Dynamics of a Three-Dimensional Soft Fiber-Reinforced Manipulator With External Loads Based on Cosserat Rod Theory

Soft fiber-reinforced actuators with fibers embedded in elastomeric structures are excellent candidates in the soft robotics, which are characterized by high flexibility and adaptability. However, few works focus on the dynamics of soft fiber-reinforced actuators owing to their nonlinear properties for large material deformation. In this article, based on Cosserat rod theory, a dynamic modeling method implicitly discretizing the time derivatives of a set of partial differential equations besides addressing a boundary-value problem of ordinary differential equation at each time step, is proposed to describe the real-time bending, twisting, and elongation deformation characteristics of the manipulator. In particular, this method accounts for a pressure-time-dependent dynamic modulus and real-time external loads. In addition, we utilize our proposed method that can realize real-time simulation of the nonlinear deformation of the manipulator with external loads to demonstrate this method’s application. Finally, both the finite element analysis and experiments are conducted to evaluate the accuracy of our method. Results show that this method can effectively predict the real-time position of the manipulator, and the maximum real-time error rate of tracking end tip is less than 4%.