Abstract
The multichannel closed-loop
1. INTRODUCTION
A closed-loop control of paralyzed limbs using
The method was found to be effective on the tracking control of two degrees of
freedom of movement of the wrist joint stimulating four muscles through experiments with neurologically intact subjects. The method
could solve the ill-posed problem in calculation of stimulus intensities. However, good tracking control was not achieved with a hemiplegic patient at
the first clinical test because of the small range of motion of the wrist
radial flexion and increased reflex function [3].
In this paper, a clinical test of the closed-loop FES control was
performed again with another hemiplegic patient who had experiences in
2. METHODS
2.1. Control Algorithm
The PID control
algorithm was described by the following equation:
where Sn,
Sth and en are stimulation intensity vector at present time n, the minimum stimulation intensity vector
for
Li and Ti are delay time
and time constant of step response, respectively, when the muscle i is stimulated separately. In case of a
muscle has two or more degrees of freedom of movement, the delay time and the time
constant obtained from every movement are averaged respectively. Dt is the sampling interval. mij- is the element of the generalized inverse matrix M - of the matrix M . Elements of matrix M
are slopes of approximated linear lines of the input-output (stimulus
intensity-joint angle) characteristics calculated by the least squares method between the minimum and the maximum stimulation intensities. The inverse matrix of M does not exist in general because M is not the square matrix (i.
2.2. Experimental Method
Wrist joint angles of
the dorsi/palmar- and the radial/ulnar-flexions of the paretic side of a right hemiplegia (63 years old, male) were controlled by stimulating the flexor carpi radialis (FCR),
the flexor carpi ulnaris (FCU), the extensor carpi radialis longus/brevis (ECR)
and the extensor carpi ulnaris (ECU). Stimulus
current
pulse amplitudes (pulse frequency: 20Hz, pulse width: 0.2ms) were regulated by the
controller and applied to the muscles through isolator (5384, NEC Medical
Systems) and surface electrodes
(F-150M, Nihon Koden). Maximum pulse amplitude was determined in order to get
enough control range without pain. The wrist joint angles were measured with the magnetic
3-D position and orientation sensor (FASTRAK, Polhemus) with 20Hz of sampling
frequency [2].
The subject sat on a chair and relaxed his right upper extremity during
experiments. The closed-loop
control was performed under two different upper limb positions: in the
direction of the gravity with the neutral position of the forearm in the
pronation/supination angle (vertical position) and in the horizontal plane with
almost full extended elbow joint and 90deg pronation of the
forearm (horizontal position). The horizontal position was maintained by
supporting the forearm and the upper arm with wooden pedestal. Parameter values of the PID controller were determined at the vertical
position, which were fixed for all control experiments. Target joint trajectory
was circle on the joint angle plane with 10s or 5s of cycle period.
3. RESULTS
Examples of the input-output characteristics of
stimulated muscles are shown in figure 1. The approximated linear lines between the minimum
and maximum intensities for
Figure 2 shows examples of control results of tracking target joint angles. In the first 5s, joint positions were moved from the relaxed position to
the starting position on the target trajectory. In the
experiments, parameters of the PID controller were not optimized
after the first determination from the input-output
characteristics and the responses to step-shaped stimulations. In the case of controlling at the vertical position, tracking control was
almost achieved although small amplitude of oscillation of joint angles was
observed. Even in the case of controlling at the horizontal position, the
tracking was not so severely deteriorated. Especially, little oscillation was
caused in the first half of the control. These results were similar to those of
the previous experiments with neurologically intact subjects. The PID
controller was considered to perform well with the hemiplegic patient.
4. DISCUSSION AND
CONCLUSIONS
The PID controller could regulate stimulus currents
properly after the PID parameter determination by simple measurements. In the experiment of this
paper, fine tuning of the PID parameters was not performed considering clinical
application since the trial and error tuning of the parameters causes burdens
on patients. Simplifying parameter determination process is one of important
factors for clinical applications of
In the experimental results, the ECU had steep
response in the input-output characteristic and little contribution to the
dorsiflexion. These were considered to be a reason of the undesirable responses
such as the oscillation of joint angles. As seen in our previous clinical test
with a hemiplegic patient, the small range of motion and
reflex like response caused oscillating responses [3]. It will be necessary to
vary controller parameters considering stimulation intensity and/or joint
angles and so on during control.
Results of this paper showed that the multichannel PID control method would
be effective in
References
[1] Watanabe T, Iibuchi K, et al.
A method of multichannel PID control of 2-degree of freedom of wrist joint movements
by functional electrical stimulation. Systems and Computers in
[2] Kurosawa K, Watanabe T, et al. Development
of a closed-loop FES system using 3-D magnetic position and orientation measurement
system. J. Automatic Control, 12(1): 23-30, 2002.
[3] Watanabe T, Matsudaira T, Kurosawa
K, et al. Wrist joint control by multichannel closed-loop FES system: system construction
and first clinical test, Proc. 7th Ann.
Conf. Int. FES Soc.: 265-267, 2002.
[4] Kurosawa K, Murakami H, Watanabe T,
et al. A study on modification method of stimulation patterns for
Acknowledgements
This study was partly supported by the Ministry of Education,
Culture, Sports, Science and