- and hind limbs. This paper explores numerically some of the solution properties of two general CPG models: arm and a CPG model for leg rhythms in bipeds (which is called leg). It is assumed that the internal dynamics of each cell is modeled by a space-clamped Hodgkin—Huxley equation and the coupling is only through the voltage term. Numerical simulations are done using XPPAUT. Secondary gaits in leg are obtained from bifurcation of the Poincaré map of a primary gait. Examples of secondary gaits are gallop, asymmetric hop, one-legged hop, and skip. In particular, the gallop is obtained by bifurcation from the primary gait two-legged jump. Numerical evidence of this is shown. Numerical simulations are given of periodic solutions in arm identified with arm/leg coordination patterns in bipeds.

Variations of neuronal parameters that do not change network output

Neuronal network modeling and experiments indicate that the same physiologically relevant patterns of the network activity can be observed for quite different sets of neuronal parameters. These findings imply that parameters, each of which affects network functionality, co-vary in real networks; i.e. the variations of these parameters must be concordant. Finding such concordant variations can advance our understanding on how the properties of individual neurons determine network functionality. In particular, they may explain variability of neuronal parameters observed in living systems, and show possible paths for homeostatic regulation. In this study, we sought local interrelations between neuronal parameters that did not change network output by using the implicit function theorem. This theorem, under certain conditions, establishes the existence and uniqueness of such interrelations, and specifies them in linear approximation. By assessing such interrelations at different points in the parameter space of a model of the leech heartbeat central pattern generator (CPG) [1], we found a linear correlation between neuronal parameters that preserve a primary output characteristic of this CPG, the cycle period. The correlated parameters were the maximal conductance of the spike-mediated synaptic current, and of the hyper-polarization activated inward current, Ih. We also found that this linear correlation was different for model neurons with different endogenous activity: silence, bursting or tonic spiking. For neurons of one type, however, the correlation was similar.

A CPG control system for a modular type mobile robot

In biological systems, the rhythm generating mechanism called the Central Pattern Generator (CPG) is supposed to play an important role in various rhythmic motions, such as locomotion, respiration, and heartbeat. Various models of CPG, for example, the Matsuoka Model and the Terman-Wang Model, have been proposed. In this paper, we introduced the Matsuoka Model as the neuron model of CPG in order to express the motion of a snake-like modular robot. The outputs of a CPG network are used as the target angles of corresponding joints of the snake-like modular robot. A microcontroller-based motion-controller was developed for each module where the system as a whole can be seen as a distributed control system. The robot can move forwards and backwards by changing weights and can change direction by adjusting command parameters from the upper layer.

四足歩行運動パターンを生成・移行可能なパルス形ハードウェアCPGモデル

The purpose of our research is to clarify information processing functions of living organisms by neural networks using pulse-type hardware neuron models and applying pulse-type hardware neural networks to engineered models. It is known that locomotion such as walking by a living organism is generated and transited by CPG (Central Pattern Generator) in the central nervous system. We investigate a pulse-type hardware CPG model using coupled oscillator composed of pulse-type hardware neuron models. A CPG model is need to generate and control quadruped locomotion. In this paper, we describe generation and transition of oscillation patterns, corresponding to quadruped locomotion patterns. As a result, it is shown that generation and transition of oscillation patterns are possible by giving external inputs of one pulse to the CPG model.

3-dimensional Locomotion of a Snake-like Robot Controlled by Cyclic Inhibitory CPG Model

With 3D movement s ability and rhythmic locomotion mode, a nature snake makes itself survive in rugged terrains. The rhythmic activities of most creatures are generated by the CPG (Central Pattern Generator). Based on this fact, the sustained-type neuron has been adopted to construct a cyclic inhibitory CPG model for a snake-like robot whose joints are perpendicularly connected in series. The cyclic inhibitory CPG was proven to be able to generate rhythmic output with the least number of differential equations. The neuron network organized by the CPGs connected in line with unilateral excitation has been introduced to control the 3D locomotion of the snake-like robot, and then the necessary condition is also presented for the CPG neuron network to sustain a rhythmic output. By implementing this control architecture to a simulator of a snake-like robot, preliminary parameters of the CPG neuron network for its 3D locomotion are obtained. Moreover, it is known that“Perambulator”can successfully exhibit 3D locomotion by using the output of the proposed CPG network. The obtained results have also provided a brand-new approach to understand the unknown neuron network of nature snake.

Design of a cyclic inhibitory CPG controller for the locomotion of a snakelike robot

The rhythmic locomotion of a creature is a self-excitation behavior of the CPG (central pattern generator), which makes it supremely adapted for environment. Based on this fact, firstly, a snake-like robot controller with cyclic inhibitory CPG model was designed, and then the stability of a single neuron, CPG model and the NON (neuron oscillator network) was analyzed. By implementing this control architecture to a simulator based on the mechanical dynamics of a real snake-like robot named Perambulator-I, we presented preliminary rules for parameter setting of the CPG controller to modulate the number of S shapes, the curve of the body shape, locomotion velocity, and the curve of the locomotion trajectory for serpentine locomotion. Moreover, we demonstrated that Perambulator-I can successfully exhibit serpentine locomotion by using the output of the proposed CPG controller. The results of this paper provide a realistic approach for designing an artificial CPG controller.

Reaction to neural signatures through excitatory synapses in central pattern generator models

The activity of central pattern generator (CPG) neurons is processed by several different readers: neurons within the same CPG, neurons in other interconnected CPGs and muscles. Taking this into account, it is not surprising that CPG neurons may use different codes in their activity. In this paper, we study the capability of a CPG model to react to neural signatures through excitatory synapses. Neural signatures are cell-specific intraburst spike timings within their spiking–bursting activity. These fingerprints are encoded in the activity of the cells in addition to the information provided by their slow wave rhythm and phase relationships. The results shown in this paper suggest that neural signatures can be a mechanism to induce fast changes in the rhythm generated by a CPG through excitatory synapses.

Systems-level modeling of neuronal circuits for leech swimming

This paper describes a mathematical model of the neuronal central pattern generator (CPG) that controls the rhythmic body motion of the swimming leech. The systems approach is employed to capture the neuronal dynamics essential for generating coordinated oscillations of cell membrane potentials by a simple CPG architecture with a minimal number of parameters. Based on input/output data from physiological experiments, dynamical components (neurons and synaptic interactions) are first modeled individually and then integrated into a chain of nonlinear oscillators to form a CPG. We show through numerical simulations that the values of a few parameters can be estimated within physiologically reasonable ranges to achieve good fit of the data with respect to the phase, amplitude, and period. This parameter estimation leads to predictions regarding the synaptic coupling strength and intrinsic period gradient along the nerve cord, the latter of which agrees qualitatively with experimental observations.