## 1 Introduction  
Robotic or similar actuation systems use a multitude of methods, each of which offer distinct advantages and disadvantages [1, 2, 3, 4, 5]. Their specific features make each of those methods suitable for various applications. Electromagnetic actuation [6, 7, 8] is used in sensors, motors or robotics, has a high power-to-weight ratio and is highly versatile [9, 10] and reliable [11, 12]. However, this form of actuation is not energy-efficient and cannot easily be scaled down to a small form factor. Pneumatic [13, 14, 15, 16, 17] or hydraulic [18, 19, 20] actuation is suitable for tasks that require high force generation, e.g., heavy machinery. For instance, in McKibben artificial muscles and prosthetics [17, 21, 22], hydraulic actuation provides large forces in macroscale systems [18, 23]. Pneumatic and hydraulic actuation also dominate in other fields [20], e.g., construction vehicles, industrial assembly lines or the U.S. Army's robot mule [24]. One of their disadvantages is the requirement of a fluid reservoir, which is prone to leaks and requires regular maintenance [25, 26, 10, 27, 28, 29, 30]. The limitations of electromagnetic, hydraulic and pneumatic actuation have motivated the search for alternative actuators in applications such as exoskeletal locomotion, walking robots, surgical robots, biomimetic underwater propulsion, prosthetics, medical servosists and small-scale biomimetic robots [8; 13; 29; 30; 31], including artificial muscles [32; 33; 34; 35; 36; 37; 38; 30; 31]. In most of these applications, high precision and energy efficiency are required. Piezoelectric actuation [39; 40; 41; 42; 43; 44; 45] is one option. Piezoelectric devices offer high precision and can generate very large forces. However, the length of motion is small, and the devices are expensive and very difficult to upscale. Yet another option is actuators based on thermal expansion, e.g., torsional muscles [41; 46] and shape-memory alloys muscles [47; 48]. These can generate large forces, but the need to cool to cycle severely limits cycling frequency and responsiveness. This method is also not energy efficient. In comparison, electrostatic actuation is scalable, energy-efficient and low-cost (if combined with 3D printing). A comparison of the different approaches is given in Table 1.  
This makes electrostatic actuation an attractive candidate mechanism. Electrostatic actuators have no moving parts that require lubrication and they also require no use of fluid systems. Therefore, actuation using electrostatic motors or capacitor motors requires little maintenance [49]. The force output of electrostatic actuators is limited; however, the force scales as the inverse square of the separation between the charged plates [36], their power consumption is very low and they are highly suited at the micro- and nanoscales. A particularly intriguing conceptual design for artificial muscles is that of dielectric elastomer actuators (DEAs) [50; 51; 52; 53; 54; 55; 56; 57]. Their actuation is based on the deformation of a polymer (elastomer) slab from the electrostatic force between the charges built on the slab's surfaces, under applied voltage [33; 36]. Finite-element analysis (FEA) simulations of artificial muscles have confirmed this size-force relationship [58]. Hence, downscaling the devices to the microscale would result in a disproportionate gain in the generated force. Creating arrays of such devices in three dimensions would increase both the resultant force output and the resultant strain. When an array is constructed with the individual DEAs arranged to be mechanically in parallel, the total force produced is equal to the sum of the forces produced by each individual unit, but the overall elongation is unchanged by the array. When an array is constructed with the individual DEAs arranged to be mechanically in series, the total elongation is equal to the sum of the elongations produced by each unit, but the overall force is unchanged by the array. Implementing a 3D array allows both benefits to be obtained simultaneously.