Cosserat Rods With Cross-Sectional Deformation for Soft Robot Modeling

Cosserat rod models are widely used to simulate, design, and control soft robots. The Cosserat framework accounts for bending, torsion, transverse shear, and elongation of a long, slender structure and correctly handles large rotations and deflections in 3D, while being far less computationally expensive than full 3D elasticity models using finite elements. However, the Cosserat model is not always appropriate for soft robotic structures since it assumes the cross sections never change size or shape. In this letter, we extend the standard Cosserat rod model to include cross-sectional deformation while retaining much of its simplicity. We add to the Cosserat model additional degrees of freedom that parameterize stretch and shear in the cross-sectional plane and their rates of change along the rod length. We then formulate several possible constitutive laws on the state variables (one linear and one non-linear) and compare them to the standard Cosserat energy expressions to gain insight. We further show how fluidic actuation and tendon actuation can be incorporated into the model, and we compare the extended Cosserat models to 3D nonlinear finite-element simulations with good agreement. Finally, we demonstrate use of this model in a robotics context to control the path-following gait of a peristaltic worm-inspired soft robot.