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A double pendulum model for human walking control 281

4Discussion

Human movement variability, its origins, and valuable information are hot
topics in the field of human motor control and rehabilitation. In this work,
we presented some biped-based models for human walking. The focus of the
models is the variabilities of stride-to-stride walking parameters. The models
are built by different combinations of four controllers (for stride length,
time, velocity, and position). This approach lends itself to application in
modeling of human walking in different environmental conditions (walking
overground or on a treadmill), subjects with different ages, or dual tasks stud-
ies. In this research, the model that contains all controllers (for stride length,
time, velocity, and position) showed acceptable similarity of α values to
experimental data for walking on the treadmill.
It is believed that the average human movement is approximately opti-
mal, for doing the same trials of a task (Arechavaleta et al., 2008). According
to this assumption, for each self-selected speed, stride length is chosen in
such a way as to minimize energy consumption (Kuo, 2001). Thus the opti-
mal values of stride length and time can be chosen as their desired values. As
shown in Fig. 6, the model with no control on steps length and time (c_VP)
cannot reach the desired optimal values. In addition, the stride length SD
value in this model is much higher than those of other models and exper-
imental data. Therefore, it seems that to save metabolic energy on the tread-
mill, besides controlling velocity and position, step length and time also need
to be controlled by the central nervous system.
Two theories have been suggested for human position control during
walking on the treadmill. One of these theories suggests that the position
on the treadmill is only corrected when the body is near to the treadmill
edges (Dingwell et al., 2010). The other theory suggests a lazy controller
for this case (Dingwell and Cusumano, 2015). The presented models are
in the direction of the second theory by choosing small values for coefficients
of position controller.
Several studies discussed the differences (Rosenblatt and Grabiner, 2010;
Lazzarini and Kataras, 2016) and similarities (Riley et al., 2007; Bollens et al.,
2010) between treadmill and overground walking. One of these differences
is statistical persistence of velocity that exists during walking overground,
but not on the treadmill (Terrier et al., 2005). The result of the c_TL model
showed similarity to walking overground w.r.t α (DFA). Consequently, this
suggests that in self-selected speed during walking overground, only step
length and time are likely controlled by the central nervous system and
no (or lazy) velocity control is required.