Domain decomposition approach for FEM quasistatic modeling and control of Continuum Robots with rigid vertebras

This paper presents a development of a new method dedicated to the modeling and control of Continuum Robots, based on the Finite Element Method (FEM) using quasi-static assumption. The modeling relies on a discretization of the continuum robots using 6 DoFs Frames along the structure of the robot that is compatible with the modeling of a sequence of rigid vertebras. When the robot´s structure relies on rods with constant sections, internal forces are computed with beam elements, placed between two adjacent frames, that applies forces and torques. In the opposite, when the robot is composed of a complex shape deformable backbone separated by the rigid vertebras, a domain decomposition strategy is used to obtain an equivalent stiffness between two vertebras using volumetric FEM. In both cases, for solving the whole robot model and inverting it in real-time, the numerical method takes advantage of the serial nature of continuum robots, using a Block-Tri-Diagonal solver. The factor of improvement in the computation time reaches several order of magnitude compared to a classical FEM model, while keeping a good precision. The method has also been implemented and tested on a real pneumatic CBHA trunk designed by Festo Robotics and some complementarity examples have been generated numerically.