Abstract
The aim of this study was to implement a new approach to feedback control of unsupported standing, and to evaluate it in tests with a paraplegic subject. In our setup, all joints above the ankles are braced and stabilising torque at the ankle is generated by electrical stimulation of the plantarflexor muscles. A previous study showed that short periods of unsupported standing with a paraplegic subject could be achieved. In order to improve consistency and reliability, and to prolong the duration of standing, we have implemented several modifications to the control strategy. The results presented here show that the new strategy allows much longer periods (up to several minutes) of unsupported standing.
Introduction
We
are investigating the use of feedback control systems which enable paraplegics
to stand without the support of their hands and arms – we call this unsupported
standing. Functional electrical stimulation (
In
a previous study [4], a nested control structure was proposed in which an inner
loop controls the moment at the ankle, while an outer loop regulates the
inclination angle of the body. It was found that this approach is feasible; a
neurologically-intact subject can be stabilised for long periods of time, and
the controller is able to maintain stability in the face of significant
disturbances. The study also showed that short periods of unsupported standing
could be achieved with a paraplegic subject [1]. We concluded that the
principal limitations to the approach included limited strength, rapid fatigue,
and significant spasticity of the paralysed muscles. While these limitations
are dependent on the condition of the particular subject in question, the
underlying parameterisation and design of the artificial controller has a
crucial effect on the length of time during which successful standing is
achieved. At the same time the controller must be robust enough to deal with
sources of uncertainty and disturbance such as fatigue and spasticity, and must
maintain upright postural stability as reliably as possible.
We
have investigated a number of modifications to the control structure proposed
in [1] (see [2] for details of the new strategy), with the aim being to improve
the consistency and reliability of unsupported standing. Initial results with
neurologically-intact subjects are given in [3]. Results from a new study with
a paraplegic subject are reported in this paper.
Methods
To
perform dynamic tests of unsupported standing, an apparatus called the
"Wobbler" was constructed. Full details of the construction and
functionality of the Wobbler are given elsewhere [4]. The Wobbler apparatus
allows measurement of the moments generated at each ankle, and of the angle of
inclination of the body. A nested control structure for unsupported standing is
shown in figure 1. An inner-loop controller Cm
regulates the total ankle moment m by
applying a muscle stimulation p. The
outer-loop controller Cq regulates the body
inclination angle q
by providing a desired (reference) moment mref for the inner loop. As all joints above
the ankle are braced in our setup, the body dynamics can be described as a
single-link inverted pendulum. This approach which is based on the design
described in [1] was modified in two significant ways. In our previous study,
the total moment requested by the outer loop was distributed equally as a
reference moment to the left and the right muscles. Thus, the stimulation would
be increased to the side which fatigued quicker, though not necessarily with an
increase in moment as the stimulation saturates. However, the other,
non-fatigued, side might still have the ability to generate additional moment.
In our present approach, the same stimulation is applied to both muscles in
such a way that the total moment generated by both sides follows the moment
requested from the outer loop. Thus, the differences in the strength of the
muscles are compensated for and the structure of the inner-loop controller is
simplified.
Figure 1: Controller
structure.
The
second important difference to the previous approach is the controller design
method. In [1], an LQG (linear quadratic Gaussian) design was used which aims
at minimising the control error and the control effort according to a given
criterion with the effect that the characteristics of the closed loop are
generally different for different plant characteristics. In our present study,
we employ a pole-placement design approach where desired closed loop
characteristics are defined by setting a rise-time and damping factor in the
time-domain. Thus the closed-loop characteristics can be specified more
directly and tuning of the controller becomes easier and more consistent.
Additionally, the inner loop which was previously neglected for the design of
the outer-loop controller, is now included as part of the plant for the outer
loop with the effect that stability can be achieved even if the bandwidth of
the inner loop is relatively low.
The
subject in this study was a 44 year old male patient with a complete lesion at
level T7/8, 4 years post-injury. Muscle training involved alternate stimulation
of the plantarflexors and dorsiflexors for initially 30min per day, which was
increased to 1h per day. The subject's muscles were trained for 12 weeks prior
to the first experimental session, and regular training continued throughout
the project. During the experimental sessions, the plantarflexors are
stimulated by pairs of 75mm diameter self-adhesive electrodes which are placed
over the midline of soleus. The stimulator uses a
pre-defined current and produces stimulating pulses in the range of 0-800 ms with a frequency of 20Hz. A
custom-made body brace (padded vacuum-formed polythene shells, reinforced and
joined by steel strips) was used to lock all joints above the ankle.
Results
Results
of standing experiments with the paraplegic subject are shown in figures 2 and
3. The inner-loop is designed with a closed-loop rise-time of 0.2s and an
observer rise-time of 0.1s while in the outer loop, the closed-loop rise-time
and the observer rise-time both equal 0.7s (see [2] for details).
Figure
2 shows a result where the subjects stands quietly with a constant reference
angle, and a disturbance is applied by pulling anteriorly
at chest level with a moment of approx 6Nm. The disturbance causes the subject
to move forward slightly, but he is stabilised by an increase of the
stimulation and the effect of the disturbance is compensated for.
Figure
3 shows a standing test where the subject stands quietly until fatigue causes
the stimulation pulse-width to saturate and the subject loses stability. We
observed that external disturbances (pulling and pushing) applied during the
test could easily de-stabilise the subject. Periods of more than 400 seconds of
unsupported standing were achieved in further tests.
Discussion/Conclusions
The
results of this study show that with the new control strategy a paraplegic
subject can be stabilised in a quiet standing position for significant periods
of time by electrical stimulation of the plantarflexor muscles. The stimulation
level is adjusted by a feedback control structure which uses measurements of
the ankle moments and of the subject's inclination angle. Small external
disturbances can be rejected.
The modifications made to the
controller design approach make the design procedure simple, quick and
reliable. Consistent results could be achieved with the same set of design
parameters at different sessions, although the muscle characteristics can vary
considerably from session to session.
Figure 2: Disturbed standing: a constant disturbance of 6Nm (pulling at the front) is applied from approx 4sec until the end.
Figure 3: Quiet standing. An external disturbance was applied at 90sec and 110sec. After the second disturbance, the subject had to be stabilised by the experimenter and unsupported standing was resumed from 130sec until the end.
The
periods of standing which could be achieved were significantly longer than
those reported in the previous study [1]. The limiting factor was muscle
fatigue. We observed that after the muscles were fatigued (e.g., after the test
shown in figure 3) no further standing was possible even after resting periods
of up to 20 min. In contrast, the approach described here allows virtually
unlimited periods of standing in neurologically-intact subjects [3]. This
suggests that our underlying control approach is satisfactory.
Only a relatively small moment could be
generated at the ankle which was sufficient to stabilise the subject for small
inclination angles. However, disturbances could easily cause loss of balance.
Although it is conceivable that larger moments at the ankle can be achieved by
training the muscles against a load, the principal limitation remains that
paralysed muscle will be significantly weaker than muscles of
neurologically-intact subjects. This underlines the need to include upper body
movement to support balance in practical functional arm-free standing. Matjacic and Bajd have carried
out a study on unsupported standing in which the upper body is free to move
[5]. The results presented here can serve as a basis for the design of
artificial lower-limb controllers for such systems.
References
[1] Hunt, K.J., Munih, M., Donaldson, N., Feedback control of unsupported standing in paraplegia. Part I: optimal control approach, Part II: experimental results, Trans. IEEE on Rehabilitation Engineering Vol. 5 (1997), pp. 331-352.
[2] Hunt, K.J., Gollee, H., Jaime, R.-P., Donaldson, N. Design of feedback controllers for
paraplegic standing. Proc. Inst. Elec. Eng., submitted for publication.
[3] Hunt, K.J., Gollee, H., Jaime, R.-P., Donaldson, N., Feedback control of unsupported standing, Technology and Health Care Vol. 7 (1999), No. 6, pp. 443-447.
[4] Donaldson, N., Munih, M., Phillips, G. F., Perkins, T., Apparatus and methods for studying artificial feedback control of the plantarflexors in paraplegics without interference from the brain, Med. Eng. Phys. Vol. 19 (1997), pp. 525-535.
[5] Matjacic,
Z., Bajd, T., Arm-free paraplegic standing. Part I:
control model synthesis and simulation. Part II: experimental results, Trans. IEEE on Rehabilitation Engineering
Vol. 6 (1998), pp. 125-150.
Acknowledgments: We would like to thank Nick Donaldson for his
contributions in the initial experiments and Ralf-Peter Jaime for assistance
during the experiments.