Dynamically Removing Partial Body Mass Using Acceleration

Transcription

Proceedings of the 2007 IEEE 10th International Conference on Rehabilitation Robotics, June 12-15, Noordwijk, The Netherlands
Dynamically Removing Partial Body Mass Using Acceleration
Feedback for Neural Training
Ou Ma, Xiumin Diao, Lucas Martinez, and Thompson Sarkodie-Gyan
Abstract - This paper describes a control strategy for an
active body suspension system for treadmill based neural
rehabilitation or training devices. Using an acceleration
feedback, the system behaves like dynamically removing part or
all of the body mass of the trainee so that he/she will truly feel
like having a reduced mass while being trained for walking,
jogging, or other leg activities on a treadmill. It will be shown
that the proposed controller can compensate any amount of
inertia force which would not be present as if the trainee had a
real reduced mass. As a result, the dynamic load on the
trainee's body as well as the supporting legs during an exercise
will also be reduced correspondingly. Simulation results are
presented to demonstrate the benefits of the actively controlled
body suspension system.
Key words - Suspension, neural training, rehabilitation,
acceleration feedback, cable robot
I. INTRODUCTION
VER twenty-six million people worldwide (a few
millions in US alone) are suffering from walking
disabilities caused by traumatic injuries, brain and spinal
cord diseases, or other health problems [1]. Healthcare
research has shown that many of them can resume their
walking capabilities by performing repetitive activities or
exercises of their legs with the assistance of rehabilitation
professionals and equipments [2, 3]. Treadmill and roboticsbased training systems for neural rehabilitation of lower
limbs such as the Gait Trainer [1] and Lokomat [4] have
attracted lots of attention from researchers and practitioners
recently [5-12]. One of the major components of such a
training system is its weight suspension subsystem. The
primary function of the equipment is to reduce the weight of
the trainee, so that he or she can walk or jog with his/her
disabled or artificial legs during training without the burden
of carrying the whole body mass. A commonly used
approach for reducing the body's weight is to use a cable
Ou Ma is with the Department of Mechanical and Aerospace
Engineering, New Mexico State University, P.O. Box 30001-3450, Las
Cruces, NM 88003 USA (corresponding author: Tel.: 505-646-6534; fax:
505-646-61 1 1; e-mail: omaAnmsu.edu).
Xiumin Diao is with the Department of Mechanical and Aerospace
Cruces, NM 88003 USA (Email: xiuminwnmsu.edu).
Lucas Martinez is with the Department of Mechanical and Aerospace
Cruces, NM 88003 USA (Email: lucasmarAnmsu.edu).
Thompson Sarkodie-Gyan is with the Department of Electrical and
Computers Engineering, University of Texas at El Paso, El Paso, TX 79938
USA (Email: tsarkodiAutep.edu).
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suspended counter-weight balance mechanism in the vertical
direction [13, 14]. In such a mechanism, the trainee's body is
suspended by a counter weight through a cable. One wishes
the trainee would feel like having a reduced weight equal to
the counter weight. Such a cable suspended passive counterweight mechanism has drawbacks from dynamics point of
view. For example, in the ascending phase, the trainee will
feel a larger weight than expected due to the weightlessness
of the counter weight. If the upward acceleration of the
trainee's body is larger than the gravity acceleration, the
trainee will feel all his/her own weight as without the counter
weight because the cable becomes slack in this case. In the
descending phase, the counter-weight balance system can
balance some or all of the trainee's weight. However, the
system will overly balance the trainee's weight because of
the inertia force on the counter weight. In other words, the
counter-weight balance system balances too much of the
trainee's weight in the descending phase while it balances
too less in the ascending phase as long as the trainee's body
has a nonzero acceleration in the vertical direction. These
undesirable effects are more significant when the leg
movement of the trainee is irregular, which usually happens
in the early stage of a neural training process in which a
regular gait has not resumed or established. This is because
an irregular movement is associated with more significant
transient dynamics and thus more inertia force on the trainee.
Another drawback is that the counter weight has to be
manually adjusted if one wants to change the weight to be
reduced. This makes it very difficult to automatically and
seamlessly adjust the counter weight during the training.
One can understand that the most ideal solution to this
problem would be to just remove a part of the trainee's mass
without really adding any external constraints. Unfortunately,
this is impossible because the mass of a person cannot be
physically removed. However, this desire of removing mass
can still be realized by an active suspension system with a
force control capability. In other words, one can design an
actively controlled suspension system to make the trainee
really feel like having a reduced mass dynamically regardless
how he or she moves (e.g., walking, jogging, jumping, etc.)
during the training. The idea is to control the tension in the
cable which hangs the trainee's body using an accelerationfeedback strategy. Acceleration feedback has the advantages
of fast response and easy implement because the acceleration
of a human body can be easily measured while he or she is in
motion. The active suspension system can guarantee the
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trainee's body to have the same dynamic characteristics (i.e.,
same dynamic response) as if a part or all of his or her body
mass were physically removed. The paper will show in
theory that the control strategy can make the resulting
closed-loop system behave exactly as if a part of the trainee's
mass were removed. A concept design of such a system will
also be presented. Simulation examples will be provided to
demonstrate the effectiveness of the system.
II. DYNAMICS ANALYSIS
Before the development of the actively controlled
suspension system, one needs to understand the dynamics of
a human body while he or she is on training using the system.
For the convenience of demonstrating the concept of the
proposed active system, the dynamics of a human body is
approximated in the vertical direction by a simple springmass model [15] as shown in Fig. 1, where ml, b1 and k1
represent the mass, damping coefficient, and stiffness of the
human body. The body gait y0 is assumed to be a motion
trajectory of the mass center of the human body.
Body mass
_
Body stiffness & damping
Yi
Body gait
Yo
If the mass of the body is reduced by an amount of m22,
then, the reduced-mass system, conceptually shown in Fig. 2,
can be described by the following equation:
(MI1 - M2)(Y0 + 1) + b1jj + k1y -(MI1 - M2)g (3)
Reduced
body mass
ml -m2
b
B
/'"oBdy gait
X
Fig. 2. Simplified dynamics model of a human body with a reduced mass
If one uses a counter-weight based passive suspension
system to "remove" the same amount of the body's mass, the
dynamics system may be illustrated in Fig. 3. In the system, a
counter weight with a mass of m2 is used to balance the
same amount of body mass, so that the trainee feels like
having an equivalent reduced mass dynamically. b2 and k2
represent the cable's damping coefficient and stiffness
coefficient, respectively. In this case, the dynamics model of
the system becomes
ml (j0 + Yj ) + b,yj> + k1y= k2y2 + bJ2 -Mlg
(4)
m2 j0 + j1 + 2 )+ bJ'2 + k2y2 = M2g
where Y2 is the deflection of the suspension cable.
Obviously, such a counter-weight based passive suspension
system is a 2-DOF system because of the cable flexibility.
X
Fig. 1. A simplified dynamics model of a human body
During walking or jogging, the human body is carried by
the legs following a body gait. In a regular walking, the gait
may be represented by a 3-D periodical function [16]. In
other activities, the gait function may be represented by an
impulse, a step or other more complicated functions. In this
paper, we limit our discussions on the sagittal plane only.
With this condition, the walking gait reduces to a sinusoidallike curve on the sagittal plane. In general, one may assume
that the body gait is represented by a general function of time
(1)
Yo = Yo(t)
Based on such a simplified model, the dynamics of the body
motion is governed by the following equation of motion
ml (y0 + Y1 ) + blyl + kly, = -mlg
(2)
where y1 is the vertical displacement of the mass center of
the body relative to the body gait. g is the gravity
acceleration.
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Fig. 3. Counter-weight based passive suspension system
Now, let us examine an active weight suspension system
1103
shown in Fig. 4. In the system, the counter weight is replaced
by a control force f applied on the suspension cable. In this
case, the cable stiffness and damping are neglected because
their effects are much insignificant than these provided by
the active control system. For example, the cable spring
stiffness is 6125 N/m (see Table 1) but the proportional gain
of our controller is only 80 N/s. In fact, one can always
select a high stiffness and low damping cable in the design of
the system. The governing equation of such a system is
(5)
m1(O +jl1) + b1 l + k1y1 = f - m1g
Rewrite (5) such that its LHS is identical to that of (3), i.e.,
(ml m2)(Yo + j1) + b1j, + kly1
-
=
f -mlg -m2(yO +y1)
(6)
Note that the left hand side of the above equation is the
same as that of the ideal reduced-mass system in (3). The
control force f can be designed to make the right hand sides
of the two equations identical and thus, the two
corresponding systems become equivalent as discussed in the
next section.
In all the above discussed cases, the dynamic load exerting
on the supporting leg or legs by the trainee's body can be
calculated as follows:
(7)
fb = b11 + k1y1
Body mass
ml
Control force
f
y
TABLE 1. MODEL PARAMETERS
b,
Parameter
Body mass
Counter weight
Body stiffness
Body damping
Cable stiffness
Cable damping
Body gait
x
Fig. 4. Active suspension system
III. ACCELERATION FEEDBACK CONTROL
To make the active suspension system shown in Fig. 4
have the identical dynamic behavior as the ideal reducedmass system shown in Fig. 2, all one needs to do is to
provide the following control force in the suspension cable
(8)
f=m2g+m2(jo+j1)
Equation (8) defines the control force which the active
suspension system has to provide in order to make the
system behave exactly as to remove a mass of m2 from the
human body. Note that the last term of (8), m2 1 , means that
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acceleration feedback is needed in the control system. It
should be pointed out that the cable will always be in tension
in a training exercise because the control force is always
pulling the cable. A push force happens in the cable only if
the control force shown in Fig.4 is pointing upward (in y
direction) which means, according to (8), the trainee has a
downward acceleration exceeding the gravity acceleration.
That is physically impossible. Thus, the physical law
guarantees that the control law will never try to push the
cable. From the above discussion, one can conclude that an
active suspension system with an acceleration feedback can
make the trainee feel exactly as having physically removed
an amount of his or her mass while he or she is in motion.
This effect cannot be achieved by the passive counter-weigh
system as discussed in Section I.
To demonstrate the benefit of using the active suspension
system to simulate the reduced-mass situation, the dynamic
responses of the three different systems shown in Figs. 2-4
are simulated in MATLAB for comparison. The basic
parameters of these dynamics models are listed in Table 1.
Bertos et al. [15] developed a 2nd order biomechanical model
for able-bodied walkers and pointed that the stiffness and
damping of the human body were related to the walking
speed. The human body's stiffness and damping parameters
in this study are chosen by assuming the human body having
an average walking speed of 2 m/s. The cable stiffness is
chosen such that the tension in the cable at maximum
deflection is equal to the reduced weight. The cable damping
is set to a value such that the cable will not cause oscillation
(like the case in the reality). In order to demonstrate the
advantages of the active weight suspension system, the
dynamic responses of the above-mentioned three systems to
a step input and a sinusoidal input are simulated and then
compared with each other.
Variable
ml
m2
ki
bi
k2
b2
Value
100
50
11000
900
6125
306
Unit
kg
kg
N/m
Ns/m
N/m
Ns/m
The dynamic responses of the three systems to a step input
are shown in Figs. 5-9. It should be emphasized that using a
step input to study the dynamic characteristics has been a
standard approach in control engineering although many
step-like practical inputs (e.g., climbing a stair) is not exactly
a step function. The results from such a study will still
provide valuable insight into the system to be investigated.
The simulation results showed that the dynamic response of
the active suspension system slightly lagged from the ideal
reduced-mass case. But their magnitudes are almost the
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same. The plots also show that the passive suspension system
has much larger position and force fluctuations in
comparison with the active suspension system. In particular,
the peak force (acting on the body and also the supporting
leg or legs) in the passive system reached 641 N while that in
the ideal reduced-mass system is only 570 N. Note that the
negative sign of the forces in Figs. 8 and 9 means that the
forces are in the negative y direction. After subtracting the
gravity force (which is 490 N), the dynamic peak force of the
passive system is nearly 89% more than that of the reducedmass situation. This is, in fact, a significant burden on the
trainee. On the contrary, the peak dynamic force (as well as
the transient force profile) in the active system is almost the
same as that in the ideal reduced-mass system. This means
that, with the active suspension system, the trainee can really
feel like having his/her mass reduced.
_ -450
z
a) -500
2 -550
:
0
-600
9 -650 _
0
0.5
1
1.5
2
2.5
time (s)
Fig. 9. Control force of the active suspension system
The dynamic responses of the three systems to a
sinusoidal input are shown in Figs. 10-14. Such an input
represents a body gait seen from regular walking or jogging
in real life. The input gait function used in this simulation
study has been validated against the experiment of a human
subject conducted at the University of Texas at El Paso.
0.05
0.1
0.05
>1
0
-0.05
0
0.5
2.5
1.5
0
0.5
1.5
2
time (s)
2.5
3
3.5
4
Fig. 10. Body gait input (assuming a sinusoidal function)
time (s)
Fig. 5. Body gait input (assuming a step function)
0.02
0.01
0.005
-0.02
-
-0.04_
0
E
-
-0. 08
0
Acti\ve suspension system
-
0
0.5
1
1.5
2
X
0.5
1
Ideal reduced-mass system
Passive suspension system
Active suspension system
-0.06 _
-0.005 ---Ideal reduced-mass systemPassi\ve suspension system
-0.01
l
2.5
1.5
2
time (s)
2.5
3
3.5
4
Fig. 11. Response of the body to the gait input
time (s)
Fig. 6. Response of the body to the gait input
0.05
0.1 _
+
0.08 _
+II
-
----~
0.5
1
1.5
2
-0.1
Passi\ve suspension system
0.02 _
0
-0.05
>s°
>° 0.04 _
0
-O 05
>,
0.06 _
:
0
E
0I
0
0.5
0.5
1
1.5
2.5
time (s)
2
time (s)
2.5
3
3.5
4
Fig. 12. Absolute response of the body to the gait input
Fig. 7. Absolute response of the body to the gait input
-350
z -400 _
en
e)
C' -450 _
a)
-500
a)
-
-500 = = = = =
0
0
u, -550
a)
o -600
U-
-650
-
-
Passi\ve suspension system
0
V
0.5
1.5
2
en
-1500
2.5
time (s)
0
0.5
1
1.5
2
time (s)
2.5
3
3.5
Fig. 13. Force exerted on the leg(s) by the body
Fig. 8. Force exerted on the leg(s) by the body
1-4244-1320-6/07/$25.00 (c)2007 IEEE
-1000 _
0
U-
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4
z
4
-400
feedback controller, acting alone, cannot achieve this goal
because the controller does not have a capability of tracking
a desired gait. To solve this problem, one can add a PID
based position control loop to the feedback control system as
shown in Fig. 15.
-500
-600
0
0.5
1
1.5
2
time (s)
2.5
3
3.5
4
Fig. 14. Control force of the active suspension system
The plots show that the active suspension system responds
the input almost identically as the ideal reduced-mass case in
both magnitude and phase. However, both the position
response and the force response of the passive suspension
system are very different from the ideal reduced-mass
system. As shown in Fig. 14, the control force of the active
suspension system is always negative and thus, the cable is
always being pulled down as shown in Fig.4. The peak
forces in the passive system and the ideal reduced-mass
system are 915 N and 578 N, respectively. This means that
the peak dynamic force in the passive system is about 383%
more than that of the reduced-mass situation. This is a huge
extra load on the trainee which should not be there. Again,
the force response of the active suspension system is almost
identical to the ideal reduced-mass system. This means the
trainee will really feel like he/she has a reduced mass as
expected.
The simulation study indicates that the actively controlled
body suspension system using an acceleration feedback
control strategy is capable of virtually removing any amount
of the body mass of the trainee, so that the trainee can really
feel like having a reduced mass dynamically regardless how
he or she moves (e.g., walking, jogging, or jumping) in the
training process. In other words, the actively controlled
suspension system can dynamically remove part of the
trainee's mass. On the contrary, the passive counter-weight
suspension system removes part of the trainee's mass at the
cost of increasing the dynamic loads. The increased dynamic
load (i.e., inertia force) can be very significant, e.g.,
0.89-3.83 times of the normal load in our examples. This
will, no doubt, add a large burden to the trainee on training.
Note that the above introduced acceleration feedback
controller is not only simple in theory but also very easy to
implement because accelerations of a human body can be
directly measured by attaching a set of accelerometers to the
body during a treadmill based training process.
IV. TRACKING A DESIRED GAIT
The analysis in the previous section revealed that one can
use an active suspension system to dynamically remove part
of the trainee's mass, so that the resulting system will be
dynamically equivalent to a real reduced-mass system. To
achieve this goal, one needs to implement an accelerationfeedback controller in the suspension system. During a
training process, one may wish the trainee's body to follow a
prescribed body gait, which may be described as a motion
trajectory of the mass center of the body. The acceleration1-4244-1320-6/07/$25.00 (c)2007 IEEE
Fig. 15. Control system of the active suspension system
The goal of the added PID loop is to guarantee the
absolute body motion, i.e., y0 + y1, to track a desired input
body gait yo. Note that the added position control loop
should have very little effect on the original acceleration
feedback loop. As shown in Fig. 15, the two control loops are
in parallel.
Figures 16-19 show that the modified controller is able to
make the body track the desired gait input (a step function in
this case) in the presence of external disturbances. Note that
the force errors between the active suspension system and
the ideal reduced-mass system were caused by the external
disturbances rather than the addition of the PID based
position control loop.
0.104
0.102
-
E
0.1
+
0.098
Without position feedback
With position feedback
0.096
0.094 _
o
0.5
1.5
2.5
time (s)
Fig. 16. Response of the body to a step gait input when the system has a
constant disturbance
z -450
_
-
0)
-500
0
/Ideal reduced-mass system
cn
UD
p
LL
-550
0
l 1
0.5
1
1.5
2
2.5
time (s)
Fig. 17. Force exerted on the leg(s) by the body when the system has a
constant disturbance
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0.104
_
0.102 _
E
>
+
0
0.1
0.
0.098
-
0.096
0.094
'
-
0
ICdeal reduced-mass system
vVithout position feedback
vVith position feedback
kl
A
0.5
time (s)
1.5
nonlinear and multi-DOF system with many uncertainties.
2.5 Another example is that possible cable slacking in an
ascending phase has not been considered in the modeling of
this paper. As a result, more detailed dynamics models and
a
more advanced control techniques will be developed in the
future research.
2
Fig. 18. Response of the body to a step gait in[put when the system has
white-noise disturbance
z -450 _
X
-
ACKNOWLEDGMENT
B. Betancourt and C.E. MacDonald of the University of
Texas at El Paso are acknowledged for providing us with
experimental data of human gaits in support of this research.
-500
O0
LL
I;
-550
.A,
0
0.5
1
1.5
2
2.5
time (s)
Fig. 19. Force exerted on the leg(s) by the body when the system has a
white-noise disturbance
It should be pointed out that, to implement the body gait
control, the position of the human body has to be tracked in
the exercise. For the above discussed single-DOF system, the
measurement of the body position is simple. However, it
becomes more difficult if one needs to track the 3-D pose
(both position and orientation) of a human body.
V. CONCLUSION AND DISCUSSION
This paper introduced a control strategy for an active body
suspension system for a treadmill based neural rehabilitation
or training devices. Using an acceleration feedback, the
system is capable of dynamically "removing" part or all of
the body mass of the trainee so that he/she will truly feel like
having a reduced mass while performing a training exercise
(i.e., walking, jogging, or even jumping) on the treadmill
based facility. It has been shown that the proposed controller
can compensate any amount of inertia force which would not
be present as if the trainee really had a reduced mass.
Ultimately, the dynamic load on the trainee's supporting leg
or legs (depending on whether one or two feet touching the
ground in the exercise) will also be reduced correspondingly.
Simulation results demonstrated the effectiveness of the
active system in comparison with the corresponding reducedmass system and a passive counter-weight balance system.
Studies have shown that a human body is undergoing a 3D motion while walking or running [16]. This means that a
complete compensation of the 3-D inertia force and moment
requires a 6-DOF suspension system which is capable of
controlling the body motion in all directions of the 3-D
space. This study is only a first step toward the study and
design of such a general body suspension system. A future
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task in this research is to study the feasibility of using a
multi-DOF cable manipulator to replace the current singleDOF suspension system. Another future task is to extend the
model to be more realistic. For example, the dynamics of the
human body in this paper was assumed to be a simple springmass system. In fact, the real human body is a flexible,
REFERENCES
[1] T. Sarkodie-Gyan, Neuro-Rehabilitation Devices, Engineering
Design, Measurement, and Control, McGraw-Hill, New York, 2006.
[2] M. Visintin, H. Barbeau, B.N. Korner, and N.E. Mayo, "A new
approach to retain gait in stroke patients through body weight support
and treadmill stimulation", Stroke, Vol. 29, pp. 1122-1128, 1998.
[3] C. Werner et al., "Treadmill training with partial body weight support
and an electromechanical gait trainer for restoration of gait in
subacute stroke patient", Stroke, Vol. 33, pp. 2895-2901, 2002.
[4] Lokomat manufacturer: http://www.beka.ru/php/content.php?id=695.
[5] S. Hesse, "A mechanized gait trainer for rehabilitation of gait",
Journal of Rehabilitation and Development, Vol. 37, No. 6, 2000.
[6] S.H. Peurala, Rehabilitation of Gait in Chronic Stroke Patients,
Ph.D. dissertation, Dept. of Neurology, Univ. of Kuopio, Finland,
2005.
[7] J. M. Hidler, D. Nichols, M. Pelliccio, and K. Brady, "Advances in
the understanding and treatment of stroke impairment using robotic
devices", Top Stroke Rehabil., Vol. 12, No. 2, pp. 21-33, 2005.
[8] Dobkin, B. H: "Overview of treadmill locomotor training with partial
body weight support: A neurophysiology sound approach whose time
has come for randomized clinical trials", Neurorehabil and Neural
Repair, Vol. 13, pp. 157-165, 1999.
[9] S. Jezernik, G. Colombo, and M. Morari, "Automatic gait-pattern
adaptation algorithms for rehabilitation with a 4-dof robotic orthosis",
IEEE Trans. on Rob. andAuto., Vol. 20, No. 3, pp. 574-582, 2004.
[10] M. Bernhardt, M. Frey, G. Colombo, and R. Riener, "Hybrid forceposition control yields cooperative behavior of the rehabilitation robot
LOKOMAT", Proc. of IEEE Int. Conf on Rehabilitation Robotics,
Chicago, IL, pp. 536-539, June 2005.
[11] J. Hollerbach, D. Grow, and C. Parker, "Developments in locomotion
interfaces", Proc. IEEE Int. Conf on Rehabilitation Robotics,
pp.522-525, June 2005.
[12] D. Surdilovic and R. Bernhardt, "Spring-Man: a new wire robot for
gait rehabilitation", Proc. IEEE Int. Conf on Robotics and Auto.,
New Orleans, LA, pp. 2031-2036, April 2004.
[13] A. Werning and S. Muller, "Laufband locomotion with body weight
support improved walking in persons with severe spinal cord
injuries", Paraplegia, Vol. 30, No. 4, pp. 229-238, 1992.
[14] A.L. Behrman and S.J. Harkema, "Locomotor training after human
spinal cord injury: a series of case studies", Physical Therapy, Vol.
80, No. 7, pp. 688-700, 2000.
[15] G.A. Bertos, D.S. Childress, and S.A. Gard, "The vertical mechanical
impedance of the locomotor system during human walking with
applications in rehabilitation", Proc. of the IEEE Int. Conf on
Rehabilitation and Robotics, Chicago, IL, June 2005, pp. 380-383.
[16] M.W. Whittle, Gait analysis: an introduction, St. Louis, MO: Heidi
Harrison Elsevier, 2007.
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Dynamically Removing Partial Body Mass Using Acceleration

Transcription

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