Page 295 - Control Theory in Biomedical Engineering

268 Control theory in biomedical engineering

(Lewek et al., 2009; Ziegler et al., 2010). Besides motor and sensory sources
of biological noises (Osborne et al., 2005), high degrees of freedom can be
considered as another source of these variabilities (Todorov and Jordan,
2002; Scott, 2004). A great number of muscles and joints provide infinite
choices for the nervous system to achieve the same goal (Engelbrecht,
2001), such as walking (Bohnsack-McLagan et al., 2016) or running
(Agresta et al., 2019). There is a popular hypothesis that assumes the nervous
system chooses an optimal solution to reach a task (Srinivasan and Ruina,
2006). This assumption is proper to express the average of attempts, how-
ever, it discusses less about movement variability (Kang and Dingwell, 2008;
Dingwell and Marin, 2006).
Stride length (L n ), time (T n ), and velocity (V n ) during walking are global
parameters that have largely been studied (Duncan, 2018; Terrier, 2016;
Decker et al., 2016; Malcolm et al., 2018). Detrended fluctuation analysis
(DFA) (Hu et al., 2001; Kantelhardt et al., 2001) is a method to determine
statistical persistence/antipersistence of signals. This method has been widely
used to analyze time series of these important parameters (Kirchner et al.,
2014; Hausdorff et al., 1999; Roerdink et al., 2019). It has been revealed that
sequences of L n , T n ,and V n during walking over the ground have high sta-
tistical persistence showing low control effort applied for each parameter
(Terrier et al., 2005). Using metronome changes T n to antipersistence time
series, however, neither S n nor L n has been changed. This represents a higher
control effort on T n (Terrier et al., 2005). For another instance, the studies on
walking on a fixed-speed treadmill showed an increase in S n antipersistent
characteristic (Terrier and D eriaz, 2012; Dingwell et al., 2010). Position on
the treadmill after each stride (P n ), is another important parameter considered
in the literature (Dingwell et al., 2010; Dingwell and Cusumano, 2015).
To answer the question of which strategy (position control or velocity
control) the nervous system employs for walking on the treadmill, J. B. Ding-
well and J. P. o. Cusumano designed four black-box models to generate the
sequence of L n and T n , based on different control strategies (Dingwell and
Cusumano, 2015). They revealed that L n , T n , V n ,and P n of the model with
a velocity control strategy could produce results similar to those of the exper-
imental data (Dingwell and Cusumano, 2015). Although such black-box
modeling is useful to simplify and clarify walking behavior, it produces no
information about the bio-mechanics of the movement. In this case, the appli-
cation of simple and conceptual dynamical robotic models can be helpful.
These models benefit both the advantages of simplicity as well as gait mechan-
ical dynamics. As a typical model in this category, we can point to the simple