Inverse dynamic design for motion control of soft machines driven by dielectric elastomer actuators

Dielectric elastomers (DEs) are a sort of electroactive polymers with large and fast responses, light masses and high energy densities. Hence, they are regarded as one of the most potential materials for artificial muscles and soft robots. Previous researches on DEs focused mainly on experimental prototypes and property optimization in a component level, while the system-level design and control of dynamic motions of DE actuators are still open problems. In this study, the computational method of inverse dynamic design (IDD) for input voltages of DE actuators is proposed by taking the electromechanical coupling mechanics and the effects of rigid-body motions into account. The proposed inverse dynamic design with nonlinear finite elements enables one to realize the high-precision modeling of soft actuators and to derive the dynamic voltages for desired trajectories in a system level. To describe the overall motions and deformations of DE actuators, the gradient constraints of the dynamic configurations of the actuators are introduced upon the assumption of time-varying uniform curvatures for the desired deformation. And then, based on the principle of energy equivalence, the dynamic voltages for the target deformations in motions are computed inversely from the Lagrange multipliers of the desired trajectories. In addition, the forward simulations by removing the constraints and applying the voltages are further conducted to validate and predict the final configurations. Finally, five numerical case studies and demonstrative experiments are presented to validate the effectiveness of the proposed method. This study endeavors to establish a universal inverse dynamic design method for the motion control of soft DE actuators, allowing for the application of theoretical methodology to engineering problems.