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K. Kodono and H. Kimura
stance phase of LF and the swing phase of RF in (F) are a little different
from those in (E), duty ratios of LF and RF at late adaptation are approx.
equal to those at early adaptation (Fig. 1-(c)). In spite of such equality of
duty ratios, since the relative phase between LF and RF is adjusted in late
adaptation, the duration of B1 at late adaptation becomes larger than the
one at early adaptation (Fig. 1-(b)). It means that exchanging leg loading
from LF to RF becomes a little smooth, and walking is stable under the
perturbation.
Let us describe more details about the duration of B1 considering the leg phase
duration, the step cycle, and the relative phase in forelimbs. Immediately after
the perturbation at the beginning of early adaptation, the duration of the stance
phase of LF (fast-leg) decreases due to the direct perturbation from the fast-belt.
Besides, the duration of the swing phase of RF (slow-leg) also decreases in spite
of no direct perturbation from the fast-belt. As a result, although there exit
large fluctuations immediately after the perturbation, the step cycle difference
between LF and RF become small (Fig. 2-(E)), and the duration of B1 is not
sufficient but at least kept. This adaptation enables split-belt walking to continue
even though it is unstable. In addition, in the second half of early adaptation,
fluctuations become less. This means that the quick contralateral coordination
mechanism between left and right legs does exist in early adaptation.
In late adaptation, since durations of the stance phase and the swing phase
of LF and RF are a little adjusted from those in early adaptation, the step
cycle difference between LF and RF becomes approx. zero (Fig. 2-(F)). Also,
the relative phase between LF and RF is adjusted properly, and the duration
of B1 is sufficiently kept. This adaptation enables stable split-belt walking to
continue. This means that the delayed learning mechanism does exist in late
adaptation [1]. In the case of split-belt walking of a decerebrate cat with longterm depression in the cerebellum being inhibited chemically, early adaptation
appears with many large fluctuations, but late adaptation does not appear. This
means that the cerebellum plays a key role in such learning functions [3]. Given
that the dynamics of walking, these adaptations are specific to quadrupedal
walking.
1.2 Proposal of the Gait Adaptation Model of a Decerebrate Cat
In this study, we aim at the constructive model
4 of gait adaptation in split-belt
walking of a decerebrate cat. The constructive model can explain the mechanism
of gait generation and adaptation as the physical phenomenon while connecting
the embodiment and sensor feedback. As one of such constructive models for
gait generation and adaptation of a quadruped, we proposed the method [7]
using leg loading and unloading for the swing-to-stance and stance-to-swing leg
4 In the constructive model, the dynamics of a single element and dynamics between
elements are defined. As a result of simulations or experiments of the interaction
between those elements and the environment, we might be able to understand the
underlying mechanisms of the non-linear dynamic system constructively.
K. Kodono and H. Kimura
stance phase of LF and the swing phase of RF in (F) are a little different
from those in (E), duty ratios of LF and RF at late adaptation are approx.
equal to those at early adaptation (Fig. 1-(c)). In spite of such equality of
duty ratios, since the relative phase between LF and RF is adjusted in late
adaptation, the duration of B1 at late adaptation becomes larger than the
one at early adaptation (Fig. 1-(b)). It means that exchanging leg loading
from LF to RF becomes a little smooth, and walking is stable under the
perturbation.
Let us describe more details about the duration of B1 considering the leg phase
duration, the step cycle, and the relative phase in forelimbs. Immediately after
the perturbation at the beginning of early adaptation, the duration of the stance
phase of LF (fast-leg) decreases due to the direct perturbation from the fast-belt.
Besides, the duration of the swing phase of RF (slow-leg) also decreases in spite
of no direct perturbation from the fast-belt. As a result, although there exit
large fluctuations immediately after the perturbation, the step cycle difference
between LF and RF become small (Fig. 2-(E)), and the duration of B1 is not
sufficient but at least kept. This adaptation enables split-belt walking to continue
even though it is unstable. In addition, in the second half of early adaptation,
fluctuations become less. This means that the quick contralateral coordination
mechanism between left and right legs does exist in early adaptation.
In late adaptation, since durations of the stance phase and the swing phase
of LF and RF are a little adjusted from those in early adaptation, the step
cycle difference between LF and RF becomes approx. zero (Fig. 2-(F)). Also,
the relative phase between LF and RF is adjusted properly, and the duration
of B1 is sufficiently kept. This adaptation enables stable split-belt walking to
continue. This means that the delayed learning mechanism does exist in late
adaptation [1]. In the case of split-belt walking of a decerebrate cat with longterm depression in the cerebellum being inhibited chemically, early adaptation
appears with many large fluctuations, but late adaptation does not appear. This
means that the cerebellum plays a key role in such learning functions [3]. Given
that the dynamics of walking, these adaptations are specific to quadrupedal
walking.
1.2 Proposal of the Gait Adaptation Model of a Decerebrate Cat
In this study, we aim at the constructive model
4 of gait adaptation in split-belt
walking of a decerebrate cat. The constructive model can explain the mechanism
of gait generation and adaptation as the physical phenomenon while connecting
the embodiment and sensor feedback. As one of such constructive models for
gait generation and adaptation of a quadruped, we proposed the method [7]
using leg loading and unloading for the swing-to-stance and stance-to-swing leg
4 In the constructive model, the dynamics of a single element and dynamics between
elements are defined. As a result of simulations or experiments of the interaction
between those elements and the environment, we might be able to understand the
underlying mechanisms of the non-linear dynamic system constructively.