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HomeScience RoboticsVol. 3, No. 16A soft, bistable valve for autonomous control
of soft actuators
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Research Article
SOFT ROBOTS
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A SOFT, BISTABLE VALVE FOR AUTONOMOUS CONTROL OF SOFT ACTUATORS
Philipp Rothemund https://orcid.org/0000-0002-0588-6993, Alar Ainla
https://orcid.org/0000-0001-8969-3752, [...] , Lee Belding, Daniel J. Preston
https://orcid.org/0000-0002-0096-0285, [...] , Sarah Kurihara, Zhigang Suo, and
George M. Whitesides https://orcid.org/0000-0001-9451-2442
gwhitesides@gmwgroup.harvard.edu+4 authors +2 authors fewerAuthors Info &
Affiliations
Science Robotics
28 Mar 2018
Vol 3, Issue 16
DOI: 10.1126/scirobotics.aar7986
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ABSTRACT
Almost all pneumatic and hydraulic actuators useful for mesoscale functions rely
on hard valves for control. This article describes a soft, elastomeric valve
that contains a bistable membrane, which acts as a mechanical “switch” to
control air flow. A structural instability—often called “snap-through”—enables
rapid transition between two stable states of the membrane. The snap-upward
pressure, ΔP1 (kilopascals), of the membrane differs from the snap-downward
pressure, ΔP2 (kilopascals). The values ΔP1 and ΔP2 can be designed by changing
the geometry and the material of the membrane. The valve does not require power
to remain in either “open” or “closed” states (although switching does require
energy), can be designed to be bistable, and can remain in either state without
further applied pressure. When integrated in a feedback pneumatic circuit, the
valve functions as a pneumatic oscillator (between the pressures ΔP1 and ΔP2),
generating periodic motion using air from a single source of constant pressure.
The valve, as a component of pneumatic circuits, enables (i) a gripper to grasp
a ball autonomously and (ii) autonomous earthworm-like locomotion using an air
source of constant pressure. These valves are fabricated using straightforward
molding and offer a way of integrating simple control and logic functions
directly into soft actuators and robots.
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INTRODUCTION
Pneumatically actuated soft robots function by networks of elastomeric channels
that inflate upon pressurization or buckle upon evacuation (1–6). Soft devices,
and their actuators, are intrinsically compliant and can move in ways that are
difficult or impossible to achieve using “hard” components. Other useful
characteristics of soft actuators and devices include (i) collaborative
behavior, that is, intrinsic safety in operating closely with humans (6–8); (ii)
the ability to adapt autonomously to different shapes (1, 9); (iii) relatively
low cost (6, 8); (iv) ease of sterilization (10); (v) the ability to manipulate
delicate objects (1, 11); and (vi) high cycle lifetime (4). One characteristic
(and deficiency, in some applications) of most current soft, pneumatic actuators
is that they still rely on hard valves and electronic components for control
(8).
Elastomers undergo large deformations, which enable functions but also present
challenges in design. Precisely controlling the motion of soft, pneumatic
actuators can be difficult, because elastomers are often nonlinear and
viscoelastic (6, 9, 12). Control is further complicated by the need for sensors
that can sustain the same strain as the actuators (11, 13–15). The compliance of
the elastomers allows the devices to conform to different shapes and
automatically limits the force they exert (a form of “material intelligence”)
(8, 16). These characteristics enable them to operate in many applications
between pressure limit set points. These set points allow soft actuators to be
controlled with the simple on/off of a pressure supply. Grippers and walkers are
two examples of successful applications operating with this type of pressure
control (1, 2, 17).
The most common methods of controlling pressure in soft robots involve hard
valves (e.g., solenoid valves) that open or close in response to a pneumatic or
electronic signal (8, 9, 18). Wood and coworkers (19) developed a band-pass
valve, which can address multiple actuators individually using a single,
modulated source of pressure. Marchese et al. (20) developed an energy-efficient
valve based on electropermanent magnets. We used a Braille display in
combination with a microfluidic circuit to control 32 actuators simultaneously
(21). Each of these valves contains hard components and is usually located
externally; this architecture requires tethering the robot with tubing. Hard
valves have been integrated onto soft robots, sacrificing complete softness (18,
20). Some attempts have been made to fabricate a soft controller (i.e., a
“switch” or other logic element) specifically for soft robots. We have directly
integrated unidirectional, soft check valves into a soft robot to vent the
combustion products of an explosion, which powered the soft robot (22). Wehner
et al. (23) developed an entirely soft, autonomous robot, which was controlled
by a soft microfluidic oscillator based on a design first introduced by Takayama
and coworkers (24).
Many designs exist for entirely soft microfluidic valves, logic circuits,
oscillators, and fluidic information processors (24–27). These designs use
Quake-type valves, in which elastomeric membranes block or permit flow through
channels depending on an applied input pressure (27). A microfluidic oscillator
relies on a network of fluidic components, which include valves (switches),
channels (resistors), chambers (capacitors), and pressure sources (24, 28). The
dimensions of the components must be balanced to achieve oscillatory behavior of
the circuit. Hui and coworkers (28) demonstrated complex microfluidic circuits
with a high density of logic elements. The small scale of the microfluidic
circuit used by Wehner et al. (23) limited the flow rate, and thus the size, of
the actuator that could be controlled. They overcame this problem to some extent
by operating the microfluidic circuit with liquid H2O2, which generated,
catalyzed by platinum, gaseous O2 inside the robot to increase the volume (23).
The small feature sizes of the microfluidic channels also required the use of
multiple fabrication techniques [soft lithography (27, 29), three-dimensional
(3D) printing, and molding] and led to difficulties (clogging of the channels)
when interfacing the microfluidic channels with the channels of the robot (23).
This paper describes a type of soft valve that uses the snap-through instability
of an elastomeric membrane to switch between different pneumatic pressures to
control the airflow through pneumatic channels. This instability provides the
valve with three properties: (i) The state of the valve is binary (“open” or
“closed”), which enables unambiguous control, despite the uncertainties
associated with nonlinear and viscoelastic deformation of the elastomers. The
valve requires power only while switching between the two states. (ii) The
membrane can be designed to be bistable. Bistability allows the fabrication of
latching valves, which remain in either open or closed states without an applied
pressure. (iii) The snap-through instability is hysteretic. As a result, the
valve is resistant to noise and can (in a feedback control scheme) generate
periodic pressure oscillations, when connected to a source of constant pressure.
The instability of flexible membranes has previously been used in the design of
hard valves (30, 31). In soft robotics, snap-through instabilities are a tool to
engineer the response of soft actuators to actuation (4, 32–34). The valve
presented in this work is different from these examples because it is an
entirely soft control element that can be integrated into existing designs for
soft, pneumatic actuators. The snap-through instability determines the pressures
at which the valve switches. We measured these pressures as a function of the
geometry and the material of the valve. We fabricated and characterized a
pneumatic switch, a device that switched air flow from two pressure sources, and
a pneumatic oscillator, a device that generates periodic motion using a source
of constant pressure. Both devices use the soft valve as the functional element.
We demonstrated the ease of implementation and utility of the valve in two
applications: (i) A soft gripper, which autonomously grasps objects upon
contact. When the “palm” of the gripper contacts the object, the valve is
triggered and causes the gripper to close around the ball. An externally applied
pressure signal resets the valve, which reopens the gripper. (ii) A soft
earthworm, which advances using a source of constant pressure. We integrated the
valve into a linear actuator. Connected to a source of constant pressure, the
valve periodically inflates and deflates the actuator, which advances because of
friction acting asymmetrically on its feet.
The valve can act as a switch for automated functions in soft devices, enabling
autonomous feedback and feedforward control in soft actuators. The pressures at
which the valve switches can be controlled by changing geometry and material.
The design of the valve is simple, modular, and scalable. The ability to
generate oscillations inside a robot makes it possible to construct a fully
soft, untethered soft robot that can react to stimuli from its environment.
RESULTS
THE SOFT, BISTABLE VALVE
The basic design of the valve uses two instabilities: snap-through instability
of a membrane and kinking of a tube (Fig. 1). The two instabilities act
cooperatively to control airflow through the valve. In this design, a bistable,
hemispherical membrane separates two chambers (Fig. 1, A and B). Elastomeric
tubing leads through each chamber. When the membrane is curved downward (state
1), the tubing in the bottom chamber kinks and blocks air flow through it,
whereas air flows freely through the tubing in the top chamber. When the
membrane is curved upward (state 2), the opposite is true; the tubing in the top
chamber kinks and blocks airflow through it, whereas the bottom chamber is open
and allows air to flow through freely. The membrane can be switched between the
two states by the pressure difference between the bottom (P+, kPa) and top (P−,
kPa) chambers (ΔP = P+ − P−, kPa).
Fig. 1 Details of the soft, bistable valve.
(A) Schematic showing the components of the valve. The valve consists of a
hemispherical, elastomeric membrane separating two chambers. Control pressures
in the bottom (P+) and top (P−) chambers deform the membrane. When the membrane
is in the downward position (state 1), it blocks air flow through a tube leading
through the bottom chamber by kinking the tube. When the membrane is in the
upward position (state 2), it blocks air flow through the top tube. (B)
Photographs of the valve in both states. (C) When the pressure difference, ΔP,
between the two chambers reaches a critical value, ΔP1, the membrane snaps to
the upward position. When the pressure difference decreases below ΔP2, the
membrane snaps back to the downward position. (D) The tubing kinks (and
un-kinks) during the snapping process. The states of the bottom tubing (Q) and
the top tubing (Q¯) are binary (i.e., open or closed) and hysteretic (movie S1).
Open in viewer
We describe this switching behavior using a bifurcation diagram, one axis being
the pressure difference ΔP and the other axis being the displacement of the
membrane (Fig. 1C). Initially, when ΔP = 0, the membrane is downward (state 1).
As ΔP increases (i.e., as the bottom chamber is pressurized), the membrane bends
toward the top chamber, and because it is constrained by the walls of the valve,
it compresses in area. At the snap-upward pressure ΔP1 (kPa), the membrane
passes through the center of the valve and expands again in the top chamber
(state 2). This behavior can—depending on the geometry of the valve—lead to a
negative tangential stiffness. When an incompressible fluid (e.g., water)
pressurizes the bottom chamber, the pressure decreases upon further deformation
(i.e., the dashed line in Fig. 1C). When a compressible gas (e.g., air) is used,
the energy stored during compression of the membrane releases, in a dynamic
“snapping” motion of the membrane, to the top chamber. When ΔP decreases, the
membrane again has to overcome the constraint of the walls of the valve to
return to state 1. To overcome this constraint and snap back to the bottom
chamber, the pressure must drop below the snap-downward pressure ΔP2 (kPa). This
type of snap-through instability is well understood and has long been the basis
for toy “poppers” (35, 36).
While the membrane is being deformed, the tubing compresses axially. Initially,
the tube bends without constricting the air flow (fig. S1). At a critical
compression, the walls of the tubing collapse, leading to a kink that blocks air
flow (fig. S1). The length of the tubing can be chosen such that the collapse
starts and finishes within the snapping motion of the membrane. Coupling these
two instabilities leads to binary, opposite states of air flow (“open/closed”)
through the bottom tubing (Q) and the top tubing (Q¯), with hysteretic switching
behavior (Fig. 1D and movie S1).
When the bistable membrane is integrated into a soft robot, the interior of an
actuator can act as one of the “chambers” of the valve. Depending on the
application, one of the chambers and/or one of the tubes can be omitted. Because
we fabricated the parts of the valve by molding, they can be directly
incorporated into the mold for a soft actuator. This integration eliminates the
need for additional fabrication techniques.
DEPENDENCE OF ΔP1 AND ΔP2 ON THE GEOMETRY
The critical pressures ΔP1 and ΔP2―the pressures at which the membrane switches
from one state to the other―depend on the geometry of the membrane and the
walls. We studied their dependence on the thickness H (mm) of the membrane and
on the inclination angle θ (°)—the angle made between the top surface of the
membrane and a plane perpendicular to the wall of the valve (Fig. 2A). We used a
syringe pump to pressurize and depressurize the bottom chamber with air while
the top chamber was kept at atmospheric pressure and recorded the pressure in
the bottom chamber as a function of time (Fig. 2A). From the measured minima and
maxima of the pressure-time curves, we determined ΔP1 and ΔP2. For some
geometries, the membrane did not snap back, even when the pressure in the bottom
chamber was reduced to atmospheric pressure (i.e., ΔP2 < 0). In these cases, we
disconnected the syringe pump after the membrane snapped upward and pressurized
the top chamber, keeping the bottom chamber at atmospheric pressure.
Fig. 2 Measurements of the critical pressures.
(A) Schematic of the apparatus used to measure ΔP1 and ΔP2 for different
geometries. (B) Critical pressures, ΔP1 and ΔP2, as a function of H. (C)
Critical pressures, ΔP1 and ΔP2, as a function of θ. (D) ΔP2 plotted against ΔP1
for valves with different H and θ values. The boundary of accessible critical
pressures is defined by ΔP2 = ΔP1, and the values of ΔP for a valve with θ =
90°, and various H. Valves with critical switching pressures within this
boundary are obtained when θ < 90°.
Open in viewer
We studied the dependence of ΔP1 and ΔP2 on the thickness of the membrane by
varying H from 0.50 to 4.25 mm, using membranes fabricated from Dragon Skin 10
NV elastomer (Smooth-On) with diameter D = 20 mm and θ = 90° (fig. S2). The
critical pressure required to snap the membrane upward (ΔP1) increased with H
(Fig. 2B). For H < 3.00 mm, the membrane did not snap back on its own but had to
be pushed back to the original position by pressurizing the other chamber (i.e.,
ΔP2 < 0). Membranes with 3.0 mm ≤ H ≤ 4.00 mm snapped back when the pressure
decreased below a positive critical value, which increased with H until ΔP2
converged with ΔP1. For H > 4.00 mm, we did not observe the snap-through
instability (i.e., the measured pressure-time curve was monotonic). We note that
membranes with H ≤ 1.00 mm did not snap quickly to the other side but
transitioned between the states in a slow process during which the pressure did
not change.
The behavior of the membrane is a result of two concurrent modes of deformation:
(i) compression and (ii) bending of the membrane. The walls impose a barrier
that must be overcome by the membrane (by compressing in area) for it to
transition to the opposite chamber. This barrier is the origin of the
snap-through instability. During the deformation, the membrane also bends. The
bending stiffness of the membrane provides a restoring force for the membrane to
return to its original position. The bending and compressional stiffness of the
membrane both increase with H (the bending stiffness scales faster than the
compressional stiffness), and therefore, ΔP1 increased as H increased. For thin
membranes (H < 3.0 mm), the restoring force was too small to overcome the
constraint of the walls without a pressure from the top chamber (i.e., ΔP2 < 0).
For H > 3.0 mm, the restoring force was large enough for the membrane to
spontaneously snap back during depressurization (ΔP2 > 0). When H approached
4.25 mm, the bending stiffness dominated over the compressional stiffness so
that the instability disappeared.
We also measured the values of ΔP1 and ΔP2 for membranes with θ ranging from 65°
to 90° while maintaining H = 3.0 mm (Fig. 2C). The angle θ determines how much
the membrane must be compressed, in hoop direction, to pass through the center
of the valve. Lower values of θ, therefore, led both to smaller ΔP1 and to
smaller differences in the critical switching pressures (ΔP1 − ΔP2). For θ <
70°, we did not observe snap-through. When θ = 70°, the membrane snapped only
when depressurizing the bottom chamber. We were also able to reduce ΔP1 by
decreasing the thickness (and thus the stiffness) of the sidewall of the valve,
which reduced the constraint on the membrane (fig. S3).
The behavior of the valve changes with the geometry of the membrane (Fig. 2D).
The range of achievable switching pressures is defined by the diagonal ΔP2 = ΔP1
(because for the snap-through instability ΔP1 > ΔP2) and the data measured for θ
= 90°. Points within this region can be obtained by reducing θ. It is possible
to increase the range of switching pressures by using a stiffer elastomer (figs.
S4 and S5). However, the size of the valve does not influence the switching
pressures (fig. S3). The curve ΔP2 = 0 splits the ΔP2 − ΔP1 plane into two
regions with distinctly different behaviors. In the region where ΔP2 > 0, the
membrane only has one stable state (downward) when ΔP = 0, so it snaps back on
its own when ΔP drops below ΔP2. These membranes can be used to fabricate
nonlatching pneumatic switches. Nonlatching switches would require a continuous
pressure signal to remain in the upward state but would not require continuous
power because air only flows during the switching process. In the region where
ΔP2 < 0, the membrane also has one metastable state (upward) when ΔP = 0. These
membranes can be used to fabricate latching pneumatic switches that require
pressure signals only during switching.
THE SOFT, BISTABLE VALVE AS A SWITCH
Figure 3A shows a soft, bistable valve that acts as a switch between two
different sources of constant pressure. The bottom tubing is connected to an air
source of pressure PS (kPa), and the top tubing is connected to the atmosphere,
which acts as the second air source. When the membrane is in the downward
position, the bottom tubing is kinked so that PS is disconnected from the
output; the top tubing remains open, and the output of the valve is atmospheric
pressure (state 1; Fig. 3A). When a control pressure P+ > ΔP1 is applied to the
bottom chamber, the membrane snaps upward, kinking the top tubing and opening
the bottom tubing, which connects PS to the output, while blocking its
connection to the atmosphere (state 2; Fig. 3A). When P+ decreases below ΔP2,
the membrane snaps back and switches the output back to the atmosphere.
Fig. 3 Soft, bistable valve acting as a pneumatic switch.
(A) The bottom tubing is connected to an air supply of constant pressure PS. The
top tubing and the top chamber are connected to the atmosphere. The top and the
bottom tubing are joined together behind the valve to form the output P of the
pneumatic switch. The pressure in the bottom chamber is controlled by a variable
pressure controller (P+). When the membrane bends downward, it kinks the bottom
tubing; when it is bent upward, it kinks the top tubing. (B) Critical pressures
ΔP1 and ΔP2 as a function of PS. (C) Output of the valve for different PS values
and rectangular pulses as control input (P+ = 11 kPa). (D) Response of the valve
to two rectangular pulses (P+ = 11 kPa) as the control input. A sinusoidal wave
(frequency, 0.5 Hz; amplitude, 5 kPa) is superposed to the second pulse. H = 3
mm, θ = 87.5°.
Open in viewer
On the basis of the geometry of the devices of Fig. 2 (H = 3.0 mm, θ = 87.5°),
we fabricated a soft valve from Dragon Skin 10 NV, using Smooth-Sil 950
(Smooth-On) for the internal tubing. The presence of the tubing within the valve
increased the critical pressures to ΔP1 = 10.2 kPa and ΔP2 = 3.3 kPa (Fig. 3B),
compared with ΔP1 = 8.4 kPa and ΔP2 = 0.5 kPa for membranes without tubing (Fig.
2C). This change in critical pressures arises because the shorter top tubing is
more resistant to axial compression than the longer bottom top tubing. The
diameter of the membrane on which the control pressure acts is ~10 times larger
than the inner diameter of the tubing, on which the supply pressure acts, and
thus, we did not observe a measurable change of the critical pressures up to PS
= 80 kPa (Fig. 3B). At pressures above 80 kPa, the pressure dislodged the tubing
from the chamber upon switching, which prevented further measurements.
The valve can also be used for signal amplification, because the snap-through
instability occurs even when PS is larger than the critical pressures (Fig. 3B).
Figure 3C shows the response of the valve to 5-s-long pressure pulses of P+ = 11
kPa as the input signal and supply pressures PS up to 80 kPa, which corresponds
to a gain (pressure amplification) of 7.3. The delay in switching results mainly
from the flow resistance of the tubing between the pressure controller and the
valve (the dip in the control pressure corresponds to the onset of the
snap-through, during which the pressure decreased because of the volume change
of the bottom chamber; the output reached its final state ~0.2 s later).
The hysteresis of the membrane makes the operation of the valve robust to noise
and allows the use of the valve as a pneumatic noise filter (a common concept
used in digital signal processing). The electronic equivalent to the bistable
valve is a Schmitt trigger (37). A Schmidt trigger is a hysteretic switch with a
continuous input (here, the input is the pressure difference between the bottom
and top chambers of the valve) and a binary output (atmospheric pressure or PS).
Noise in the control signal only transmits to the output when it is larger than
the hysteresis of the Schmidt trigger. To demonstrate this property, we applied
two 8-s pressure pulses of P+ = 11 kPa to the bottom chamber of the valve. To
simulate noise, we superposed, on the second pulse, a sinusoidal pressure signal
(frequency, 0.5 Hz) with an amplitude of about half of the hysteresis (~5 kPa;
Fig. 3D). The pressure source could supply only positive pressures, and thus,
the negative portion of the sine wave before and after the second pulse was
clipped. Because the amplitude of the noise was smaller than the hysteresis of
the valve, it did not influence the output pressure (i.e., the valve effectively
filtered the noise) (Fig. 3D). When the noise amplitude is larger than the
hysteresis, the noise of the control signal transmits to the output (fig. S6).
A PNEUMATIC GRIPPER FOR AUTONOMOUS GRASPING
We designed a soft gripper that autonomously closes when it contacts an object
and can be reopened with an external pressure signal. The gripper consists of
five fast pneu-net bending actuators (38) arranged circularly around a soft
valve, with a contact sensor integrated in the palm of the gripper (Fig. 4A).
The contact sensor consists of an elastomeric cap, which surrounds a tube that
connects the bottom chamber of the valve to the atmosphere. When an object
compresses the cap, the venting tube kinks and blocks the flow of air. An air
supply (pressure P+, kPa) is connected to the bottom chamber of the valve. A
ring channel distributes air to the bending actuators (Fig. 4A). The ring
channel is connected, through the bottom tubing of the valve, to a second air
supply (pressure PS) and, through the top tubing of the valve, to the
atmosphere. When the membrane is in the downward position, the ring channel is
connected to the atmosphere, leaving the actuators dormant. When the membrane is
in the upward position, the ring channel is connected to PS and the actuators
are pressurized. The pressure supply PS is also connected to the top chamber,
through an external valve, so that pressure in the top chamber can be switched
from atmospheric to PS.
Fig. 4 Gripper that grasps autonomously.
(A) The gripper consists of five bending actuators, connected to a ring-shaped
channel, around a soft, bistable valve. When the membrane in the valve is in its
downward position, the pressure supply to the ring channel (PS) is blocked, and
it is connected to the atmosphere. A second pressure supply (P+) leads to the
bottom chamber of the valve and out through the contact sensor at the palm of
the hand. The top chamber can be connected through an external valve to the
atmosphere or the pressure supply PS. (B) Equivalent electrical circuit that
represents the pneumatic control in the autonomous gripper. (C to H) Photographs
of the gripper and schematics of the valve autonomously (C to E) closing around
a tennis ball and (F to H) releasing the ball (movies S2 and S3).
Open in viewer
We can explain the function of the pneumatic circuit with an analogous electric
circuit (Fig. 4B), in which the actuators act as a pneumatic capacitor, the
valve acts as a Schmidt trigger, the tubing and the channels act as resistors,
and the contact sensor and the external valve act as switches. When the tubing
in the contact sensor is open, the electronic switch is closed. Air flows from
the pressure source P+ through the bottom chamber of the valve to the
atmosphere. The flow resistance of the tubing into and out of the bottom chamber
acts as a “voltage” divider so that the pressure in the bottom chamber (positive
input of the Schmidt trigger) lies below the switching pressure ΔP1. When an
object kinks the tubing through the contact sensor, the switch in the contact
sensor opens, and the pressure inside the bottom chamber increases to P+. The
Schmidt trigger switches, and air flows into the capacitor (the fingers of the
gripper, which actuate). When we switch the top chamber of the valve (negative
input of the Schmidt trigger) to the pressure source PS, the Schmidt trigger
switches back, and the capacitor empties to the environment (the fingers of the
gripper vent, and the gripper opens).
We fabricated the gripper using Dragon Skin 30 (Smooth-On), Smooth-Sil 950, and
Dragon Skin 10 NV. For the air supplies, we used P+ = 55 kPa and PS = 69 kPa. We
used the gripper to pick up a tennis ball (movie S2). Before the gripper
contacted the ball, air vented through the contact sensor to the environment
(Fig. 4C). When the contact sensor touched the ball, the weight of the gripper
kinked the tube leading through it (Fig. 4D). The bottom chamber of the valve
then pressurized, causing the membrane to snap upward (fig. S7 and movie S3),
which connected the bending actuators to PS. From movie S2, we determined that
the gripper closed in less than 1 s after contacting the ball. After the gripper
was closed (Fig. 4E), we could lift the ball (Fig. 4F). Because the valve is
bistable, the gripper stayed closed after picking up the ball, even when the
ball moved and was no longer closing the contact sensor. To reset the valve and
vent the gripper, we connected the top chamber to the pressure source, PS (Fig.
4G). The gripper opened in less than 1 s. After switching the top chamber of the
valve back to atmosphere (Fig. 4H), we could reuse the gripper (movie S2).
FEEDBACK CONTROL FOR OSCILLATORY MOTION USING AN AIR SOURCE OF CONSTANT PRESSURE
On the basis of the soft, bistable valve, we designed a soft oscillator that
uses an air supply of constant pressure to generate periodic pressure
oscillations (Fig. 5A). In this design, the top tubing of the valve is connected
to an air supply of pressure PS, and the bottom tubing is connected to the
atmosphere. Feedback is established by connecting the bottom tubing and the
bottom chamber of the valve (i.e., P+ = P). A vertical channel within the wall
of the valve connects the top tubing to the bottom chamber of the valve. To
characterize the oscillator, we connected it to a glass jar. Figure 5B shows the
electrical analog of the pneumatic circuit.
Fig. 5 Pneumatic oscillator driven by an air source of constant pressure.
(A) When the membrane is downward, air flows from the pressure source PS into a
jar of volume V, but the tubing between the jar and the atmosphere is blocked.
When the pressure P in the bottom chamber exceeds ΔP1, the membrane snaps upward
and blocks air flow from the pressure source PS, and the jar vents to the
environment. When P decreases below ΔP2, the membrane snaps downward, and the
jar pressurizes again (movie S4). (B) Equivalent electrical circuit that
represents the pneumatic feedback control. (C) Oscillations in the jar at PS =
11 kPa. (D) Rise time (tR) as a function of PS, with different V values. (E)
Fall time (tF) as a function of PS, with different V values. Error bars in (D)
and (E) show the SD of the mean over a 60-s measurement interval. H = 3 mm and θ
= 87.5°.
Open in viewer
When the output pressure of the valve P is smaller than ΔP1, the membrane bends
downward (state 1; Fig. 5A), and air flows from the pressure supply, through the
top tubing, to the glass jar. Because of the feedback (Fig. 5B), the membrane
snaps upward (state 2; Fig. 5A) when the pressure in the glass jar exceeds the
critical pressure ΔP1. The glass jar vents through the bottom tubing to the
atmosphere until the pressure drops below ΔP2, at which point the membrane snaps
back to state 1. This behavior leads to periodic oscillation of P between ΔP2
and ΔP1 (movie S4). Without the instability (i.e., if the transitions between
the two states were continuous), the valve would equilibrate in a state in which
the tubing through both chambers is partially open so that the air flow into the
jar equals the air flow out of the jar and oscillations would not occur.
We fabricated a soft oscillator using Dragon Skin 10 NV for the valve (H = 3 mm,
θ = 87.5°) and Smooth-Sil 950 for the internal tubing. We connected the soft
oscillator to a glass jar, with a volume of V = 150 ml (we adjusted the volume
of the jar by filling it with water). Using a pressure input of PS = 11 kPa, we
recorded the pressure inside the jar as a function of time (Fig. 5C). The valve
periodically, and autonomously, pressurized (rise time tR = 0.3 s) and
depressurized (fall time tF = 0.4 s) the jar, which oscillated between P = 0.24
kPa and P = 0.98 kPa.
Figure 5 (D and E) shows the dependence of tR and tF on the supply pressure PS
for capacitors with volumes (V) ranging between 100 and 300 ml. The times tR and
tF scaled with the volume of the capacitor, because less air is required to
change the pressure in a smaller volume. Increasing PS led to smaller values of
tR. However, the fall time tF depends on the pressure difference between the
capacitor and the atmosphere at the time the valve switches (i.e., ΔP1), and
because ΔP1 does not change with PS, tF was not substantially affected by PS. We
observed the fastest oscillations (2 Hz) for V = 100 ml and PS = 11 kPa and the
slowest oscillations (0.7 Hz) for V = 300 ml and PS = 10 kPa. The lower limit
for PS is determined by the critical pressure, ΔP1 (here 0.98 kPa), so we
observed no oscillations at PS = 9 kPa. Experimentally, we observed an upper
limit for PS, which depended on the volume of the jar (the last data point of
each measured curve), when tR ranged between 0.23 and 0.28 s. Beyond this upper
limit, the valve did not oscillate, because the membrane equilibrated to a state
in which both channels of the valve were not completely kinked (movie S5 and
fig. S8). For volumes V = 50 ml, we did not observe stable oscillations,
possibly because tR was too short, even for PS = 10 kPa. To test whether the
upper limit of PS is dictated by the duration of tR, we introduced a 2-cm-long
tube, with an inner diameter of 0.79 mm, between the pressure supply and the
valve to increase the flow resistance. We obtained stable oscillations, even at
PS = 50 kPa and V = 50 ml (fig. S9), suggesting that tR is the limiting factor
and not PS or V.
The compliance of all parts of the valve allows deformation of the valve without
damage. An oscillator (operated with PS = 10 kPa at V = 250 ml) restarted
oscillating autonomously after we had crushed it with a 2-kg weight (movie S6).
To determine whether the behavior of the valve changes over time, we recorded
the oscillations of a valve, using a constant pressure input of PS = 11 kPa,
connected to a glass jar (V = 150 ml). After 105 cycles, we measured a 5%
decrease of ΔP1 and a 3% decrease of the oscillation frequency (fig. S10). The
critical pressure ΔP2 did not change noticeably.
AN AUTONOMOUS EARTHWORM-LIKE WALKER
We demonstrate that the valve can be used as a feedback controller for soft
robots. Using the soft oscillator, we designed a soft robot with earthworm-like
motion that uses air from a source of constant pressure (PS) (Fig. 6A). The
critical pressures of the valve determine the pressures between which the robot
oscillates. The worm consists of a linear bellows actuator surrounded by a
cylindrical sleeve (which acts as a restoring spring). One end of the bellows
actuator contains the soft oscillator, whereas the other end is capped with an
elastomeric disc. Both ends of the robot have elastomeric feet, angled at 10°,
to create asymmetric friction during expansion and contraction.
Fig. 6 Autonomous soft robot with earthwork-like locomotion using an air source
of constant pressure.
(A) The earthworm consists of a linear bellows actuator with cylindrical sleeve
as a restoring spring and a soft, bistable valve, integrated into the rear of
the actuator. The design of the valve is the same as that for the pneumatic
oscillator, with the bottom chamber of the valve connected to the bellows
actuator. The bellows actuator bends upward during inflation and downward during
deflation, which causes asymmetric contact between the feet and the ground,
leading to asymmetric friction and directional movement. (B) Photographs of the
moving earthworm at three points in time (movie S7). (C) Pressure inside the
robot and positions of front end, rear end, and center as a function of time for
PS = 17 kPa. The red dots indicate the times when the photographs in (B) were
taken.
Open in viewer
Figure 6B shows snapshots of the earthworm moving on a smooth surface, connected
to an air supply of pressure PS = 17 kPa (movie S7). When the bellows actuator
inflated, frictional forces at the feet caused the earthworm to bend upward.
This bending caused the front foot to contact the ground with its leading edge
only, whereas the back foot touched the ground with its entire surface (Fig.
6A). Thus, the front foot slid forward and the back foot stuck. During
deflation, the bellows actuator bent downward so that the front foot stuck and
the back foot moved forward (Fig. 6A). Oscillations in the position of the front
and back of the actuator are caused, predominantly, by tilting of the ends
during bending. The worm stretched and compressed each cycle by 12%, and the
worm advanced at a rate of 8.4 cm/min (Fig. 6C). The oscillation period was 1.8
s.
DISCUSSION
This article describes a design concept for a pneumatic valve that consists
entirely of soft components. The valve functions based on a snap-through
instability and uses pneumatic signals for control. The valve can be used for
latching and nonlatching switches, signal amplifiers, and noise filters. When
integrated in a feedback loop, the soft valve can inflate and deflate a soft
actuator—autonomously and periodically—using a constant pressure input. The
bistable valve achieves these functions in a way that is fundamentally different
from the microfluidic logic circuits reported previously (23–26, 28): In
microfluidic circuits, the complex interplay of pneumatic capacitors, resistors,
and valves enables function on a system level; the snap-through instability of a
hemispherical membrane and kinking of a tube enable function on the component
level. This makes the function of a microfluidic circuit more sensitive to the
downstream components (e.g., the soft robot) and its behavior more difficult to
predict. In Quake-type valves, which are used in many microfluidic circuits
(23–27), for example, membranes work against the controlled flow. The control
pressure therefore depends on the pressure of this flow, and it is not
straightforward to achieve a large pressure gain. The control of the bistable
valve (the differential pressure across the membrane) is decoupled from the
controlled flow (the air flow inside of the tubing). This makes the control
pressure independent of the controlled flow, and the mechanical advantage of the
membrane on the smaller tubing can provide a large gain (which, in this work,
was limited by the strength of the connection between the tubing and the valve).
These comments are not intended to criticize microfluidic systems. Although not
demonstrated yet for soft robots, they can theoretically be scaled up to
circumvent the difficulties of fabrication and of integration encountered by
Wehner et al. (23) (whereas the bistable valve will be difficult to scale down)
and will likely require fewer individual parts than the bistable valve. The
bistable valve, on the other hand, allows simpler implementation of some
functions. The bistable valve is therefore complementary to the elements of
classical microfluidics. On the large scale, both can be combined to achieve a
balance of system complexity, robustness of design, and ease of fabrication.
Here, we used a hemispherical membrane as the control element of the valve, but
there are other structures that show reversible snap-through behavior and may be
equally suitable for autonomous actuation of soft devices (35, 39). We used
pneumatic channels that ran parallel to the bistable membrane, although other
designs are possible [e.g., feeding the tubing directly through the membrane, to
fabricate pressure-release valves, or pressure-limiting valves (fig. S11)]. The
two chambers of the valve can be parts of two different actuators, to switch the
valve depending on their differential pressure, to obtain coordinated motion.
To fabricate autonomous, untethered, soft robots, the valve may also be used in
combination with energy sources that are directly integrated into a soft device
(40, 41). If the surrounding walls are designed to maintain structural integrity
under negative pressure, the valve may also be used with vacuum. However, if an
incompressible fluid (e.g., water) is used to control the valve, the
incompressibility of the fluid may prevent the membrane from snapping (in that
case, feedforward control is still possible). For the oscillator to work with an
incompressible fluid, and a mechanism analogous to that which we describe, the
walls of the valve or the soft robot can be designed to provide enough
compliance for the snap-through instability to occur.
Although parts of the valves can be directly integrated into the mold of the
actuators they control, they still require additional bonding steps during
assembly. We envision that, by using a 3D printer that prints elastomeric
materials, an entirely soft actuator, including the control elements, could be
printed as one monolithic piece (23, 42–44). Another limitation of the bistable
valve is that ΔP1 and ΔP2 do not depend only on the geometry and material of the
membrane and the tubing but also on the surrounding structure. To obtain the
desired switching behavior, one has to design the membrane together with the
soft actuators. The mechanics of the snap-through instability is well understood
so that computational models (e.g., a finite element simulation) can aid the
design and optimization of the geometry of the membrane. The characterization
performed in this work (Fig. 2 and fig. S3) gives general guidelines for how
changes in geometry influence the switching pressures.
Elastomers allow large and repeated deformation without failure. The
snap-through instability makes the control digital and unambiguous, unaffected
by the uncertainties associated with nonlinear and viscoelastic deformation or
by small perturbations from the external environment. Through the automatic
gripper and the autonomous “earthworm,” we demonstrate that simple logic and
control elements can be directly integrated into soft robots; this integration
decreases their dependence on hard control elements and is a step toward the
design and fabrication of entirely soft, complex, autonomous robots.
MATERIALS AND METHODS
OBJECTIVES AND DESIGN OF THE STUDY
The objective of this study is to demonstrate that elastic instabilities can be
used to control airflow in soft robots and enable automated functions.
Structures that have instabilities can be directly integrated into the design of
the actuators and fabricated with the same tools (molding). Here, we used a
hemispherical membrane because it is easy to fabricate and has minimal geometric
parameters. We used the autonomous gripper and the autonomous earthworm as
practical examples for feedforward and feedback control with the soft valve.
FABRICATION OF SAMPLES
All parts were casted in the 3D printed molds (Stratasys Dimension Elite,
Stratasys Objet30). Input files for the 3D printer for all molds are provided in
the Supplementary Materials (data files S1 to S6). We used the elastomers Dragon
Skin 10 NV, Dragon Skin 30, Ecoflex 30, and Smooth-Sil 950 (all Smooth-On) as
materials. The Supplementary Materials contains a description of the preparation
of the pre-polymer solutions, the assembly of the molds, the casting process,
and a step-by-step description of the fabrication.
TESTING METHODS
We pressurized the devices for the measurements of the critical pressures with a
Harvard PHD ULTRA syringe pump and measured the pressures with a LEX 1 (KELLER)
pressure sensor. The pressures for the characterization of the pneumatic switch
were regulated with ITV0010-2BL (SMC Pneumatics) electro-pneumatic pressure
regulators, and the pressures were measured with ADP5151 (Panasonic Electronic
Components) pressure sensors. We controlled the input pressures for the
automatic gripper, the soft oscillator, and the walker by regulating an in-house
air supply manually. As external valves, we used manually controlled needle
valves and ITV0010-2BL regulators. We recorded the pressures with the LEX 1
sensors and a U5244-000002-002BA sensor (TE Connectivity). The data of the LEX 1
sensor were recorded with its software. All other control and recording was done
through a DAQ card (NI USB-6218) on a PC by MATLAB. The Supplementary Materials
contains detailed descriptions of each experiment.
ACKNOWLEDGMENTS
We thank J. C. Weaver for help with printing the molds for the transparent
valve. Funding: The research presented in this paper was funded by the
Department of Energy, Office of Basic Energy Sciences, Division of Materials
Science and Engineering under award ER45852. P.R. and Z.S. acknowledge support
from the Harvard Materials Research Science and Engineering Center supported by
the NSF (DMR 14-20570). A.A. thanks the Swedish Research Council (VR) for a
postdoctoral fellowship. L.B. is funded by a Natural Sciences and Engineering
Research Council of Canada Postdoctoral Fellowship from the Government of
Canada. Author contributions: P.R., A.A., and G.M.W. developed the concept.
P.R., A.A., D.J.P., Z.S., and G.M.W. designed the experiments. P.R., L.B., and
S.K. fabricated and characterized the devices to measure the critical pressures.
L.B. and D.J.P. fabricated and characterized the pneumatic switch. P.R., A.A.,
and L.B. fabricated and characterized the soft gripper. P.R., A.A., L.B., and
D.J.P. fabricated and characterized the soft oscillator. P.R. and A.A.
fabricated and characterized the earthworm. Z.S. and G.M.W. supervised the
experiments. P.R., L.B., and G.M.W. wrote the manuscript. A.A., S.K., and Z.S.
edited the manuscript. Competing interests: G.M.W. owns equity in Soft Robotics
Inc. and is a member of its board of directors. Soft Robotics Inc. develops soft
robots. P.R., A.A., L.B., Z.S., and G.M.W. filed a patent application (no.
62/607,509) for the soft valve. The other authors declare that they have no
competing interests. Data and materials availability: All data needed to
evaluate the study are presented in the main text or the Supplementary
Materials. Contact G.M.W. for any questions regarding experimental raw data.
SUPPLEMENTARY MATERIAL
SUMMARY
Materials and Methods
Fig. S1. Kinking of tubing.
Fig. S2. Geometry of devices for measuring the critical pressures.
Fig. S3. Critical pressures as functions of wall thickness and scale.
Fig. S4. Critical pressures as a function of the shear modulus.
Fig. S5. Material characterization.
Fig. S6. Influence of large input noise on the output.
Fig. S7. Gripper with a valve without a top chamber.
Fig. S8. Oscillator in intermediate state.
Fig. S9. Oscillations at large input pressures with an additional pneumatic
resistance.
Fig. S10. Characterization of soft oscillator after 105 cycles.
Fig. S11. Alternative designs.
Fig. S12. Molds for the devices for measuring the critical pressures.
Fig. S13. Assembly of the devices for measuring the critical pressures.
Fig. S14. Molds for the tubing used inside the chambers of the valves.
Fig. S15. Assembly of the tubing used inside the chambers of the valve.
Fig. S16. Molds for the transparent valve.
Fig. S17. Assembly of the transparent valve.
Fig. S18. Molds for the pneumatic switch.
Fig. S19. Assembly of the pneumatic switch.
Fig. S20. Molds for the autonomous gripper.
Fig. S21. Assembly of the autonomous gripper.
Fig. S22. Molds for the oscillator.
Fig. S23. Assembly of the oscillator.
Fig. S24. Molds for the earthworm-like walker.
Fig. S25. Assembly of the earthworm-like walker.
Movie S1. Switching with the soft, bistable valve.
Movie S2. Autonomous grasping with the soft autonomous gripper.
Movie S3. Soft autonomous gripper without a top chamber.
Movie S4. Soft oscillator.
Movie S5. Soft oscillator equilibrating in intermediate state.
Movie S6. Soft oscillator restarts after crushing.
Movie S7. Autonomous earthworm-like walker.
Data file S1. Molds for the devices to measure the critical pressures.
Data file S2. Molds for the tubing used inside of the chambers of the valve.
Data file S3. Molds for the transparent valve.
Data file S4. Molds for the pneumatic switch.
Data file S5. Molds for the autonomous gripper.
Data file S6. Molds for the oscillator.
Data file S7. Molds for the earthworm-like walker.
Reference (45)
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Volume 3 | Issue 16
March 2018
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ACKNOWLEDGMENTS
We thank J. C. Weaver for help with printing the molds for the transparent
valve. Funding: The research presented in this paper was funded by the
Department of Energy, Office of Basic Energy Sciences, Division of Materials
Science and Engineering under award ER45852. P.R. and Z.S. acknowledge support
from the Harvard Materials Research Science and Engineering Center supported by
the NSF (DMR 14-20570). A.A. thanks the Swedish Research Council (VR) for a
postdoctoral fellowship. L.B. is funded by a Natural Sciences and Engineering
Research Council of Canada Postdoctoral Fellowship from the Government of
Canada. Author contributions: P.R., A.A., and G.M.W. developed the concept.
P.R., A.A., D.J.P., Z.S., and G.M.W. designed the experiments. P.R., L.B., and
S.K. fabricated and characterized the devices to measure the critical pressures.
L.B. and D.J.P. fabricated and characterized the pneumatic switch. P.R., A.A.,
and L.B. fabricated and characterized the soft gripper. P.R., A.A., L.B., and
D.J.P. fabricated and characterized the soft oscillator. P.R. and A.A.
fabricated and characterized the earthworm. Z.S. and G.M.W. supervised the
experiments. P.R., L.B., and G.M.W. wrote the manuscript. A.A., S.K., and Z.S.
edited the manuscript. Competing interests: G.M.W. owns equity in Soft Robotics
Inc. and is a member of its board of directors. Soft Robotics Inc. develops soft
robots. P.R., A.A., L.B., Z.S., and G.M.W. filed a patent application (no.
62/607,509) for the soft valve. The other authors declare that they have no
competing interests. Data and materials availability: All data needed to
evaluate the study are presented in the main text or the Supplementary
Materials. Contact G.M.W. for any questions regarding experimental raw data.
AUTHORS
AFFILIATIONSEXPAND ALL
PHILIPP ROTHEMUND HTTPS://ORCID.ORG/0000-0002-0588-6993
John A. Paulson School of Engineering and Applied Sciences, Harvard University,
29 Oxford Street, Cambridge, MA 02138, USA.
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford
Street, Cambridge, MA 02138, USA.
Kavli Institute for Bionano Science and Technology, Harvard University, 29
Oxford Street, Cambridge, MA 02138, USA.
View all articles by this author
ALAR AINLA HTTPS://ORCID.ORG/0000-0001-8969-3752
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford
Street, Cambridge, MA 02138, USA.
View all articles by this author
LEE BELDING
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford
Street, Cambridge, MA 02138, USA.
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DANIEL J. PRESTON HTTPS://ORCID.ORG/0000-0002-0096-0285
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford
Street, Cambridge, MA 02138, USA.
View all articles by this author
SARAH KURIHARA
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford
Street, Cambridge, MA 02138, USA.
View all articles by this author
ZHIGANG SUO
John A. Paulson School of Engineering and Applied Sciences, Harvard University,
29 Oxford Street, Cambridge, MA 02138, USA.
Kavli Institute for Bionano Science and Technology, Harvard University, 29
Oxford Street, Cambridge, MA 02138, USA.
View all articles by this author
GEORGE M. WHITESIDES* HTTPS://ORCID.ORG/0000-0001-9451-2442
GWHITESIDES@GMWGROUP.HARVARD.EDU
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford
Street, Cambridge, MA 02138, USA.
Kavli Institute for Bionano Science and Technology, Harvard University, 29
Oxford Street, Cambridge, MA 02138, USA.
Wyss Institute of Biologically Inspired Engineering, 60 Oxford Street,
Cambridge, MA 02138, USA.
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FUNDING INFORMATION
National Science Foundation: DMR 14–20570
U.S. Department of Energy: # ER45852
Natural Sciences and Engineering Research Council of Canada: PDF - 502379 - 2017
Swedish Research Council (VR): International PostDoc
NOTES
*
Corresponding author. Email: gwhitesides@gmwgroup.harvard.edu
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* Philipp Rothemund et al.
,
A soft, bistable valve for autonomous control of soft actuators.Sci.
Robot.3,eaar7986(2018).DOI:10.1126/scirobotics.aar7986
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MEDIA
FiguresMultimedia
FIGURES
Fig. 1 Details of the soft, bistable valve.
(A) Schematic showing the components of the valve. The valve consists of a
hemispherical, elastomeric membrane separating two chambers. Control pressures
in the bottom (P+) and top (P−) chambers deform the membrane. When the membrane
is in the downward position (state 1), it blocks air flow through a tube leading
through the bottom chamber by kinking the tube. When the membrane is in the
upward position (state 2), it blocks air flow through the top tube. (B)
Photographs of the valve in both states. (C) When the pressure difference, ΔP,
between the two chambers reaches a critical value, ΔP1, the membrane snaps to
the upward position. When the pressure difference decreases below ΔP2, the
membrane snaps back to the downward position. (D) The tubing kinks (and
un-kinks) during the snapping process. The states of the bottom tubing (Q) and
the top tubing (Q¯) are binary (i.e., open or closed) and hysteretic (movie S1).
GO TO FIGUREOPEN IN VIEWER
Fig. 2 Measurements of the critical pressures.
(A) Schematic of the apparatus used to measure ΔP1 and ΔP2 for different
geometries. (B) Critical pressures, ΔP1 and ΔP2, as a function of H. (C)
Critical pressures, ΔP1 and ΔP2, as a function of θ. (D) ΔP2 plotted against ΔP1
for valves with different H and θ values. The boundary of accessible critical
pressures is defined by ΔP2 = ΔP1, and the values of ΔP for a valve with θ =
90°, and various H. Valves with critical switching pressures within this
boundary are obtained when θ < 90°.
GO TO FIGUREOPEN IN VIEWER
Fig. 3 Soft, bistable valve acting as a pneumatic switch.
(A) The bottom tubing is connected to an air supply of constant pressure PS. The
top tubing and the top chamber are connected to the atmosphere. The top and the
bottom tubing are joined together behind the valve to form the output P of the
pneumatic switch. The pressure in the bottom chamber is controlled by a variable
pressure controller (P+). When the membrane bends downward, it kinks the bottom
tubing; when it is bent upward, it kinks the top tubing. (B) Critical pressures
ΔP1 and ΔP2 as a function of PS. (C) Output of the valve for different PS values
and rectangular pulses as control input (P+ = 11 kPa). (D) Response of the valve
to two rectangular pulses (P+ = 11 kPa) as the control input. A sinusoidal wave
(frequency, 0.5 Hz; amplitude, 5 kPa) is superposed to the second pulse. H = 3
mm, θ = 87.5°.
GO TO FIGUREOPEN IN VIEWER
Fig. 4 Gripper that grasps autonomously.
(A) The gripper consists of five bending actuators, connected to a ring-shaped
channel, around a soft, bistable valve. When the membrane in the valve is in its
downward position, the pressure supply to the ring channel (PS) is blocked, and
it is connected to the atmosphere. A second pressure supply (P+) leads to the
bottom chamber of the valve and out through the contact sensor at the palm of
the hand. The top chamber can be connected through an external valve to the
atmosphere or the pressure supply PS. (B) Equivalent electrical circuit that
represents the pneumatic control in the autonomous gripper. (C to H) Photographs
of the gripper and schematics of the valve autonomously (C to E) closing around
a tennis ball and (F to H) releasing the ball (movies S2 and S3).
GO TO FIGUREOPEN IN VIEWER
Fig. 5 Pneumatic oscillator driven by an air source of constant pressure.
(A) When the membrane is downward, air flows from the pressure source PS into a
jar of volume V, but the tubing between the jar and the atmosphere is blocked.
When the pressure P in the bottom chamber exceeds ΔP1, the membrane snaps upward
and blocks air flow from the pressure source PS, and the jar vents to the
environment. When P decreases below ΔP2, the membrane snaps downward, and the
jar pressurizes again (movie S4). (B) Equivalent electrical circuit that
represents the pneumatic feedback control. (C) Oscillations in the jar at PS =
11 kPa. (D) Rise time (tR) as a function of PS, with different V values. (E)
Fall time (tF) as a function of PS, with different V values. Error bars in (D)
and (E) show the SD of the mean over a 60-s measurement interval. H = 3 mm and θ
= 87.5°.
GO TO FIGUREOPEN IN VIEWER
Fig. 6 Autonomous soft robot with earthwork-like locomotion using an air source
of constant pressure.
(A) The earthworm consists of a linear bellows actuator with cylindrical sleeve
as a restoring spring and a soft, bistable valve, integrated into the rear of
the actuator. The design of the valve is the same as that for the pneumatic
oscillator, with the bottom chamber of the valve connected to the bellows
actuator. The bellows actuator bends upward during inflation and downward during
deflation, which causes asymmetric contact between the feet and the ground,
leading to asymmetric friction and directional movement. (B) Photographs of the
moving earthworm at three points in time (movie S7). (C) Pressure inside the
robot and positions of front end, rear end, and center as a function of time for
PS = 17 kPa. The red dots indicate the times when the photographs in (B) were
taken.
GO TO FIGUREOPEN IN VIEWER
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dielectric elastomer actuators
Research ArticleJune 2019
A soft ring oscillator
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HomeScience RoboticsVol. 3, No. 16A soft, bistable valve for autonomous control
of soft actuators
Back To Vol. 3, No. 16
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FiguresTables
View figure
Fig. 1
Fig. 1 Details of the soft, bistable valve.
(A) Schematic showing the components of the valve. The valve consists of a
hemispherical, elastomeric membrane separating two chambers. Control pressures
in the bottom (P+) and top (P−) chambers deform the membrane. When the membrane
is in the downward position (state 1), it blocks air flow through a tube leading
through the bottom chamber by kinking the tube. When the membrane is in the
upward position (state 2), it blocks air flow through the top tube. (B)
Photographs of the valve in both states. (C) When the pressure difference, ΔP,
between the two chambers reaches a critical value, ΔP1, the membrane snaps to
the upward position. When the pressure difference decreases below ΔP2, the
membrane snaps back to the downward position. (D) The tubing kinks (and
un-kinks) during the snapping process. The states of the bottom tubing (Q) and
the top tubing (Q¯) are binary (i.e., open or closed) and hysteretic (movie S1).
View figure
Fig. 2
Fig. 2 Measurements of the critical pressures.
(A) Schematic of the apparatus used to measure ΔP1 and ΔP2 for different
geometries. (B) Critical pressures, ΔP1 and ΔP2, as a function of H. (C)
Critical pressures, ΔP1 and ΔP2, as a function of θ. (D) ΔP2 plotted against ΔP1
for valves with different H and θ values. The boundary of accessible critical
pressures is defined by ΔP2 = ΔP1, and the values of ΔP for a valve with θ =
90°, and various H. Valves with critical switching pressures within this
boundary are obtained when θ < 90°.
View figure
Fig. 3
Fig. 3 Soft, bistable valve acting as a pneumatic switch.
(A) The bottom tubing is connected to an air supply of constant pressure PS. The
top tubing and the top chamber are connected to the atmosphere. The top and the
bottom tubing are joined together behind the valve to form the output P of the
pneumatic switch. The pressure in the bottom chamber is controlled by a variable
pressure controller (P+). When the membrane bends downward, it kinks the bottom
tubing; when it is bent upward, it kinks the top tubing. (B) Critical pressures
ΔP1 and ΔP2 as a function of PS. (C) Output of the valve for different PS values
and rectangular pulses as control input (P+ = 11 kPa). (D) Response of the valve
to two rectangular pulses (P+ = 11 kPa) as the control input. A sinusoidal wave
(frequency, 0.5 Hz; amplitude, 5 kPa) is superposed to the second pulse. H = 3
mm, θ = 87.5°.
View figure
Fig. 4
Fig. 4 Gripper that grasps autonomously.
(A) The gripper consists of five bending actuators, connected to a ring-shaped
channel, around a soft, bistable valve. When the membrane in the valve is in its
downward position, the pressure supply to the ring channel (PS) is blocked, and
it is connected to the atmosphere. A second pressure supply (P+) leads to the
bottom chamber of the valve and out through the contact sensor at the palm of
the hand. The top chamber can be connected through an external valve to the
atmosphere or the pressure supply PS. (B) Equivalent electrical circuit that
represents the pneumatic control in the autonomous gripper. (C to H) Photographs
of the gripper and schematics of the valve autonomously (C to E) closing around
a tennis ball and (F to H) releasing the ball (movies S2 and S3).
View figure
Fig. 5
Fig. 5 Pneumatic oscillator driven by an air source of constant pressure.
(A) When the membrane is downward, air flows from the pressure source PS into a
jar of volume V, but the tubing between the jar and the atmosphere is blocked.
When the pressure P in the bottom chamber exceeds ΔP1, the membrane snaps upward
and blocks air flow from the pressure source PS, and the jar vents to the
environment. When P decreases below ΔP2, the membrane snaps downward, and the
jar pressurizes again (movie S4). (B) Equivalent electrical circuit that
represents the pneumatic feedback control. (C) Oscillations in the jar at PS =
11 kPa. (D) Rise time (tR) as a function of PS, with different V values. (E)
Fall time (tF) as a function of PS, with different V values. Error bars in (D)
and (E) show the SD of the mean over a 60-s measurement interval. H = 3 mm and θ
= 87.5°.
View figure
Fig. 6
Fig. 6 Autonomous soft robot with earthwork-like locomotion using an air source
of constant pressure.
(A) The earthworm consists of a linear bellows actuator with cylindrical sleeve
as a restoring spring and a soft, bistable valve, integrated into the rear of
the actuator. The design of the valve is the same as that for the pneumatic
oscillator, with the bottom chamber of the valve connected to the bellows
actuator. The bellows actuator bends upward during inflation and downward during
deflation, which causes asymmetric contact between the feet and the ground,
leading to asymmetric friction and directional movement. (B) Photographs of the
moving earthworm at three points in time (movie S7). (C) Pressure inside the
robot and positions of front end, rear end, and center as a function of time for
PS = 17 kPa. The red dots indicate the times when the photographs in (B) were
taken.
Reference #1