Dynamic Modeling Incorporating Water Damping for a Fiber-Reinforced Soft Actuator Based on Euler–Bernoulli and Cosserat Rod Theories

Soft actuators are gaining increasing popularity in various fields, including marine engineering and biomedical engineering. However, due to their nonlinear properties and significant material deformation, dynamic modeling of soft actuators for motion behavior is quite a challenge, especially for underwater environments. This article ingeniously combines Euler–Bernoulli theory and Cosserat rod theory to propose an efficient and accurate dynamic model for solving the underwater motion behavior of fiber-reinforced soft actuators. Under the assumption of neglecting external forces, we first utilize Euler–Bernoulli theory to establish a mathematical model describing the relationship between water pressure and the bending deformation of the soft actuator. This model is then employed as a boundary condition when solving the dynamic model. Based on this, we use Cosserat rods theory to depict the dynamic behavior of the soft actuator's motion in an underwater environment. In particular, we analyze the impact of its own gravity, buoyancy, and water damping on the motion of the soft actuator. To validate the proposed dynamic model, we fabricated a novel fiber-reinforced soft actuator and a water-driven control system. Subsequently, we conducted a series of model validation experiments. Experimental results show the model maximum error rate is below 13%, thereby confirming the effectiveness of the model, which can predict the motion behavior of the soft actuator under different water-driven pressures.