Sensory feedback in CNN-based central pattern generators

Central Pattern Generators (CPGs) are a suitable paradigm to solve the problem of locomotion control in walking robots. CPGs are able to generate feed-forward signals to achieve a proper coordination among the robot legs. In literature they are often modelled as networks of coupled nonlinear systems. However the topic of feedback in these systems is rarely addressed. On the other hand feedback is essential for locomotion. In this paper the CPG for a hexapod robot is implemented through Cellular Neural Networks (CNNs). Feedback is included in the CPG controller by exploiting the dynamic properties of the CPG motor-neurons, such as synchronization issue and local bifurcations. These universal paradigms provide the essential issues to include sensory feedback in CPG architectures based on coupled nonlinear systems. Experiments on a dynamic model of a hexapod robot are presented to validate the approach introduced.     

Modular neuromuscular control of human locomotion by central pattern generator

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

Partly shared spinal cord networks for locomotion and scratching

Animals produce a variety of behaviors using a limited number of muscles and motor neurons. Rhythmic behaviors are often generated in basic form by networks of neurons within the central nervous system, or central pattern generators (CPGs). It is known from several invertebrates that different rhythmic behaviors involving the same muscles and motor neurons can be generated by a single CPG, multiple separate CPGs, or partly overlapping CPGs. Much less is known about how vertebrates generate multiple, rhythmic behaviors involving the same muscles. The spinal cord of limbed vertebrates contains CPGs for locomotion and multiple forms of scratching. We investigated the extent of sharing of CPGs for hind limb locomotion and for scratching. We used the spinal cord of adult red-eared turtles. Animals were immobilized to remove movement-related sensory feedback and were spinally transected to remove input from the brain. We took two approaches. First, we monitored individual spinal cord interneurons (i.e., neurons that are in between sensory neurons and motor neurons) during generation of each kind of rhythmic output of motor neurons (i.e., each motor pattern). Many spinal cord interneurons were rhythmically activated during the motor patterns for forward swimming and all three forms of scratching. Some of these scratch/swim interneurons had physiological and morphological properties consistent with their playing a role in the generation of motor patterns for all of these rhythmic behaviors. Other spinal cord interneurons, however, were rhythmically activated during scratching motor patterns but inhibited during swimming motor patterns. Thus, locomotion and scratching may be generated by partly shared spinal cord CPGs. Second, we delivered swim-evoking and scratch-evoking stimuli simultaneously and monitored the resulting motor patterns. Simultaneous stimulation could cause interactions of scratch inputs with subthreshold swim inputs to produce normal swimming, acceleration of the swimming rhythm, scratch-swim hybrid cycles, or complete cessation of the rhythm. The type of effect obtained depended on the level of swim-evoking stimulation. These effects suggest that swim-evoking and scratch-evoking inputs can interact strongly in the spinal cord to modify the rhythm and pattern of motor output. Collectively, the single-neuron recordings and the results of simultaneous stimulation suggest that important elements of the generation of rhythms and patterns are shared between locomotion and scratching in limbed vertebrates.     

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

The central pattern generators (CPGs) in the spinal cord strongly contribute to locomotor behavior. To achieve adaptive locomotion, locomotor rhythm generated by the CPGs is suggested to be functionally modulated by phase resetting based on sensory afferent or perturbations. Although phase resetting has been investigated during fictive locomotion in cats, its functional roles in actual locomotion have not been clarified. Recently, simulation studies have been conducted to examine the roles of phase resetting during human bipedal walking, assuming that locomotion is generated based on prescribed kinematics and feedback control. However, such kinematically based modeling cannot be used to fully elucidate the mechanisms of adaptation. In this article we proposed a more physiologically based mathematical model of the neural system for locomotion and investigated the functional roles of phase resetting. We constructed a locomotor CPG model based on a two-layered hierarchical network model of the rhythm generator (RG) and pattern formation (PF) networks. The RG model produces rhythm information using phase oscillators and regulates it by phase resetting based on foot-contact information. The PF model creates feedforward command signals based on rhythm information, which consists of the combination of five rectangular pulses based on previous analyses of muscle synergy. Simulation results showed that our model establishes adaptive walking against perturbing forces and variations in the environment, with phase resetting playing important roles in increasing the robustness of responses, suggesting that this mechanism of regulation may contribute to the generation of adaptive human bipedal locomotion.     

Hard-wired central pattern generators for quadrupedal locomotion

Animal locomotion is generated and controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of producing rhythmic output. In the present work, it is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound. Transitions between the different gaits are generated by varying the network's driving signal and/or by altering internal oscillator parameters. The above in numero results are obtained without changing the relative strengths or the polarities of the system's synaptic interconnections, i.e., the network maintains an invariant coupling architecture. It is also shown that the ability of the hard-wired CPG network to produce and switch between multiple gait patterns is a model-independent phenomenon, i.e., it does not depend upon the detailed dynamics of the component oscillators and/or the nature of the inter-oscillator coupling. Three different neuronal oscillator models — the Stein neuronal model, the Van der Pol oscillator, and the FitzHugh-Nagumo model -and two different coupling schemes are incorporated into the network without impeding its ability to produce the three quadrupedal gaits and the aforementioned gait transitions.     

Bio-inspired design strategies for central pattern generator control in modular robotics

New findings in the nervous system of invertebrates have shown how a number of features of central pattern generator (CPG) circuits contribute to the generation of robust flexible rhythms. In this paper we consider recently revealed strategies that living CPGs follow to design CPG control paradigms for modular robots. To illustrate them, we divide the task of designing an example CPG for a modular robot into independent problems. We formulate each problem in a general way and provide a bio-inspired solution for each of them: locomotion information coding, individual module control and inter-module coordination. We analyse the stability of the CPG numerically, and then test it on a real robot. We analyse steady state locomotion and recovery after perturbations. In both cases, the robot is able to autonomously find a stable effective locomotion state. Finally, we discuss how these strategies can result in a more general design approach for CPG-based locomotion.     

CPG Control for Biped Hopping Robot in Unpredictable Environment

A CPG control mechanism is proposed for hopping motion control of biped robot in unpredictable environment.Based on analysis of robot motion and biological observation of animal's control mechanism,the motion control task is divided into two simple parts:motion sequence control and output force control.Inspired by a two-level CPG model,a two-level CPG control mechanism is constructed to coordinate the drivers of robot joint,while various feedback information are introduced into the control mechanism.Interneurons within the control mechanism are modeled to generate motion rhythm and pattern promptly for motion sequence control; motoneurons are modeled to control output forces of joint drivers in real time according to feedbacks.The control system can perceive changes caused by unknown perturbations and environment changes according to feedback information,and adapt to unpredictable environment by adjusting outputs of neurons.The control mechanism is applied to a biped hopping robot in unpredictable environment on simulation platform,and stable adaptive motions are obtained.     

Predictive and reactive tuning of the locomotor CPG

The neural control of locomotion involves a constant interplaybetween the actions of a central pattern generator (CPG) andsensory input elicited by bodily movement. With respect to theCPG, recent analysis of fictive locomotion has shown that durationsof flexion and extension tend to covary along specific linesin plots of phase duration versus cycle duration. The slopesof these lines evidently depend on internal states that varyamong preparations, but, within a preparation, remain rathersteady from one sequence to the next. These relationships canbe reproduced in a simple oscillator model having two pairsof preset parameters, suggesting that steady internal drivesto flexor and extensor half-centers determine how phase durationscovary. Regarding the role of sensory inputs, previous experimentshave revealed state-dependent rules that govern phase-switchingindependently of the CPG rhythm. In addition, sensory inputis known to modulate motoneuronal activation through stretchreflexes. To explore how sensory input combines with the locomotorCPG, we used a neuromechanical model with muscle actuators,proprioceptive feedback, sensory phase-switching rules, anda CPG. Interestingly, sequences of stable locomotion were alwaysassociated with phase durations that conformed to an extensor-dominatedphase-duration characteristic (where extension durations varymore than flexion durations). This is the characteristic seenin normal animals, but not necessarily in fictive locomotion,where movement and associated sensory input are absent. Thissuggests that to produce the biomechanical events required forstability, an extensor-dominated phase-duration characteristicis required. In the model, when the preset CPG phase durationswere well matched to coincide the biomechanical requirements,CPG-mediated phase switching produced stable cycles. When CPGphase durations were too short, phases switched prematurelyand the model soon fell. When CPG phase durations were too long,sensory rules fired and overrode the CPG, maintaining stability.We posit that under normal circumstances, descending input fromhigher centers continually adjusts the operating point of theCPG on the preset phase-duration characteristic according toanticipated biomechanical requirements. When the predictionsare good, CPG-generated phase durations closely match thoserequired by the kinetics and kinematics, and little or no sensoryadjustment occurs. We propose the term "neuromechanical tuning"to describe this process of matching the CPG to the biomechanicalrequirements.     

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.     

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

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

Reflexes and preflexes: on the role of sensory feedback on rhythmic patterns in insect locomotion

Neuromuscular systems are stabilized and controlled by both feedforward and feedback signals. Feedforward pathways driven by central pattern generators (CPGs), in conjunction with preflexive mechanical reaction forces and nonlinear muscle properties, can produce stable stereotypical gaits. Feedback is nonetheless present in both slow and rapid running, and preflexive mechanisms can join with neural reflexes originating in proprioceptive sensors to yield robust behavior in uncertain environments. Here, we develop a single degree-of-freedom neuromechanical model representing a joint actuated by an agonist/antagonist muscle pair driven by motoneurons and a CPG in a periodic rhythm characteristic of locomotion. We consider two characteristic feedback modes: phasic and tonic. The former encodes states such as position in the timing of individual spikes, while the latter can transmit graded measures of force and other continuous variables as spike rates. We use results from phase reduction and averaging theory to predict phase relationships between CPG and motoneurons in the presence of feedback and compare them with simulations of the neuromechanical model, showing that both phasic and tonic feedback can shift motoneuronal timing and thereby affect joint motions. We find that phase changes in neural activation can cooperate with preflexive displacement and velocity effects on muscle force to compensate for externally applied forces, and that these effects qualitatively match experimental observations in the cockroach.     

A mathematical model of adaptive behavior in quadruped locomotion

Locomotion involves repetitive movements and is often executed unconsciously and automatically. In order to achieve smooth locomotion, the coordination of the rhythms of all physical parts is important. Neurophysiological studies have revealed that basic rhythms are produced in the spinal network called, the central pattern generator (CPG), where some neural oscillators interact to self-organize coordinated rhythms. We present a model of the adaptation of locomotion patterns to a variable environment, and attempt to elucidate how the dynamics of locomotion pattern generation are adjusted by the environmental changes. Recent experimental results indicate that decerebrate cats have the ability to learn new gait patterns in a changed environment. In those experiments, a decerebrate cat was set on a treadmill consisting of three moving belts. This treadmill provides a periodic perturbation to each limb through variation of the speed of each belt. When the belt for the left forelimb is quickened, the decerebrate cat initially loses interlimb coordination and stability, but gradually recovers them and finally walks with a new gait. Based on the above biological facts, we propose a CPG model whose rhythmic pattern adapts to periodic perturbation from the variable environment. First, we design the oscillator interactions to generate a desired rhythmic pattern. In our model, oscillator interactions are regarded as the forces that generate the desired motion pattern. If the desired pattern has already been realized, then the interactions are equal to zero. However, this rhythmic pattern is not reproducible when there is an environmental change. Also, if we do not adjust the rhythmic dynamics, the oscillator interactions will not be zero. Therefore, in our adaptation rule, we adjust the memorized rhythmic pattern so as to minimize the oscillator interactions. This rule can describe the adaptive behavior of decerebrate cats well. Finally, we propose a mathematical framework of an adaptation in rhythmic motion. Our framework consists of three types of dynamics: environmental, rhythmic motion, and adaptation dynamics. We conclude that the time scale of adaptation dynamics should be much larger than that of rhythmic motion dynamics, and the repetition of rhythmic motions in a stable environment is important for the convergence of adaptation. Received: 10 July 1997 / Accepted in revised form: 13 March 1998     

Synchronization and stochastic resonance of the small-world neural network based on the CPG

According to biological knowledge, the central nervous system controls the central pattern generator (CPG) to drive the locomotion. The brain is a complex system consisting of different functions and different interconnections. The topological properties of the brain display features of small-world network. The synchronization and stochastic resonance have important roles in neural information transmission and processing. In order to study the synchronization and stochastic resonance of the brain based on the CPG, we establish the model which shows the relationship between the small-world neural network (SWNN) and the CPG. We analyze the synchronization of the SWNN when the amplitude and frequency of the CPG are changed and the effects on the CPG when the SWNN’s parameters are changed. And we also study the stochastic resonance on the SWNN. The main findings include: (1) When the CPG is added into the SWNN, there exists parameters space of the CPG and the SWNN, which can make the synchronization of the SWNN optimum. (2) There exists an optimal noise level at which the resonance factor Q gets its peak value. And the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the noise intensity. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.     

Computer simulation study on central pattern generator: from biology to engineering

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.     

Hormone‐mediated modulation of the electromotor CPG in pulse‐type weakly electric fish. Commonalities and differences across species

Like stomatogastric activity in crustaceans, vocalization in teleosts and frogs, and locomotion in mammals, the electric organ discharge (EOD) of weakly electric fish is a rhythmic and stereotyped electromotor pattern. The EOD, which functions in both perception and communication, is controlled by a two‐layered central pattern generator (CPG), the electromotor CPG, which modifies its basal output in response to environmental and social challenges. Despite major anatomo‐functional commonalities in the electromotor CPG across electric fish species, we show that Gymnotus omarorum and Brachyhypopomus gauderio have evolved divergent neural processes to transiently modify the CPG outputs through descending fast neurotransmitter inputs to generate communication signals. We also present two examples of electric behavioral displays in which it is possible to separately analyze the effects of neuropeptides (mid‐term modulation) and gonadal steroid hormones (long‐term modulation) upon the CPG. First, the nonbreeding territorial aggression of G. omarorum has been an advantageous model to analyze the status‐dependent modulation of the excitability of CPG neuronal components by vasotocin. Second, the seasonal and sexually dimorphic courtship signals of B. gauderio have been useful to understand the effects of sex steroids on the responses to glutamatergic inputs in the CPG. Overall, the electromotor CPG functions in a regime that safeguards the EOD waveform. However, prepacemaker influences and hormonal modulation enable an enormous versatility and allows the EOD to adapt its functional state in a species‐, sex‐, and social context‐specific manners.     

Transmitter-dependent involvement of the respiratory interneurons in the locomotor rhythm in the pulmonate mollusc Lymnaea

Pedal cell RPeD1 of the pond snail L. stagnalis becomes involved in a central rhythm identified as an activity of the central pattern generator (CPG) for locomotion. The RPeD1 rhythm developed as driven by a synaptic input in isolated CNS preparations treated with 0.05 mM serotonin (5HT) or 0.1 mM 5-hydroxytryptophan (5HTP). The 5HT-induced co-ordinated rhythmic activity was retained by each of two pedal ganglia after complete isolation thus suggesting that the respective CPG lies entirely within the pedal portion of the CNS and is paired. The findings suggest that the RPeD1 switching from one network to another represents a neurotransmitter-dependent phenomenon.     

Biologically inspired control of physically simulated bipeds

Summary The basic rhythmicity underlying animal locomotion is created by dedicated neural structures called central pattern generators (CPGs). We describe the implementation of such structures in simulation and their successful use for the control of bipedal walking. Artificial evolution (in the form of genetic algorithms) is used as the optimisation procedure. Two CPG types are illustrated, the more advanced of which being based on recent theoretical findings on the nature of neural architectures required to drive animal locomotion. It is shown that CPGs in conjunction with simple reflex responses as well as an appropriate mechanical implementation of the biped are capable of producing stable walking patterns on planar surfaces. This finding corroborates circumstantial experimental evidence that limited bipedal locomotion is possible without the employment of higher level control centres.     

A Bionic Neural Network for Fish-Robot Locomotion

A bionic neural network for fish-robot locomotion is presented. The bionic neural network inspired from fish neural net- work consists of one high level controller and one chain of central pattern generators （CPGs）. Each CPG contains a nonlinear neural Zhang oscillator which shows properties similar to sine-cosine model. Simulation re, suits show that the bionic neural network presents a good performance in controlling the fish-robot to execute various motions such as startup, stop, forward swimming, backward swimming, turn right and turn left.     

Trot Gait Design and CPG Method for a Quadruped Robot

Developing efficient walking gaits for quadruped robots has intrigued investigators for years. Trot gait, as a fast locomotion gait, has been widely used in robot control. This paper follows the idea of the six determinants of gait and designs a trot gait for a parallel-leg quadruped robot, Baby Elephant. The walking period and step length are set as constants to maintain a relatively fast speed while changing different foot trajectories to test walking quality. Experiments show that kicking leg back improves body stability. Then, a steady and smooth trot gait is designed. Furthermore, inspired by Central Pattern Generators （CPG）, a series CPG model is proposed to achieve robust and dynamic trot gait. It is generally believed that CPG is capable of producing rhythmic movements, such as swimming, walking, and flying, even when isolated from brain and sensory inputs. The proposed CPG model, inspired by the series concept, can automatically learn the previous well-designed trot gait and reproduce it, and has the ability to change its walking frequency online as well. Experiments are done in real world to verify this method.