Page 296 - Control Theory in Biomedical Engineering

A double pendulum model for human walking control 269

and well-known mass-spring model suggested to re-generate the pattern of
ground-reaction force of walking (Aloulou and Boubaker, 2011, 2015). This
model explains locomotion stability (Aloulou and Boubaker, 2010). The pen-
dulum can be also mentioned as another effective and simple model
(Boubaker and Iriarte, 2017). It has been used to study walking stability on
aramp(Nourian Zavareh et al., 2018; Nazarimehr et al., 2017)as well as
the optimality of step size and velocity of walking over the ground (Kuo,
2001, 2002). To the best of the authors’ knowledge, there is no study based
on the pendulum model to investigate T n , L n , V n ,and P n variabilities during
walking on the treadmill.
In this chapter, simple models using a double pendulum model for con-
trol of walking on the treadmill are developed. These models focus on
important parameters of walking, that is, T n , L n , V n , and P n , and their var-
iabilities. Initially, four controllers are designed for each of these parameters
during walking on the treadmill. Afterward, models using different combi-
nations of these controllers are proposed. Then, by adding noises to model
parameters, variabilities are included. Finally, the results of a comparison
between these different models are presented.

2 Material and method
2.1 Double pendulum model
In this chapter, a double pendulum is used as a human walking model (Kuo,
2002; Garcia et al., 1998)as shown in Fig. 1. In this model two major phases of
walking, single support and double support, are considered. g is gravitational
constant, L is leg length, m is foot mass, and M is hip mass. ϕ and θ are defined

Fig. 1 Representation of both single and double support phase of the model. (A) Single
support phase. (B) Double support phase.