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1.
Hard-wired central pattern generators for quadrupedal locomotion 总被引:5,自引:0,他引:5
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. 相似文献
2.
Rhythmic body motions observed in animal locomotion are known to be controlled by neuronal circuits called central pattern
generators (CPGs). It appears that CPGs are energy efficient controllers that cooperate with biomechanical and environmental
constraints through sensory feedback. In particular, the CPGs tend to induce rhythmic motion of the body at a natural frequency,
i.e., the CPGs are entrained to a mechanical resonance by sensory feedback. The objective of this paper is to uncover the
mechanism of entrainment resulting from the dynamic interaction of the CPG and mechanical system. We first develop multiple
CPG models for the reciprocal inhibition oscillator (RIO) and examine through numerical experiments whether they can be entrained
to a simple pendulum. This comparative study identifies the neuronal properties essential for the entrainment. We then analyze
the simplest model that captures the essential dynamics via the method of harmonic balance. It is shown that robust entrainment
results from a strong, positive-feedback coupling of a lightly damped mechanical system and the RIO consisting of neurons with the complete adaptation property 相似文献
3.
Classification of coupling patterns among spontaneous rhythms and ventilation in the sympathetic discharge of decerebrate cats 总被引:2,自引:0,他引:2
A. Porta G. Baselli N. Montano T. Gnecchi-Ruscone F. Lombardi A. Malliani S. Cerutti 《Biological cybernetics》1996,75(2):163-172
The spontaneous low- and high-frequency rhythms in the sympathetic discharge of decerebrate artificially ventilated cats
are affected by external ventilation. Two graphical methods (i.e. the space-time separation plot and the frequency tracking
locus) are used to classify the non-linear interactions. The observed behaviours in the sympathetic discharge consist of phase-locked
periodic dynamics (at various frequency ratios with ventilation), quasiperiodic and aperiodic patterns. They depend on the
experimental condition. In control condition the sympathetic discharge appears more frequently locked to each ventilatory
cycle (1 : 1 dynamics). However, some cases of quasiperiodic dynamics are found. A sympathetic activation stimulus, such as
inferior vena cava occlusion, is able to synchronise slow rhythms in the sympathetic discharge to a subharmonic of ventilation.
During a sympathetic inhibition stimulus, such as aortic constriction, 1 : 1 dynamics is detected but the amplitude of the
sympathetic responses can be modulated by unlocked slow rhythms. Moreover, some cases of aperiodic dynamics are observed.
Vagotomy reduces the 1 : 1 coupling between sympathetic outflow and ventilation. Vagotomy plus spinalisation disrupts periodic
dynamics in the sympathetic discharge so that irregular and complex patterns are found.
Received: 19 July 1995/Accepted in revised form: 20 May 1996 相似文献
4.
B. W. Verdaasdonk H. F. J. M. Koopman F. C. T. van der Helm 《Biological cybernetics》2009,101(1):49-61
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. 相似文献
5.
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 相似文献
6.
John Nassour Patrick Hénaff Fethi Benouezdou Gordon Cheng 《Biological cybernetics》2014,108(3):291-303
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. 相似文献
7.
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. 相似文献
8.
K Lukowiak 《Journal de physiologie》1991,85(2):63-70
1. Central pattern generators (CPGs) underlie a wide variety of rhythmic behaviours such as locomotion and respiration in most multi-cellular organisms. 2. The CPG's are capable of generating a patterned output without phasic sensory input. 3. The organization of the CPG is due to both intrinsic properties of the individual neurons and their network interactions. 4. To gain an understanding of the mechanisms which underlie rhythmicity a CPG has been reconstructed in culture. This will allow investigators to test directly the mechanisms underlying the generation of rhythmic output and will allow the direct testing of the mechanisms by which various modulators affect the CPG. 相似文献
9.
M. Ullström J. Hellgren Kotaleski J. Tegnér E. Aurell S. Grillner A. Lansner 《Biological cybernetics》1998,79(1):1-14
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 相似文献
10.
Oscillating neuronal circuits, known as central pattern generators (CPGs), are responsible for generating rhythmic behaviours such as walking, breathing and chewing. The CPG model alone however does not account for the ability of animals to adapt their future behaviour to changes in the sensory environment that signal reward. Here, using multi-electrode array (MEA) recording in an established experimental model of centrally generated rhythmic behaviour we show that the feeding CPG of Lymnaea stagnalis is itself associated with another, and hitherto unidentified, oscillating neuronal population. This extra-CPG oscillator is characterised by high population-wide activity alternating with population-wide quiescence. During the quiescent periods the CPG is refractory to activation by food-associated stimuli. Furthermore, the duration of the refractory period predicts the timing of the next activation of the CPG, which may be minutes into the future. Rewarding food stimuli and dopamine accelerate the frequency of the extra-CPG oscillator and reduce the duration of its quiescent periods. These findings indicate that dopamine adapts future feeding behaviour to the availability of food by significantly reducing the refractory period of the brain's feeding circuitry. 相似文献
11.
In natural motor behaviour arm movements, such as pointing or reaching, often need to be coordinated with locomotion. The underlying coordination patterns are largely unexplored, and require the integration of both rhythmic and discrete movement primitives. For the systematic and controlled study of such coordination patterns we have developed a paradigm that combines locomotion on a treadmill with time-controlled pointing to targets in the three-dimensional space, exploiting a virtual reality setup. Participants had to walk at a constant velocity on a treadmill. Synchronized with specific foot events, visual target stimuli were presented that appeared at different spatial locations in front of them. Participants were asked to reach these stimuli within a short time interval after a “go” signal. We analysed the variability patterns of the most relevant joint angles, as well as the time coupling between the time of pointing and different critical timing events in the foot movements. In addition, we applied a new technique for the extraction of movement primitives from kinematic data based on anechoic demixing. We found a modification of the walking pattern as consequence of the arm movement, as well as a modulation of the duration of the reaching movement in dependence of specific foot events. The extraction of kinematic movement primitives from the joint angle trajectories exploiting the new algorithm revealed the existence of two distinct main components accounting, respectively, for the rhythmic and discrete components of the coordinated movement pattern. Summarizing, our study shows a reciprocal pattern of influences between the coordination patterns of reaching and walking. This pattern might be explained by the dynamic interactions between central pattern generators that initiate rhythmic and discrete movements of the lower and upper limbs, and biomechanical factors such as the dynamic gait stability. 相似文献
12.
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. 相似文献
13.
We used a computational model of rhythmic movement to analyze how the connectivity of sensory feedback affects the tuning
of a closed-loop neuromechanical system to the mechanical resonant frequency (ωr). Our model includes a Matsuoka half-center oscillator for a central pattern generator (CPG) and a linear, one-degree-of-freedom
system for a mechanical component. Using both an open-loop frequency response analysis and closed-loop simulations, we compared
resonance tuning with four different feedback configurations as the mechanical resonant frequency, feedback gain, and mechanical
damping varied. The feedback configurations consisted of two negative and two positive feedback connectivity schemes. We found
that with negative feedback, resonance tuning predominantly occurred when ωr was higher than the CPG’s endogenous frequency (ωCPG). In contrast, with the two positive feedback configurations, resonance tuning only occurred if ωr was lower than ωCPG. Moreover, the differences in resonance tuning between the two positive (negative) feedback configurations increased with
increasing feedback gain and with decreasing mechanical damping. Our results indicate that resonance tuning can be achieved
with positive feedback. Furthermore, we have shown that the feedback configuration affects the parameter space over which
the endogenous frequency of the CPG or resonant frequency the mechanical dynamics dominates the frequency of a rhythmic movement. 相似文献
14.
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. 相似文献
15.
The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. In particular, analytical conditions are obtained under which harmonic balance predicts existence of an oscillation at a frequency near the resonance frequency. Our result reveals that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative integral feedback and positive rate feedback. 相似文献
16.
Systems-level modeling of neuronal circuits for leech swimming 总被引:2,自引:0,他引:2
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. 相似文献
17.
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. 相似文献
18.
Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment 总被引:14,自引:0,他引:14
A new principle of sensorimotor control of legged locomotion in an unpredictable environment is proposed on the basis of neurophysiological knowledge and a theory of nonlinear dynamics. Stable and flexible locomotion is realized as a global limit cycle generated by a global entrainment between the rhythmic activities of a nervous system composed of coupled neural oscillators and the rhythmic movements of a musculo-skeletal system including interaction with its environment. Coordinated movements are generated not by slaving to an explicit representation of the precise trajectories of the movement of each part but by dynamic interactions among the nervous system, the musculo-skeletal system and the environment. The performance of a bipedal model based on the above principle was investigated by computer simulation. Walking movements stable to mechanical perturbations and to environmental changes were obtained. Moreover, the model generated not only the walking movement but also the running movement by changing a single parameter nonspecific to the movement. The transitions between the gait patterns occurred with hysteresis. 相似文献
19.
A connectionist central pattern generator for the aquatic and terrestrial gaits of a simulated salamander 总被引:1,自引:0,他引:1
Ijspeert AJ 《Biological cybernetics》2001,84(5):331-348
20.
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. 相似文献