Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator

The neuronal network underlying lamprey swimming has stimulated extensive modelling on different levels of abstraction. The lamprey swims with a burst frequency ranging from 0.3 to 8–10 Hz with a rostro-caudal lag between bursts in each segment along the spinal cord. The swimming motor pattern is characterized by a burst proportion that is independent of burst frequency and lasts around 30%–40% of the cycle duration. This also applies in preparations in which the reciprocal inhibition in the spinal cord between the left and right side is blocked. A network of coupled excitatory neurons producing hemisegmental oscillations may form the basis of the lamprey central pattern generator (CPG). Here we explored how such networks, in principle, could produce a large frequency range with a constant burst proportion. The computer simulations of the lamprey CPG use simplified, graded output units that could represent populations of neurons and that exhibit adaptation. We investigated the effect of an active modulation of the degree of adaptation of the CPG units to accomplish a constant burst proportion over the whole frequency range when, in addition, each hemisegment is assumed to be self-oscillatory. The degree of adaptation is increased with the degree of stimulation of the network. This will make the bursts terminate earlier at higher burst rates, allowing for a constant burst proportion. Without modulated adaptation the network operates in a limited range of swimming frequencies due to a progressive increase of burst duration with increasing background stimulation. By introducing a modulation of the adaptation, a broad burst frequency range can be produced. The reciprocal inhibition is thus not the primary burst terminating factor, as in many CPG models, and it is mainly responsible for producing alternation between the left and right sides. The results are compared with the Morris-Lecar oscillator model with parameters set to produce a type A and type B oscillator, in which the burst durations stay constant or increase, respectively, when the background stimulation is increased. Here as well, burst duration can be controlled by modulation of the slow variable in a similar way as above. When oscillatory hemisegmental networks are coupled together in a chain a phase lag is produced. The production of a phase lag in chains of such oscillators is compared with chains of Morris-Lecar relaxation oscillators. Models relating to the intact versus isolated spinal cord preparation are discussed, as well as the role of descending inhibition. Received: 1 April 1997 / Accepted in revised form: 20 March 1998     

Simple models for excitable and oscillatory neural networks

 Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey.. Received: 25 November 1996 / Revised version: 9 December 1997     

Intersegmental coordinating system of the lamprey central pattern generator for locomotion

Summary In the lamprey,Ichthyomyzon unicuspis, the wave of activity required for normal swimming movements can be generated by a central pattern generator (CPG) residing in the spinal cord. A constant phase coupling between spinal segments can be organized by intersegmental coordinating neurons intrinsic to the cord. The rostral and caudal segmental oscillators of the CPG have different preferred frequencies when separated from each other. Therefore the system must maintain the segmental oscillators of the locomotor CPG at a single common frequency and with the proper relative timing. Using selective lesions and a split-bath, it is demonstrated that the coordinating system is comprised of at least 3 subsystems, short-axon systems in the lateral and medial tracts and a long axon system in the lateral tracts. Each alone can sustain relatively stable coordinated activity.Abbreviations CPG central pattern generator - NMDA N-methyl-D-aspartate - VR ventral root     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns—rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.     

Intersegmental phase lags in the lamprey spinal cord: Experimental confirmation of the existence of a boundary region

A critical feature of the motor pattern generated by the lamprey spinal cord is an intersegmental delay that is constant down the cord and scales with cycle duration. This has been modelled as the output of a chain of coupled oscillators, within a general mathematical framework developed by Kopell and Ermentrout (1986, 1988). The analysis predicts that for asymmetric coupling of equally-activated oscillators, the intersegmental phase lag will be uniform along the chain except in a boundary layer at one end. Here we provide experimental evidence that a boundary layer does occur at the rostral end of an isolated preparation of lamprey spinal cord. In the context of the mathematical analysis, this indicates that ascending coupling is dominant in the control of intersegmental phase lag in the lamprey.     

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.     

On the derivation and tuning of phase oscillator models for lamprey central pattern generators

Using phase response curves and averaging theory, we derive phase oscillator models for the lamprey central pattern generator from two biophysically-based segmental models. The first one relies on network dynamics within a segment to produce the rhythm, while the second contains bursting cells. We study intersegmental coordination and show that the former class of models shows more robust behavior over the animal's range of swimming frequencies. The network-based model can also easily produce approximately constant phase lags along the spinal cord, as observed experimentally. Precise control of phase lags in the network-based model is obtained by varying the relative strengths of its six different connection types with distance in a phase model with separate coupling functions for each connection type. The phase model also describes the effect of randomized connections, accurately predicting how quickly random network-based models approach the determinisitic model as the number of connections increases.     

Estimating the Strength and Direction of Functional Coupling in the Lamprey Spinal Cord

A method of estimating coupling strength between two neural oscillators based on their spikes trains (Kiemel and Cohen, J. Comput. Neurosci. 5: 267–284, 1998) is tested using simulated data and then applied to experimental data from the central pattern generator (CPG) for swimming in the lamprey. The method is tested using a model of two connectionist oscillators and a model of two endogenously bursting cells. For both models, the method provides useful estimates of the relative strength of coupling in each direction, as well as estimates of total strength. The method is applied to pairs of motor-nerve recordings from isolated 50-segment pieces of spinal cords from adult silver lampreys (Ichthyomyzon unicuspus). The strength and direction of coupling is estimated under control conditions and conditions in which intersegmental coupling between the two recording locations is weakened by hemisections of the spinal cords and/or chambers containing an inhibitory solution that blocks firing in postsynaptic cells. The relevance of these measures in constraining models of the CPG is discussed.     

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.     

Spinal Mechanisms in the Control of Lamprey Swimming

SYNOPSIS. The lamprey, an anguilliform fish, swims using lateralundulatory movement; a transverse wave passes backward, fromhead to tail, the amplitude of the wave increasing as it movestailward. The wave of muscle activity producing this movementtravels down the body faster than the mechanical wave. The wayin which certain features of anguilliform movement contributeto its efficiency have been described. The neural activity underlyingswimming is characterized by: 1) rhythmical alternation betweenthe two sides of a single segment; 2) a burst duration thatremains a constant proportion of the cycle time and is independentof the cycle frequency; 3) rostrocaudal phase lag that is constantand also independent of the cycle frequency. Local circuitsin the lamprey spinal cord can generate this locomotory patternin the absence of sensory feedback following activation of excitatoryamino acid receptors; the pattern is centrally generated. Ithas been hypothesized that the spinal central pattern generatorfor locomotion consists of a series of segmental burst generatorscoupled together by an intersegmental coordinating system. Theintersegmental coordinating system functions to keep the frequenciesof the oscillators along the cord constant and to provide theappropriate rostrocaudal phase lag. Mechanosensitive units withinthe spinal cord are sensitive to movement of the spinal cord\notochordand movement of the spinal cord/notochord can entrain the burstpattern. Entrainment occurs through movement-related feedbackonto neurons at the local level. The possible roles this movement-relatedfeedback plays during locomotion are discussed.     

Entrainment, Instability, Quasi-periodicity, and Chaos in a Compound Neural Oscillator

We studied the dynamical behavior of a class of compound central pattern generator (CPG) models consisting of a simple neural network oscillator driven by both constant and periodic inputs of varying amplitudes, frequencies, and phases. We focused on a specific oscillator composed of two mutually inhibiting types of neuron (inspiratory and expiratory neurons) that may be considered as a minimal model of the mammalian respiratory rhythm generator. The simulation results demonstrated how a simple CPG model— with a minimum number of neurons and mild nonlinearities— may reproduce a host of complex dynamical behaviors under various periodic inputs. In particular, the network oscillated spontaneously only when both neurons received adequate and proportionate constant excitations. In the presence of a periodic source, the spontaneous rhythm was overriden by an entrained oscillation of varying forms depending on the nature of the source. Stable entrained oscillations were inducible by two types of inputs: (1) anti-phase periodic inputs with alternating agonist-antagonist drives to both neurons and (2) a single periodic drive to only one of the neurons. In-phase inputs, which exert periodic drives of similar magnitude and phase relationships to both neurons, resulted in varying disruptions of the entrained oscillations including magnitude attenuation, harmonic and phase distortions, and quasi-periodic interference. In the absence of significant phasic feedback, chaotic motion developed only when the CPG was driven by multiple periodic inputs. Apneic episodes with repetitive alternation of active (intrinsic oscillation) and inactive (cessation of oscillation) states developed when the network was driven by a moderate periodic input of low frequency. %and amplitudes of intermediate strength, Similar results were demonstrated in other, more complex oscillator models (that is, half-center oscillator and three-phase respiratory network model). These theoretical results may have important implications in elucidating the mechanisms of rhythmogenesis in the mature and developing respiratory CPG as well as other compound CPGs in mammalian and invertebrate nervous systems.     

On the definition of central pattern generator and its sensory control

A central pattern generator (CPG) is defined here as a neural network responsible for the production of the timing cues of a rhythmic motor output pattern in the isolated CNS. For the intact animal, model considerations show that this term is neither clearly delimited from the concept of a reflex chain nor from the concept of a pattern generator with functional principles different from those of the CPG. Therefore, it cannot be concluded from the existence of a CPG in the isolated nervous system that this CPG also provides the decisive timing cues in the intact animal. Consequences for the study of the neural basis of rhythmic movements are shown.     

Modeling of Substance P and 5-HT Induced Synaptic Plasticity in the Lamprey Spinal CPG: Consequences for Network Pattern Generation

Consequences of synaptic plasticity in the lamprey spinal CPG are analyzed by means of simulations. This is motivated by the effects substance P (a tachykinin) and serotonin (5-hydroxytryptamin; 5-HT) have on synaptic transmission in the locomotor network. Activity-dependent synaptic depression and potentiation have recently been shown experimentally using paired intracellular recordings. Although normally activity-dependent plasticity presumably does not contribute to the patterning of network activity, this changes in the presence of the neuromodulators substance P and 5-HT, which evoke significant plasticity. Substance P can induce a faster and larger depression of inhibitory connections but potentiation of excitatory inputs, whereas 5-HT induces facilitation of both inhibitory and excitatory inputs. Changes in the amplitude of the first postsynaptic potential are also seen. These changes could thus be a potential mechanism underlying the modulatory role these substances have on the rhythmic network activity.The aim of the present study has been to implement the activity dependent synaptic depression and facilitation induced by substance P and 5-HT into two alternative models of the lamprey spinal locomotor network, one relying on reciprocal inhibition for bursting and one in which each hemicord is capable of oscillations. The consequences of the plasticity of inhibitory and excitatory connections are then explored on the network level.In the intact spinal cord, tachykinins and 5-HT, which can be endogenously released, increase and decrease the frequency of the alternating left-right burst pattern, respectively. The frequency decreasing effect of 5-HT has previously been explained based on its conductance decreasing effect on K _Ca underlying the postspike afterhyperpolarization (AHP). The present simulations show that short-term synaptic plasticity may have strong effects on frequency regulation in the lamprey spinal CPG. In the network model relying on reciprocal inhibition, the observed effects substance P and 5-HT have on network behavior (i.e., a frequency increase and decrease respectively) can to a substantial part be explained by their effects on the total extent and time dynamics of synaptic depression and facilitation. The cellular effects of these substances will in the 5-HT case further contribute to its network effect.     

Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator

Establishing, maintaining, and modifying the phase relationships between extensor and flexor muscle groups is essential for central pattern generators in the spinal cord to coordinate the hindlimbs well enough to produce the basic walking rhythm. This paper investigates a simplified computational model for the spinal hindlimb central pattern generator (CPG) that is abstracted from experimental data from the rodent spinal cord. This model produces locomotor-like activity with appropriate phase relationships in which right and left muscle groups alternate while extensor and flexor muscle groups alternate. Convergence to this locomotor pattern is slow, however, and the range of parameter values for which the model produces appropriate output is relatively narrow. We examine these aspects of the model’s coordination of left-right activity through investigation of successively more complicated subnetworks, focusing on the role of the synaptic architecture in shaping motoneuron phasing. We find unexpected sensitivity in the phase response properties of individual neurons in response to stimulation and a need for high levels of both inhibition and excitation to achieve the walking rhythm. In the absence of cross-cord excitation, equal levels of ipsilateral and contralateral inhibition result in a strong preference for hopping over walking. Inhibition alone can produce the walking rhythm, but contralateral inhibition must be much stronger than ipsilateral inhibition. Cross-cord excitatory connections significantly enhance convergence to the walking rhythm, which is achieved most rapidly with strong crossed excitation and greater contralateral than ipsilateral inhibition. We discuss the implications of these results for CPG architectures based on unit burst generators.     

From swimming to walking: a single basic network for two different behaviors

 In this paper we consider the hypothesis that the spinal locomotor network controlling trunk movements has remained essentially unchanged during the evolutionary transition from aquatic to terrestrial locomotion. The wider repertoire of axial motor patterns expressed by amphibians would then be explained by the influence from separate limb pattern generators, added during this evolution. This study is based on EMG data recorded in vivo from epaxial musculature in the newt Pleurodeles waltl during unrestrained swimming and walking, and on a simplified model of the lamprey spinal pattern generator for swimming. Using computer simulations, we have examined the output generated by the lamprey model network for different input drives. Two distinct inputs were identified which reproduced the main features of the swimming and walking motor patterns in the newt. The swimming pattern is generated when the network receives tonic excitation with local intensity gradients near the neck and girdle regions. To produce the walking pattern, the network must receive (in addition to a tonic excitation at the girdles) a phasic drive which is out of phase in the neck and tail regions in relation to the middle part of the body. To fit the symmetry of the walking pattern, however, the intersegmental connectivity of the network had to be modified by reversing the direction of the crossed inhibitory pathways in the rostral part of the spinal cord. This study suggests that the input drive required for the generation of the distinct walking pattern could, at least partly, be attributed to mechanosensory feedback received by the network directly from the intraspinal stretch-receptor system. Indeed, the input drive required resembles the pattern of activity of stretch receptors sensing the lateral bending of the trunk, as expressed during walking in urodeles. Moreover, our results indicate that a nonuniform distribution of these stretch receptors along the trunk can explain the discontinuities exhibited in the swimming pattern of the newt. Thus, separate limb pattern generators can influence the original network controlling axial movements not only through a direct coupling at the central level but also via a mechanical coupling between trunk and limbs, which in turn influences the sensory signals sent back to the network. Taken together, our findings support the hypothesis of a phylogenetic conservatism of the spinal locomotor networks generating axial motor patterns from agnathans to amphibians. Received: 12 October 2001 / Accepted in revised form: 16 May 2002 Correspondence to: T. Bem (e-mail: tiaza.bem@ibib.waw.pl)     

Involvement of GnRH neuron in the spermatogonial proliferation of the scallop, Patinopecten yessoensiss

The aim of this study was to quantitatively analyze a pattern of proliferation of gonial cells and to demonstrate neural involvement in spermatogonial proliferation of the scallop by the in vitro experiment. Immunocytochemistry for incorporated BrdU was used to identify mitotically active gonial cells. The pattern of proliferation of gonial cells was divided into two phases: phase I; oogonia and spermatogonia slowly proliferate through the growing stage: phase II; oogonia develop into oocytes and spermatogonia start to proliferate rapidly from the mature stage through the spawning stage. The neurons detected with anti-mammalian (m)GnRH antibody were distributed sparsely in the pedal ganglion and predominantly in the cerebral ganglion of both sexes at the growing stage. The extracts from the cerebral and pedal ganglion (CPG) of both sexes collected at the growing stage promoted proliferation of spermatogonia in the in vitro culture of the testicular tissue as well as mGnRH. However, CPG extract had no effect on oogonial proliferation. The increased mitotic activity induced by CPG and mGnRH was abolished by the addition of mGnRH antagonists and anti-mGnRH antibody, suggesting that the spermatogonial proliferation is regulated by GnRH-like peptide in CPG of the scallop. The same mitotic activity as CPG extract and mGnRH was observed in the hemocyte lysate, but not in the serum. These findings suggest that the spermatogonial proliferation at phase II in the scallop may be under the neuroendocrine control by GnRH neuron in CPG.     

Resonance tuning in a neuro-musculo-skeletal model of the forearm

In rhythmic movements, humans activate their muscles in a robust and energy efficient way. These activation patterns are oscillatory and seem to originate from neural networks in the spinal cord, called central pattern generators (CPGs). Evidence for the existence of CPGs was found for instance in lampreys, cats and rats. There are indications that CPGs exist in humans as well, but this is not proven yet. Energy efficiency is achieved by resonance tuning: the central nervous system is able to tune into the resonance frequency of the limb, which is determined by the local reflex gains. The goal of this study is to investigate if the existence of a CPG in the human spine can explain the resonance tuning behavior, observed in human rhythmic limb movement. A neuro-musculo-skeletal model of the forearm is proposed, in which a CPG is organized in parallel to the local reflexloop. The afferent and efferent connections to the CPG are based on clues about the organization of the CPG, found in literature. The model is kept as simple as possible (i.e., lumped muscle models, groups of neurons are lumped into half-centers, simple reflex model), but incorporates enough of the essential dynamics to explain behavior—such as resonance tuning—in a qualitative way. Resonance tuning is achieved above, at and below the endogenous frequency of the CPG in a highly non-linear neuro- musculo-skeletal model. Afferent feedback of muscle lengthening to the CPG is necessary to accomplish resonance tuning above the endogenous frequency of the CPG, while feedback of muscle velocity is necessary to compensate for the phase lag, caused by the time delay in the loop coupling the limb to the CPG. This afferent feedback of muscle lengthening and velocity represents the Ia and II fibers, which—according to literature—is the input to the CPG. An internal process of the CPG, which integrates the delayed muscle lengthening and feeds it to the half-center model, provides resonance tuning below the endogenous frequency. Increased co-contraction makes higher movement frequencies possible. This agrees with studies of rhythmic forearm movements, which have shown that co-contraction increases with movement frequency. Robustness against force perturbations originates mainly from the CPG and the local reflex loop. The CPG delivers an increasing part of the necessary muscle activation for increasing perturbation size. As far as we know, the proposed neuro-musculo-skeletal model is the first that explains the observed resonance tuning in human rhythmic limb movement.     

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.     

A self-organizing model of walking patterns of insects

It is well known that the motor systems of animals are controlled by a hierarchy consisting of a brain, central pattern generator, and effector organs. An animal's walking patterns change depending on its walking velocities, even when it has been decerebrated, which indicates that the walking patterns may, in fact, be generated in the subregions of the neural systems of the central pattern generator and the effector organs. In order to explain the self-organization of the walking pattern in response to changing circumstances, our model incorporates the following ideas: (1) the brain sends only a few commands to the central pattern generator (CPG) which act as constraints to self-organize the walking patterns in the CPG; (2) the neural network of the CPG is composed of oscillating elements such as the KYS oscillator, which has been shown to simulate effectively the diversity of the neural activities; and (3) we have introduced a rule to coordinate leg movement, in which the excitatory and inhibitory interactions among the neurons act to optimize the efficiency of the energy transduction of the effector organs. We describe this mechanism as the least dissatisfaction for the greatest number of elements, which is a self-organization rule in the generation of walking patterns. By this rule, each leg tends to share the load as efficiently as possible under any circumstances. Using this self-organizing model, we discuss the control mechanism of walking patterns.