Geometrically Exact Finite Element Formulation for Tendon-Driven Continuum Robots

Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms. For some continuum robots, the constant curvature assumption-based kinematic modeling can be accurate and effective. While for other cases, such as soft robots or robot-environment interactions, the constant curvature assumption can be inaccurate. To model the complex deformation of continuum robots, the geometrically exact beam theory (may also be called the Cosserat rod theory) has been used to develop computational mechanics models. Different from previous computational models that used finite difference schemes for the spatial discretization, here we develop a three-dimensional geometrically exact beam theory-based finite element model for tendon-driven continuum robots. Several numerical examples are presented to show the accuracy, efficiency, and applicability of our new computational model for tendon-driven continuum robots.