Integrated Logic for Dielectric Elastomers: Replicating the Reflex of the Venus Flytrap

Dielectric elastomers (DEs) are electroactive polymers commonly used in soft robotics. Bulky and stiff high‐voltage circuits are usually needed to control their operation. This article presents autonomous control in a multi‐functional device made entirely of DEs. A gripper made of DE actuators is controlled by dielectric elastomer sensors through an electrical circuit. The circuit itself is composed of a network of actuators and sensors. The final structure requires only a constant power supply to work and produces its controlling signals. Every component can be manufactured simultaneously with the same materials and processes. At first, the logical control of the gripper is demonstrated by directly connecting a sensor to the gripper that opens when the sensor is stretched. Then, a DE level‐triggered flip‐flop (also called latch) is introduced to have bi‐stability between open and closed states. Finally, the latch is integrated inside the gripper, allowing it to sense objects. The device autonomously grips an object that is placed in it, resembling the closing mechanism of the plant Dionaea muscipula, also known as the Venus flytrap.

where e 0 is the vacuum permittivity, e r the relative permittivity of the elastomer, V the applied voltage, and d the thickness of the membrane (distance between capacitor's plates). DEAs show electro-mechanical properties similar to biological muscles (e.g., high strain, energy density, and actuation speed). Thus they are a promising material for bio-inspired robotic applications. [6,7] Another appealing aspect of DEs is multi-functionality. DE devices can perform more than one task at the same time (e.g., actuation and sensing). [4,8,9] There are many ways of producing dielectric elastomer sensors, the type used in this work is depicted in Figure 1b. It is called a dielectric elastomer switch (DES) because it can switch between two resistance values that differ by several orders of magnitude when stretched or compressed. The exact range depends on the fabrication method. O'Brien et al. first demonstrated DESs. [10] These devices are realized by depositing a piezoresistive ink on a substrate. The electrical conduction in the ink follows the percolation theory. [11] In the stretched state, the concentration of conductive particles is low and there are only a few electrically conductive percolation paths due to particle contact. Therefore, the resistance is very high. In the compressed state, the particle's concentration is higher, more percolation paths are formed, and the resistance drops. From a digital point of view, it is possible to realize the equivalent of a transistor by coupling a DEA and a DES on the same elastomer membrane, as shown in Figure 1c,d. [12,13] When high voltage is applied to the DEA, it expands and compresses the DES, lowering its resistance R DES . The resulting structure is the dielectric elastomer transistor (DET), and it works similarly to a conventional transistor where T 1 , T 2 , and T 3 are the equivalents of gate, drain, and source.
Devices that can process information directly in the domain where the information originates are increasingly becoming a topic of interest. For example, a pneumatic actuator needs to be interfaced with valves and electronic controls, but it can perform simple tasks autonomously if provided with a pneumatic circuit instead. [14,15] Similarly, lab-on-chip applications do not need to interface microfluidic structures with external electrical components when a comparable function can be achieved internally Dielectric elastomers (DEs) are electroactive polymers commonly used in soft robotics. Bulky and stiff high-voltage circuits are usually needed to control their operation. This article presents autonomous control in a multifunctional device made entirely of DEs. A gripper made of DE actuators is controlled by dielectric elastomer sensors through an electrical circuit. The circuit itself is composed of a network of actuators and sensors. The final structure requires only a constant power supply to work and produces its controlling signals. Every component can be manufactured simultaneously with the same materials and processes. At first, the logical control of the gripper is demonstrated by directly connecting a sensor to the gripper that opens when the sensor is stretched. Then, a DE level-triggered flip-flop (also called latch) is introduced to have bi-stability between open and closed states. Finally, the latch is integrated inside the gripper, allowing it to sense objects. The device autonomously grips an object that is placed in it, resembling the closing mechanism of the plant Dionaea muscipula, also known as the Venus flytrap.

Introduction
Dielectric elastomers (DEs) are electroactive polymers that can be employed as actuators, sensors, generators, and logic circuits. [1][2][3][4] Dielectric elastomer actuators (DEAs) follow the simple principle of a charging capacitor to transduce electrical energy into mechanical energy. The capacitor is made of a soft elastomer, and the electrodes are compliant. Applying a high voltage to the capacitor results in thickness compression and in-plane expansion, as shown in Figure 1a. This happens because opposite charges on the two electrodes attract each other and identical charges on the single electrode repel each by logic microfluidics [16] and its two forms logic micropneumatics [17] and chemofluidics. [18][19][20] Unconventional circuits can also be used for distributed signal processing and local response to environmental interactions. [21] Contrary to these examples, DEs work with electricity. However, several problems can be addressed using DE circuits instead of conventional ones. The high voltages in the range of ≈1-5 kV that are needed for appropriate operation of DEs require expensive and bulky high-voltage circuits that cannot easily be integrated into the DE structure, made of polymer. DE circuits, instead, are directly compatible and integrable inside DE devices. McKay et al. used DESs to self-prime a dielectric elastomer generator. [22] Henke et al. proposed a caterpillar-inspired robot driven by a dielectric elastomer oscillator. [23] This work focuses on the use of DE logic circuits to drive DEAs. The potential of this approach is shown by controlling a DE gripper. In the first example, the gripper is controlled by a DES. The DES is implemented in the form of a push button. If the button is pushed, the DES is stretched, and the gripper opens. Then, a level-triggered flip-flop (also called latch) is introduced to make the gripper bi-stable between open and closed states. Finally, a DES is integrated inside the gripper, allowing it to detect objects that are placed inside it. The final device autonomously grips objects that touch it, replicating the reflexive motion of the Venus flytrap plant in the presence of a prey. [24]

Experimental Section
The acrylic tape VHB4905 by 3M was used as elastic membrane for the here presented DE devices. All the needed devices (DETs, DESs, and gripper) can be made from a single membrane piece. The first step was to pre-stretch a piece of this tape. The volume (V) of the elastomer can be expressed as where d is the initial thickness of the membrane, l 1,2 are the initial in-plane side lengths, and λ 1,2,3 are the stretch factors applied to the elastomer in the three directions. The piece of tape is equi-biaxially pre-stretched with a pre-stretch λ 1 = λ 2 = λ pre = 2.0, and the DESs for the DETs were deposited by stamping with a PDMS mold. The membrane was then stretched up to λ pre = 2.9, and the DESs for sensing are deposited as before. Finally, the membrane was stretched up to the final pre-stretch value of λ pre = 3.6, and different rigid frames, previously cut with a laser cutter, were attached to the membrane to maintain the pre-stretch and form the final devices. The pre-stretch was needed to improve the performance of this type of DEAs. [26] The DETs and DESs used a 3 mm thick PMMA frame, the gripper had a 0.25 mm thick one made of PET. Finally, the DEAs' electrodes and the electrical connections were hand-painted with a brush using conductive carbon grease (Nye's Nyogel 756G). Figure 2 shows the finished devices and their geometric dimensions as well as an illustration of the final device, inspired by the Venus Flytrap.

Types of Dielectric Elastomer Switches
The DESs were made of a mixture, kneaded by hand,  V is low, the resistance of the DES (R DES ) is in the high resistance state. d) DET in the on-state: when T1 V is high, R DES is in the low resistance state.
pre-stretch values were necessary to make DESs work properly. Figure 3 illustrates the concept. The difference between the pre-stretch at the time of deposition of a DES and the final prestretch, which was fixed at λ pre = 3.6 for this work, produced an initial stretch of the devices that tailored their properties to the different applications. Stretchable DESs were used for the buttons. They needed to change resistance when stretched. In Figure 3, the left end of the curve corresponds to a stretch close to zero. The working point can be moved to the right of this point, along the curve, by adding an initial stretch. This step was done to have sensors that change resistance as soon as they were stretched. Therefore, stretchable DESs were deposited on the membrane when λ pre = 2.9. Afterward, the membrane, and consequently the DESs, was stretched up to the final pre-stretch λ pre = 3.6 and the DESs were fixed to PMMA frames. At rest, the resistance of a stretchable DES was represented by the red dot. When it was stretched, its resistance followed the red arrow along the curve. Conversely, DESs used for DETs had to change resistance when compressed. Their working point needed a larger shift to the right with respect to stretchable DESs. This was achieved with more initial stretch. Compressible DESs were deposited when λ pre = 2.0 and stretched until λ pre = 3.6. Their resistance at rest was represented by the green square. When this type of DESs was compressed, its resistance followed the green arrow along the curve. For clarity, in the rest of the text the term DES will be used for the sensors when they were alone (stretchable DESs) and the resistance of a DES internal to the DET (compressible DESs) will be referred to as DET resistance.

Dielectric Elastomer Gripper
The DE gripper is based on the dielectric elastomer minimumenergy structure (DEMES) principle. [27,28] The specific geometry of the gripper used in this work was derived experimentally by trying and evolving different geometries into the final design. The DEMES was realized with a thin PET sheet bonded to a   pre-stretched elastic membrane. At rest state, the PET frame folded in the direction where the structure was weaker due to the elastic restoring forces of the pre-stretched membrane. Thanks to this mechanism combined with the adhesion of the VHB tape used as the substrate, it was possible to grip different objects. Two holes were cut into the PET film to deposit the DEA electrodes as shown in Figure 2c. Applying a high voltage to the DEA made it expand and exert a force that opened the gripper (Figure 4). The holes defined the points where the structure bends and their dimensions can be changed to affect the gripper's operation. Larger holes weakened the bending stiffness of the PET frame and increased the gripping force and bending angle. However, there was only a limited amount of force that the DEA can generate to open the gripper. Thus, if the holes were too big, the gripping force was too strong, and it would be impossible to open the gripper with the DEA. On the contrary, if the holes were too small, the gripping force would not be enough to grip any object. A balance between these aspects was experimentally found with the structure in Figure 2c. Finally, a support structure that kept the gripper hanging was also produced by laser-cut PMMA plates.

Results
The electrical measurements in this section were performed with LabView, using a NI-9205 module (DAQ). A custom-built pre-amplifier, possessing a voltage divider, was used to step down the high voltage by 1:1000 to a magnitude safe to measure with the NI module. A supplementary video that shows the gripper in action is also available.

Sensing System
The first structure presented is the sensing system. It is composed of a DES and a fixed resistor R f = 200 MΩ, placed as shown in Figure 5a. The DES is stretched by pushing a button made of PMMA. The output voltage of the voltage divider is where V CC is the input voltage supplied by the high-voltage power supply, [29] set constant to 3.5 kV, and R DES the variable resistance of the DES. The value of R f was chosen considering the minimum and maximum values of R DES , which range from 10 7 to 10 11 Ω (from Figure 5b). The goal is to vary V out between 0 V and V CC . This is achievable with R f = 200 MΩ because the ratio between the resistances in Equation (3) is close to 0 when R DES is at minimum and close to 1 when it is at maximum. Choosing the R f value too high or low would compromise this balance and reduce the maximum span of V out . As shown in Figure 5b, when the button is pushed, the DES is stretched and its resistance increases sharply. Therefore the voltage increases following Equation (3). When the button is released, the resistance of the sensor drops to the original low value and so does the voltage. The gripper's DEA is connected between V out and 0 V, thus the gripper opens when the button is pushed and closes when the button is released as shown in Figure 5c. In this configuration, the sensing system can be considered "normally off" because, if the DES is not stretched, the output is at low voltage. However, it is possible to make the "normally on" configuration just by switching the position of the DES and R f in the circuit. In this situation, pushing the button would make the gripper close.

Gripper with Latch
A set-reset (SR) latch circuit is shown in Figure 6a. The truth table, below it, explains how it works. It is composed of two NOR logic gates and acts as a memory device. When in the rest position (SR0), it is capable of maintaining the state that was    showed that it is possible to replicate the SR latch with DEs. [30] Figure 6b,c shows the SR latch realized for this work. The electrical connections inside the latch are made with screws and copper tape. External cables are used to connect the latch to the rest of the system: voltage generator, fixed resistors R f , sensors, and gripper. The PMMA frames for the DETs are smaller than in previous works (39 × 37 mm instead of 70 × 50 mm) [12,13] , easing the integration of the circuit. In addition, the inputs S and R are now controlled by two DES button systems as the one described in Figure 5. In this way, pushing one of the buttons activates the corresponding input. Figure 6d shows the measurements of the signals S, R, Q, and Q. In Figure 6e the SR latch is visible at the base of the gripper support structure. The electrodes of the gripper are connected between Q and 0 V. When the button S is pushed, the input S raises to 1, Q does the same and the gripper opens. Instead, when the button R is pushed, Q goes to 0 and the gripper closes. If no button is pushed (S=R=0), the gripper maintains the previous state, either open or closed. Bi-stability in DEs is usually achieved with external electrical control. A common approach is to use multiple DEAs that act as antagonist pairs. [31,32] Controlling which DEA is actuated, it is possible to switch the structure between stable states. The DE gripper presented by Wang et al., also inspired by the Venus flytrap, switches when a very short voltage pulse is applied to the DEAs. [33] The device in Figure 6 can achieve bi-stability with a simple system architecture, due to the integrated logical control. A DE latch works as the memory element and maintains the structure in the previously set state. Therefore, there is no need for complex external control and the device can operate with just a constant supply of voltage. Furthermore, the command to switch comes from a DE sensor that can be integrated inside the gripper, leading to the final configuration of Figure 7. In this configuration, the reset button of the latch is integrated into the gripper's body. A DES is placed in a laser-cut hole in the middle of the PET holding frame as illustrated in Figure 2e,g. Figure 7 displays the photos taken during a test. The first row shows the reflex of the gripper triggered with a pen. When the DES internal to the gripper is stretched, the device closes as a Venus flytrap detecting an insect. The second row displays the autonomous grip of a small container by the DE Venus flytrap. When the container pushes on the DES, it triggers the trap that holds the object until the release button is pressed.

Conclusion
DEs are usually controlled by stiff, bulky, and expensive high-voltage electronics. Circuits made of the same electroactive polymer are more suited for the task. They can be easily integrated into the material itself and replace complex microelectronic components, thus enabling a much simpler system architecture. This article demonstrates the principles of integrated control and autonomous operation of DEs. After a logic function has been chosen to drive a DEA, a DE circuit can be manufactured to perform it. For this work, a SR latch was selected because it provides the bi-stability needed to replicate the Venus flytrap movement. Several DE structures (gripper, DETs, DESs) were adapted to work in an interconnected and multi-functional structure in which the sensors gather information from the environment, the circuit processes it, and the actuator acts accordingly. The SR latch was provided with input controls through sensors (DESs). The gripper was based on DEMES technology and the geometry was chosen for its simple design and compatibility with the production process. The gripper used the same pre-stretch value as DETs and DESs, thus it could be produced in parallel with them, and DESs could be easily embedded in it. Afterward, multiple ways to control DEAs were shown. The DE gripper was operated with the simple pressure of a DES and with a latched input. Bi-stability of DEAs was demonstrated without the need for external electrical control. The final device, inspired by the Venus flytrap plant, was capable of autonomously gripping objects that were placed in it. All the different control configurations were realized with only an externally generated voltage. This work fits in a broader research topic about unconventional logic devices. Examples are the pneumatic circuits used to control pneumatic actuators and microfluidic circuits for labon-chip applications. This approach allows information to be processed in the same domain in which it originates, creating simpler, autonomous devices and shows potential for additional features such as distributed logic, and local response to environmental interactions.