Mathematical modeling of soft robots is complicated by the description of the continuously deformable three-dimensional shape that they assume when subjected to external loads. In this article we present the deformation space formulation for soft robots dynamics, developed using a finite element approach. Starting from the Cosserat rod theory formulated on a Lie group, we derive a discrete model using a helicoidal shape function for the spatial discretization and a geometric scheme for the time integration of the robot shape configuration. The main motivation behind this work is the derivation of accurate and computational efficient models for soft robots. The model takes into account bending, torsion, shear, and axial deformations due to general external loading conditions. It is validated through analytic and experimental benchmark. The results demonstrate that the model matches experimental positions with errors <1% of the robot length. The computer implementation of the model results in SimSOFT, a dynamic simulation environment for design, analysis, and control of soft robots.
Keywords: Cosserat rods; continuum robots; differential geometry; dynamics; mathematical modeling; soft robotics.