Abstract
The aim of this
paper is to investigate modelling and control of paraplegic leg cyclical
motion. A humanoid leg is developed in Visual Nastran software in the setting
position, and used with Matlab/Simulink to develop a fuzzy logic control (FLC)
strategy to control the knee joint movement. The FLC output is the
FLC shows
effectiveness in controlling especially in the absence of mathematical model
for the plant. This control strategy can also be used for functional cyclical
exercises such as ergometry cycling and rowing. Simulation results verifying
the control strategy are presented and discussed.
Two types of knee
joint functional movements are investigated and the tracking performance is
satisfactory.
1.
INTRODUCTION
Many people
throughout the world suffer from spinal cord injury, which is usually caused by
accident or disease. Spinal cord injury (SCI) results in loss of mobility and
sensation. Despite the damage that blocks the transmission of motor signals to
the functional muscles, the muscles are still working and can be activated by
external stimulators [1], so a person who has no voluntary control of his
muscle will be able to move with external stimulators. Functional electrical
stimulation (
The success of any
Many studies have
used different nonlinear control strategies to control the knee joint movement
by using the quadriceps stimulation [4] [6] [7]]. [9] used FLC to control
cycling movement induced by
The control of
single limb movements of paraplegics represents an important preliminary stage
towards more complex motor functions such as standing and cycling in paraplegia
[3].
A leg model with
knee extensors is developed in this study and used to develop a suitable
strategy for controlling a sinusoidal movement of the knee joint; the developed
controller can be use to control more complex cyclical movements, such as
rehabilitation cycling and rowing exercises.
2. METHODS
2.1. Leg model
The leg model has
been designed in Visual Nastran (VN) software, which is used to build
mechanical models and simulate them in real time. Models drawn in other
specified computer aided design CAD programs can also be transferred to VN to
be simulated.
It is of vital importance
that the dimensions of the leg are chosen correctly. This is because the
simulation results will be dependent upon the dimensions. In this study, the
human model is assumed to be of 175cm in height and 75 kg in weight. Using the
data given in Winter's standard human dimensions [8], the thigh length is 42.8
cm and its weight is 7.5 kg, also the shank length is 43 cm and its weight is
3.49kg. The leg model can thus be created in VN software using these
parameters.
A thigh and a
shank were built in VN software and connected with a motor joint, which forms
the knee joint (see Figure 1). The angle between the thigh and the shank is
measured in the simulation process and imported to a Matlab/Simulink design to
be controlled. The control signal applied to the VN model is the torque at the
knee joint.
Figure 1 Leg model in Visual Nastran softwar
2.2. Muscle model
The muscle model
is a transfer function between electrical stimulation and the resultant knee
torque [5]. This function was identified by means of a parametric approach that
considered the family of ARX models and using a least square method on the
error between real data and the output of the model.
A simple single
pole model with a static gain dependent on stimulation frequency proved able to
identify the relationship between stimulation and active joint torque fairly
accurately [5]. This muscle model is suitable for the range of the knee
movement in this study. The muscle model is to mimic the quadriceps muscle
group in the thigh, which straighten the knee joint. Thus, the muscle model
works as a knee extensor.
2.3. Controller
A fuzzy logic (FL) controller was developed to
control the leg movement and force the leg to follow a reference sinusoidal
signal. Choosing fuzzy controller inputs and outputs is a very critical
process, because it is important to be sure that all the information needed
about the plant is available through the controller inputs. As can be seen from
Figure 2, the control signal is the stimulation pulses applied to the muscle
model, which in turn produces a torque to the knee joint in VN model. The
inputs of the FL controller are the error (between the actual and reference
knee trajectories), and the change of error. The reference signal is chosen as
a sine wave which has a frequency of π rad/sec. This signal aims to move
the knee joint sinusoidal, from 81.7°
to 101.7°, as a result the shank of the lower limb will move in a cyclical
movement, and this movement will be controlled by the FL controller.
Each of the FL controller inputs has five
membership functions (MFs). This results in 25 fuzzy rules described in Table
1, where e and Δe are the error and change of error respectively.
Figure 2 The controller design via
Simulink
Table 1 The FL rule bas
|
De e |
NB |
NS |
Z |
PS |
PB |
|
NB |
NB |
NB |
NS |
Z |
Z |
|
NS |
NB |
NS |
NS |
Z |
Z |
|
Z |
NB |
NS |
Z |
PS |
PB |
|
PS |
Z |
Z |
PS |
PS |
PB |
|
PB |
Z |
Z |
PB |
PB |
PB |
NB=Negative big NS=Negative small Z=Zero PS=Positive small PB=Positive big
3. RESULTS
The leg movement was controlled to follow a typical sine wave. The total
movement range was 40°. The controller is tested for different ranges of
motion. The FL controller controls only the knee extensors by applying
stimulation pulses to the muscle model. The muscle model is controlled by
changing the pulse width; however the amplitude and the frequency of the
stimulation pulses are constant. It is too difficult to control such a system
with linear controllers, because the plant is nonlinear. FLC is a very good
alternative for controlling the (leg and muscle) system especially in the
absence of mathematical models. Figure 3 show the error plot between the reference and actual knee
trajectories, where the range of error is [-2°, 2°] for the typical sinusoidal
movement, Figures 4 and 5 illustrate the actual and reference knee trajectories
for two types of movement. It is noted that the output matches the desired
trajectory closely.
Figure 3 Error between the reference and
actual knee trajectories for typical sinusoidal motion