# Review of Soft Actuators Controlled with Electrical Stimuli: IPMC, DEAP, and MRE
## 2 Recent Progress in Development and Applications of Soft Actuators
### Dielectric Electroactive Polymers (DEAPs)
#### 2.2.2 Actual Trends in the Application of DEAP in Soft Robotics  
The principle of operation of the actuator is similar to the electromechanical transduction of a parallel two-plate capacitor. When an electric potential is applied across the polymer membrane coated with compliant electrodes on both sides, the material is compressed in thickness and expands in the lateral direction. This process is well explained in many publications [47; 65; 66; 67]. Figures 5 and 6 show graphically how the actuator membrane stretches under the influence of the applied voltage. Due to this design, a mechanical actuating force is generated. The effective mechanical pressure, called Maxwell stress along the thickness direction, is given by the formula (1):  
\[\sigma_{e}=-\epsilon_{0}\epsilon_{F}E^{2} \tag{1}\]  
Figure 5: Diagram of DEAP actuator with power off. Figure 6: Diagram of DEAP actuator with power on. where \(E\) is applied electric fields, \(e_{0}\) is electric permittivity of free space and \(e_{r}\) is the relative permittivity. In recent years, a lot of research has been carried out to improve the parameters of DEAP actuators by adding initial mechanical stress to the polymer membrane [68; 69]. Through theoretical modeling and numerical analyses, it is revealed that pre-stretch helps to reduce the drive voltage required to induce a desired bending deformation. Pre-stretching the actuator membrane improves the response speed and removes the boundary constraint caused by the inactive actuation area of the actuator. He et al. investigated the effects of pre-stretch on the bending deformation of the DEA actuator [70]. In [71], cyclic tensile properties of VHB4905 and VHB4910 were investigated, and the actuation displacement and output force of the DEA are analyzed and discussed in detail with different pre-stretching indexes. It has been shown, that the stress-strain curves of VHB materials show hysteresis under cyclic loading. The thinner the thickness of the VHB, the larger the unit stress and the unit hysteresis loss rate. The hysteresis in DEA materials, resulting in nonlinearities of the system, limits their performance when operating in an open-loop configuration. So pre-strain plays an important role in generating large strain, however, there are several disadvantages due to the pre-strain, such as stress relaxation and hysteresis. Their ranges depend on the materials used and are still a key issue for the actuator. DEAP actuators can provide quiet operation, low weight, high power density, and fast response. These features have enabled these actuators to be used in robotics and haptic applications. In work [72], the authors demonstrate a rolled dielectric elastomer actuator being used as a telepresence device in a heartbeat measurement application. While at work [73] it is proposed a thin, highly flexible, and lightweight vibrotactile dielectric elastomer actuator, which is experimentally optimized to provide a variety of haptic sensations in real time (see Figure 7). [PERSON] et al. [74] developed two kinds of six-legged robots based on the spring roll actuator. In the field of soft robots, grasping objects of different shapes and types is one of the most challenging problems. [PERSON] et al. [75] presented a new design of DEA with multisegments. The repetitive segments enable the gripper to grab objects of different sizes and shapes. The crucial aspect of DEAP actuators is the type of bias. Based on the early works on DEAP actuators, it is known that properly applied bias can extend its working range. In the literature, the following types of bias are known: mass, linear spring, negative non-linear spring with positive linear spring, permanent magnet, and pneumatic [76; 77; 78; 79; 80]. Currently, the best result in terms of the working range is obtained by combining a negative non-linear spring with a positive linear spring [81]. The nonlinear bias can be applied to obtain a fast movement like in work [82], where the inspiration is taken from biological systems.