Dzeladini, F. (Master Project)



Bipedalism is considered as one of the first distinctive feature developed by the early hominids, compared to their cousins apes. This unique characteristic of human beings has always intrigued scientists and thus has been extensively studied. In the past decades, modeling of human walking has gained particular interest in research, with the venue of computers and increasing computational power. Modeling of human walking is of particular interest in the biomechanical and medical field, as it can give insights in the design of limb prosthesis, providing crucial information regarding the movement of the limb.
Moreover, it is also important for the design of limb orthoses, devices used to modify the skeletal and neuromuscular systems, which are used in rehabilitation by assisting movement of people with walking difficulty (e.g. due to neurodegenerative diseases, such as multiple sclerosis or due to spinal cord injury), or assisting people with injuries during their rehabilitation.
To grasp the context of this project, it is necessary to introduce animal movement
modeling. Animal movement can be modeled as a system of differential equations, coupled
trough interactions of the system with the environment (i.e. sensors to send information
to the system, and actuators send information to the environments). In this framework,
walking can be viewed as a limit cycle; the system oscillates, its trajectory is confined
around the mean of the system trajectory. This limit cycle possesses a relative resistance
to perturbations, i.e., the walking can be more or less stable.
Walking gaits of various animals have been modeled using this framework of differential
equations, and more specifically, using network of coupled oscillators. In these models,
oscillators are coupled among themselves and thus influence each other. Nerve signals
generating swimming in the Lampreys have been modeled using such a system. When the
lamprey swims, nerve influxes are observed as activity burst, repeated at defined intervals.
These bursts are observed along the spinal cord, with a delay in the burst onset that is
proportional to the position along the spinal cord. These neural oscillatory networks are
called central pattern generator (CPG), and have also been observed in the locomotion of
other animals, such as the salamander or the cheetah.
These oscillatory networks were successfully used to model several swimming animals.
However, results obtained with walking animals have been rather disappointing, except for
the salamander, whose movements are relatively simple and slow. This is not surprising,
since this system does not take into account interaction with the environment for shaping
the movement, which should be more important for walking animals.

Previous work

To show the importance of interaction with the environment, work by H. Geyer and his group (2010) should be introduced. They have developed a human walking model solely based on reflexes (i.e. interactions between the body and the environment). This model includes limb dynamic information (muscles, tendons and sensors) and shows the importance of reflexes pathways in movements shape. Applied to the human, this model, based on simple reflex rules, is capable of producing a stable gait, comparable to the real human gait.
In an adaptation of the model made by J. Wang (2012), both walking and running
were obtained by simply varying the parameters of the system. Implementing both the H.
Geyer (referred to as the FBL model, for Feedback Based Locomotion) and the J. Wang
model (referred to as FBL+) is the purpose of the first part of this project.

Extension of the Feedback Based Locomotion Model

The presented FBL model shows the importance of the interaction between the body
and the environment. Biologically, it is known that reflex loops do exist, but a walking
100% based on reflexes is not possible. The presence of a feedforward component allowing
control of gait parameter (such as speed, frequency, step size) seems obvious. The question
is therefore: What is the feedforward component and how can it be integrated to the
existing model? It is plausible – though extensively debated and unproven – that a CPG
component acting on locomotion exist in the human spinal cord. In this project we make
the hypothesis of the presence of such a component. Since reflexes can generate signals that
place the system in a limit cycle, and taken into account the hypothesis that a feedforward
component exist, we can make the new hypothesis that the feedforward component must
be hidden behind those reflex signals.
The analysis of the signals generated by the reflex loops of the FBL model is the
starting point of the second part of this report, where it is demonstrated that when the
FBL model produces a stable locomotion, most of the signals oscillate at a quasi constant
frequency, with only slight variation in shape. Most stable signals are then modeled as
oscillators that can generate waves of arbitrary shapes and/or basal constant input.
We then test the properties of such a system by combining/replacing some reflex loops
by their feedforward counterparts (either as a basal input or as a CPG). We show that, not
only those new models are stable with characteristics close to the original model, but with
online control they showed a clear increase of the robustness compared to the FBL and
FBL+ models. Moreover, modifications of some general parameters of the feedforward
component allow easy changes in gait characteristics, such as gait speed.

General view of the Feedback Based Locomotion model


Details and information flow in the FBL model and its extensions




Figure A
The different kind of interneurons; the sensory interneurons (INSEN ), the basal activity
interneurons (INBAS ) and the CPG interneurons (INCPG ) That forms the spinal cord model responsible for walking.
Figure B
The information flow from interneurons (IN) to musces (MTU) through motoneurons (MN); the FBL, FBL- and 3FBL models only differ at the spinal level, model of muscles are kept the same.
Figure C
Table describing the relationships between IN and MN for the three models (columns: MN, lines: IN) Left: the initial FBL model. Middle: the reduced FBL model (FBL-). Right: the 3FBL model.





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