Dielectric elastomer actuators (DEAs) have garnered extensive attention especially in soft robotic applications over the past few decades owing to the advantages of lightweight, large strain, fast response and high energy density. However, because the DEAs suffer from nonlinear elasticity, inherent viscoelastic creep, hysteresis and vibrational dynamics, the modeling, control and self-sensing of DEAs are challenging, thereby hindering the practical applications of DEAs. In order to address these challenges, numerous studies have been conducted. In this review, various physics-based modeling methods and phenomenological modeling methods for predicting the electromechanical response of DEAs are presented and discussed. Different control methods for DEAs are reviewed, which are classified into open-loop feedforward control, feedback control, feedforward-feedback control and adaptive feedforward control. Physics-based self-sensing methods and data-driven self-sensing methods for reconstructing the DEA displacement without the need for additional sensors are discussed. Finally, the existing problems and new opportunities for the further studies are summarized.

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