A self-organizing model of walking patterns of insects

Kimura, Shinichi; Yano, Masafuni; Shimizu, Hiroshi

doi:10.1007/s004220050053

Cited by 6 publications

(13 citation statements)

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“…For locomotion pattern generation, Kimura et al (1993Kimura et al ( , 1994 simulated the change in the walking pattern of insects against locomotion speed, load eect, and limb amputation. They designed the oscillator coordination such that the load of each limb was distributed evenly.…”

Section: Discussionmentioning

confidence: 99%

“…Neurophysiological studies indicate that the basic rhythms are intrinsically generated in spinal neuronal networks, which include neural oscillators (Grillner 1975;Delcomyn 1980). Such a rhythm generator is called a central pattern generator (CPG), and it has been mathematically modeled using coupled oscillator dynamics in many studies (Cohen et al 1982;SchoÈ ner et al 1990;Yuasa and Ito 1990;Kimura et al 1993Kimura et al , 1994Collins and Richmond 1994;Taga 1995a, b). However, discussion on how the rhythmic behavior changes in a variable environment is insucient.…”

Section: Introductionmentioning

confidence: 99%

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A mathematical model of adaptive behavior in quadruped locomotion

Ito

Yuasa

羅

et al. 1998

Biological Cybernetics

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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 related 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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A mathematical model of adaptive behavior in quadruped locomotion

Ito

Yuasa

羅

et al. 1998

Biological Cybernetics

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“…However, locomotor systems inevitably possess unpredictability due to interaction with the changing environment. Related models which present motor control systems as two dynamical systems have been studied (Beer 1990;Doya and Yoshizawa 1992;Ekeberg 1993;Kimura et al 1993;Sch6ner 1993). To adapt to a changing environment in real time, a mechanism which produces a trajectory in real time using the current state of the system is needed.…”

Section: Introductionmentioning

confidence: 99%

A model of the neuro-musculo-skeletal system for human locomotion

1995

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Adaptive gaits of humans were produced as a result of emergent properties of a model based on the neurophysiology of the central pattern generator and the biomechanics of the human musculoskeletal system. We previously proposed a neuromusculoskeletal model for human locomotion, in which movements emerged as a stable limit cycle that was generated through the global entrainment among the neural system, composed of neural oscillators, the musculoskeletal system, and the environment. In the present study, we investigated the adaptability of this model under various types of environmental and task constraints. Using a computer simulation, it was found that walking movements were robust against mechanical perturbations, loads with a mass, and uneven terrain. Moreover, the speed of walking could be controlled by a single parameter which tonically drove the neural oscillators, and the step cycle could be entrained by a rhythmic input to the neural oscillators.

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“…We have produced a mathematical model which selforganizes insect walking patterns real-time by using feedback information regarding muscle load (Kimura et al 1993). As part of this model, we introduced a new rule to coordinate leg movement in which the information is circulated to optimize the efficiency of the energy transduction of each effector organ.…”

Section: Introductionmentioning

confidence: 99%

“…We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al 1993).As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector organ. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load.…”

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confidence: 99%

A self-organizing model of walking patterns of insects

1994

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Abstract.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.

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A self-organizing model of walking patterns of insects

Cited by 6 publications

References 0 publications

A mathematical model of adaptive behavior in quadruped locomotion

A mathematical model of adaptive behavior in quadruped locomotion

A model of the neuro-musculo-skeletal system for human locomotion

A self-organizing model of walking patterns of insects

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