Model-Based Pressure and Torque Control for Innovative Pneumatic Soft-Actuators
André Wilkening
FWBI – Friedrich-Wilhelm-Bessel-Institute Research Society
and Institute of Automation, University of Bremen, Germany
Miroslav Mihajlov
ITK Enineering AG, Stuttgart, Germany
Oleg Ivlev
FWBI – Friedrich-Wilhelm-Bessel-Institute Research Society
and Institute of Automation, University of Bremen, Germany
ABSTRACT
This paper describes a model-based pressure and torque control concept for innovative
pneumatically driven actuators with rotary elastic chambers. These soft-actuators have been
developed to operate in human environment, especially for physical interaction with people in
service and rehabilitation tasks. Owing to the inherent compliancy of the working chambers,
these actuators possess additional (compared to conventional fluidic actuators) nonlinearities,
causing specific problems related to their modeling and control. The pressure and torque control
concepts were investigated and tested by using a knee motion therapy device as test-bed. The
torque control is used to compensate the weight of the device mechanics as well as the patient’s
lower leg. Next step is the realization of "Assist-as-Need" behaviour for rehabilitation tasks.
NOMENCLATURE
p chamber pressure bar
m mass flow rate Nl/min
V chamber volume m3
R gas constant 287 J/kgK
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T temperature 297 K
U voltage V
torque Nm
1 INTRODUCTION
Actuators with inherent compliance (soft-actuators) are predestinated for service and
rehabilitation tasks. The well-known fluidic artificial muscles belong to this category and
their working principle is quite analogous to the biological one. Different designs of
pneumatic muscles are reviewed in /Dae02/. This type of muscles generate pulling
forces, for the realization of a revolute joint a mechanical transmission is necessary
which leads to complex kinematic structures. One example is the realization of an
exoskeleton for use in physiotherapy /Tsa03/. In contrast to that, actuators with rotary
elastic chambers (REC-actuators) present a revolute type of artificial muscle and have
been developed preliminary for working in direct environment with humans /Ivl09/. Due
to the design, the actuators can be directly integrated in revolute robot joints, without
any additional transmission elements. However, all kinds of fluidic actuators behave
strongly nonlinear which not only depends on the air compressibility in the chambers.
Thus, an exact control becomes a difficult task. This paper describes a model-based
pressure and torque control using low-noise servo-valves. For rehabilitation tasks a low-
noise therapy device is desirable. Hence, the PWM controlled switching valves used in
/Mih08/ are unsuitable. As fundamental base, the nonlinear characteristics of REC-
actuators and of servo-valves have been determined in experimental manner. The
pressure control was investigated, using two different types of servo-valves, and
compared to pressure proportional valves. Furthermore a model-based torque control
was developed using a knee motion therapy device as test-bed, to achieve a
compensation of gravitation of patient’s lower leg and mechanics. This successfully
tested torque control can be used as a base for prospective rehabilitation tasks.
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2 PNEUMATIC SOFT-ACTUATORS
By means of passive inherent compliance the REC-actuator is predestined to operate in
service or rehabilitation tasks. The mode of operation is quite similar to conventional
single vane fluidic motors, which consist of two chambers and a fixed rotary vane. A
general difference is the replacement of the rigid chambers by the elastic chambers.
Due to strongly nonlinearities of soft-actuators, which not only depends on the air
compressibility in the chambers, control becomes a difficult task. Unfortunately, because
of the material properties of the membrane the actuator hysteresis effects are
unavoidable. The actuator with pleated Rotary Elastic Chambers (pREC), which can be
seen in Figure 1, has a diameter of 100 mm and a height of 90 mm. Owing to the two
half cylinders made of aluminium and the ultra slim bearing the actuator housing is
lightweight and of high stiffness. The weight of one chamber is 50 g and the total
actuator weight is approximately 500 g. Effective working range is currently limited to an
angle of ± 45°, while the maximal torque is 20 Nm developed at the working pressure of
5 bar.
Figure 1: pleated Rotary Elastic Chamber (pREC) actuator
3 MODEL-BASED PRESSURE CONTROL USING MASS FLOW MAPS OF SERVO-
VALVES
This section describes the model-based pressure control law for pneumatic pREC-
actuators developed in /Mih08/, which has been realized and tested using servo-valves
instead of on-off valves. To compensate nonlinearities of servo-valves an inverted model
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of determined flow map of valves has been used, similar to /Wol06/. To verify the
properties of low-noise servo-valves, a model was created in an experimental manner,
because theoretical mass flow equations are only approximations of current mass flow.
Two types of servo vales were analyzed and compared by using below presented
model-based pressure control, namely the FESTO MPYE-5-1/8LF-010-B servo-valve
and the GAS-Automation WS 15 G1/8 servo-valve. Considering that in a closed
chamber just the dynamic mass flow rate is measurable, two test plants were used
(inflow and exhaust flow) to describe the dynamics in a steady state. Figure 2 shows the
experimental setups.
Figure 2: Experimental setups for measuring, a) inflow rate, b) exhaust flow rate
The adjustable cut-off valve (valve 2) limits the mass flow, which was measured by using
the mass flow sensor ifm electronic SD6000 and for lower mass flows the
SensorTechnics FHA. By independently variegate the servo-valve and the cut-off valve,
different combinations of pressure and mass flow could be achieved. To measure the
actual chamber and supply pressure two SensorTechnics SCX pressure sensors were
used. By means of very high mass flow rates the pressure supply slightly alternates.
Thus, for simplification, it is assumed to be constant. To achieve a model that describes
the complete behaviour of valves, inflow and exhaust flow map were combined. Figure
3 shows the models of the valves. Note, that only the FESTO valve map contains of a
major dead zone, whereby a more precisely closing behaviour is afforded.
a)
b)
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a)
0 2.5 5 7.5 10
0123456
-200
0
200
voltage [V]pressure [bar]
mas
s flo
w r
ate
[Nl/m
in]
b)
0 2.5 5 7.5 10
0123456
-200
0
200
voltage [V]pressure [bar]
mas
s flo
w r
ate
[Nl/m
in]
Figure 3: Experimentally determined mass flow map of valves, a) FESTO MPYE-5-
1/8LF-010-B, b) GAS-Automation WS 15 G1/8
One obtains a nonlinear function of the mass flow depending on supply voltage and
chamber pressure, whereby the supply pressure is assumed to be constant.
constppUfm ss ,, (1)
The pREC-actuator comes with complex volume characteristic which has a stake in the
pressure dynamics.
2,1,,,,,,; ippfVppufmVpmRTV
p siisiiiiii
i
(2)
Based on the pressure dynamics (2) the control law for the closed loop system is
assumed to be:
i
iiiidpi V
VpppKmRTG
(3)
Thus, the mass flow rate is chosen as:
i
iiiidp
ii
V
VpppK
RT
Vm
(4)
Note that the law based on the feedback linearization approach is composed of two
terms. The first term expresses a volume proportional P controller and the second term
describes a compensation of mass flow rate. This second term should compensate
pressure variation based on a fast change of volume. With the chosen control law a
decoupling of the pressure subsystem and the mechanical subsystem as well as a
compensation of previously described nonlinearities of valves should be given. The
desired mass flow rate in (4) describes a virtual actuating variable, whereby obviously
the real one is the supply voltage of servo-valves, which is obtained by using the
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inverted model of servo-valves. One achieves a function of supply voltage depending on
the mass flow rate and the chamber pressure.
constppmfU s ,,1 (5)
At first the step responses of applied pressure step references have been compared
using GAS-Automation and FESTO servo-valve. Afterwards the step responses using
FESTO servo-valve MPYE-5-1/8LF-010-B and FESTO pressure proportional valve
MPYE G 1/8 have been compared. Objective was to show the advantage of using
developed model-based pressure control instead of internal pressure control of FESTO
MPYE G 1/8 valves. Finally an analysis of tracking behaviour to sinusoidal reference
pressure signal as well as pressure response to fast angle variation was done by using
those two different types of FESTO valves. Figure 4 shows positive and negative step
responses using FESTO and GAS-Automation servo-valves, whereby step reference
was applied in an interval of pd = [1,5] bar.
a)
0 0.1 0.2 0.3 0.4 0.50
2
4
6
time [s]
pres
sure
[ba
r]
b)
0 0.1 0.2 0.3 0.4 0.50
2
4
6
time [s]
pres
sure
[ba
r]
Figure 4: Closed loop response of pREC-actuator with FESTO servo-valves in red and
with GAS-Automation servo vales in blue, a) positive desired pressures, b) negative
desired pressures
The comparison shows proper results with a more homogeneous performance using
FESTO servo-valves (red curve). Settling times as well as steady state errors are
smaller. This can be explained by better valve characteristics of FESTO valves, in
particular being able to supply a larger flow rate plus the attribute of hard closing. In
contrast the soft closing behaviour of GAS-automation valves leads to damped step
responses (blue curve). For this experiment the pREC-actuator was fixed in its zero
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position. The following Table 1 presents the results of the pressure step response
comparison.
ts(s) ess(mbar)
FESTO MPYE-5-1/8LF-010-B ≤0.12 ≤30
GAS-Automation WS 15 G1/8 ≤0.21 ≤50
Table 1: Specific values of the step responses using FESTO and GAS-Automation
servo-valves
To show the improvement, the FESTO servo-valve MPYE-5-1/8LF-010-B and the
FESTO pressure proportional valve MPYE G 1/8 with internal pressure control have
been compared. At First the pressure step responses are shown in Figure 5.
a)
0 0.1 0.2 0.3 0.4 0.50
2
4
6
time [s]
pres
sure
[ba
r]
b)
0 0.1 0.2 0.3 0.4 0.50
2
4
6
time [s]
pres
sure
[ba
r]
Figure 5: Closed loop response of pREC-actuator with FESTO servo-valve MPYE-5-
1/8LF-010-B in red and with FESTO pressure proportional valve MPYE G 1/8 in blue, a)
positive desired pressures, b) negative desired pressures.
The model-based pressure control (red curve) shows a much shorter reaction time as
the internal pressure control (blue curve). Table 2 summarizes the results of above
shown step response comparison. Steady state errors are larger as twice the number,
when using the internal pressure control.
ts(s) ess(mbar)
FESTO MPYE-5-1/8LF-010-B ≤0.12 ≤30
FESTO MPYE G 1/8 ≤0.32 ≤70
Table 2: Specific values of step responses using FESTO servo-valve and FESTO
pressure proportional valve
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A further attribute of performance is the pressure response to fast angle variation, which
can be seen in Figure 6.
a)
0 2 4 61.5
2
2.5
3
3.5
time [s]
pres
sure
[ba
r]
0 2 4 6
-20
0
20
40
angl
e [°
]
b)
0 2 4 61.5
2
2.5
3
3.5
time [s]
pres
sure
[ba
r]
0 2 4 6
-20
0
20
40
angl
e [°
]
Figure 6: Closed loop response to fast angle variations, a) FESTO MPYE-5-1/8LF-010-B
and the model-based pressure control, b) FESTO MPYE G 1/8 with internal pressure
control
Figure 7 shows a sinusoidal pressure reference tracking. Two types of pressure control
methods were analyzed and compared by using a frequency of 1 Hz, 6 Hz and 10 Hz.
The Offset is chosen to 2.5 bar and the amplitude to 1 bar.
a)
0 1 2 323
0 1 2 323
pres
sure
[ba
r]
0 1 2 323
time [s]
b)
0 1 2 323
0 1 2 323
pres
sure
[ba
r]
0 1 2 323
time [s]
Figure 7: Sinusoidal pressure reference tracking, above: frequency = 1Hz, central:
frequency = 6Hz, below: frequency = 10Hz, blue curve: reference pressure, red curve:
actual pressure, a) FESTO MPYE-5-1/8LF-010-B and the model-based pressure
control, b) FESTO MPYE G 1/8 with internal pressure control
The comparison shows far better performance of the model-based pressure control,
whereby even with a frequency of 10 Hz a tracking is achieved. In contrast, the internal
pressure control shows a weakness already with using low frequencies. For higher
frequencies a tracking is not given any more.
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4 MODEL-BASED TORQUE CONTROL FOR REHABILITATION DEVICES
Robot assisted motion therapy applications require an enhanced attention to patient’s
safety. Hence, a demand for safe robot solutions, using the properties of soft, i.e.
inherently compliant actuators, is increasing. To perform preliminary functional tests and
to investigate prospective patient-centred (assistive) control strategies the proof-of-
concept prototype with pREC-actuators has been used, which is shown in Figure 8. As
a passive load a leg dummy filled with a synthetic material to get a realistic weight of the
lower leg is applied. The thigh and the lower leg are connected through a single-axis
mechanical knee joint from Otto-Bock. The active forces occurring while patient activities
have been simulated manually. The test-bed is driven by two pREC-actuators to double
the maximum actuator torque and beyond that, the plant consists of two pressure
sensors, one angular encoder and two servo-valves.
Figure 8: Test-bed for knee motion therapy equipped with two pREC-actuators
As base for assistive control concepts a model-based torque control has been
developed. Objective was to achieve compensation of gravitation of mechanics and
patient’s lower leg, without using expensive torque sensors. Due to this advantage
rehabilitation after heavy neurological injuries or strokes will be possible. Instead of
torque sensors inverted torque characteristics of actuators are used. Note that torque
characteristics of pREC-actuator are nonlinear functions of chamber pressure and actual
vane angle.
sppf ,, (6)
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Besides these characteristics the actuator turns out to possess hysteresis behaviour.
Thus, to determine torque characteristics of pREC-actuator an experimental method
was used. Rising hysteresis is noticeable relating to the rising pressure. To create an
interpolated and extrapolated model, which is shown in Figure 9.a, the mean values of
these characteristics have been used. The main idea of model-based torque control is to
use inverted torque characteristics of actuators as a mapping of pressure. In case of
compensation of gravitation, the desired torque equals the torque of payload, included
patient’s lower leg plus device mechanics, which have been calculated in analytical
manner. By using the delta principle the desired torque is apportioned to the upper and
lower chamber. The outputs of the inverted torque models are pressure values that are
used as desired pressure values of the previously presented model-based pressure
control. The structure is shown in Figure 9.b.
a)
0 1 2 3 4 5 66-25
-500
2550
0
10
20
pressure [bar]angle [°]
torq
ue [
Nm
]
b)
dT1 dP1
dP2 2,1, PP
2,1 UU
dT2
0T
Figure 9: a) Interpolated and extrapolated torque characteristic of pREC-actuator, b)
Structure of model-based torque control
To prove the developed concept the leg dummy was manually moved while measuring
angle, velocity, desired and actual torque as well as the resulting torque error, which are
shown in Figure 10. The maximum torque error in motion yields to e<|0.18| Nm, with a
maximum angle change of 48.61 °/s. Under static conditions this error decreases to
e<|0.01| Nm.
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a)
0 5 10 15-20
-10
0
10
20
time [s]
angl
e [°
]
b)
0 5 10 15-60
-40
-20
0
20
40
60
time [s]
velo
city
[°/
s]
c)
0 5 10 151
2
3
4
time [s]
torq
ue [
Nm
]
d)
0 5 10 15
-0.2
-0.1
0
0.1
0.2
0.3
time [s]
torq
ue e
rror
[N
m]
Figure 10: Compensation of gravitation of patients lower leg and mechanics of test-bed;
a) angle, b) velocity, c) desired (blue curve) and actual (red curve) torque, d) torque
error
CONCLUSION
A model-based pressure control was investigated and tested, whereby corresponding
valve and torque characteristics have been determined. A model-based pressure control
law was analyzed by using two types of servo-valves. Results of developed pressure
control using FESTO MPYE-5-1/8LF-010-B servo-valve were compared with the results
using internal pressure control of the FESTO MPYE G 1/8 valve. Comparison shows
proper results with a homogeneous performance using the developed model-based
pressure control. Based on this control a model-based torque control has been
developed and tested by using a knee motion therapy device as test-bed. The main idea
was to use inverted torque characteristics instead of expensive torque sensors.
Objective was to achieve compensation of gravitation of patient’s lower leg combined
with the mechanics, to obtain a fundamental base for prospective rehabilitation tasks.
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ACKNOWLEGMENT
This work is supported by the German Federal Ministry of Education and Research
(BMBF) through the grant 16SV2290 (joint research projects PortaSOR “New generation
of portable soft robotic arms”) and the grant 01EZ0769 (KoBSAR “Compact assistive-
restorative motion therapy devices, based on fluidic soft actuators with rotary elastic
chambers”).
REFERENCES
/Dae02/ Daerden, F. and Lefeber D., Pneumatic artificial muscles: actuators for
robotics and automation, European Journal of Mechanical and
Environmental Engineering, 47(1), 2002, 10–21, 2002
/Tsa03/ Tsagarakis N., Caldwell D., Development and Control of a ‘Soft-Actuated’
Exoskeleton for Use in Physiotherapy and Training, Autonomous Robots,
15, pp 21-33, 2003
/Ivl09/ Ivlev, O., Soft Fluidic Actuators of Rotary Type for Safe Physical Human-
Machine Interaction, 11th IEEE Int. Conf. on Rehab. Robotics (ICORR
2009), Kyoto, Japan, pp.1-5, 23-26 June 2009
/Wol06/ Wolbrecht E.T., Leavitt J., Reinkensmeyer D.J., Bobrow J.E., Control of
a Pneumatic Orthosis for Upper Extremity Stroke Rehabilitation,
Proceedings of the 28th IEEE EMBS Annual International Conference,
New York City, USA, Aug 30-Sept 3, 2006
/Mih08/ Mihajlov, M. Modelling and Control Strategies for Inherently Compliant
Fluidic Mechatronic Actuators with Rotary Elastic Chambers, Ph.D. thesis,
Institute of Automation, Univ. of Bremen., Bremen, Germany, ISBN 978-3-
8322-7275-3, 2008
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