Dielectric elastomer actuators (DEAs) are a promising actuation technology in soft robotics owing to their large voltage-induced deformation and rapid response. However, most existing DEA design paradigms are empirical or intuitive, lacking the mathematical modeling and optimization methodology to exploit their actuation capabilities for prescribed motion tasks. In this paper, we present an automatic design methodology to maximize the concerned displacement(s) of DEAs by topology optimization of the applied spatial electric fields (SEFs). Our method is enabled by integrating the freeform SEF profile captured by implicit level sets, and the constitutive model of DEAs incorporating geometric and material nonlinearities and the electromechanical coupling effect, into a gradient-based optimizer. We implement our method for motions of single and multiple degrees of freedom (DOFs) of planar DEAs, and the optimized SEFs have been found to improve the output displacements by more than 75% compared with their intuitive counterparts. We further demonstrate a proof-of-concept application in which our designed two-DOF DEAs can actively drive various host structures to shape-morph from flat sheets to desired three dimensional configurations. Overall, our paper represents the first step toward automatic design of soft DEAs for diverse potential applications in soft machines and robots.

Soft robots, primarily made out of intrinsically soft materials, have flourished greatly in the past decade due to their advantages such as flexibility and adaptability over rigid-bodied robots. A rich repertoire of soft robots designed from intuitive or biomimetic approaches have been developed to provide new solutions for robots. However, these design approaches are limited by the designers' experience and inspiration, and a systematic design methodology for soft robots is still missing. We tackle this issue by mathematically recasting the design problem under the framework of topology optimization problem. To demonstrate the effectiveness of the proposed methodology, in this paper, we develop a pneumatically actuated soft gripper consisting of three fingers, each finger is able to undergo a free travel bending and deliver a grasping force. Hence, each gripper finger is designed as a continuum compliant mechanism to achieve its maximal bending deformation. The proposed soft gripper with complex shape is directly fabricated through 3D printing technology. Experimental results show that the deflected soft finger is able to achieve a 41° free travel bending and generate 0.68N blocked force upon 0.11MPa actuation pressure. This work represents an important step towards the goal of designing soft robots automatically.