Analytic solutions for the static equilibrium configurations of externally loaded cantilever soft robotic arms

In this paper we derive the analytic solutions for the statics of cantilever soft arm under external loading. The main motivation behind this work is the development of manageable and ready-to-use mathematical models of soft robotic arm for various purposes. We formulate the problem exploiting the Lie group structure of the arms' configuration space. This allows using the powerful mathematical tools from differential geometry. The model builds upon the theory of Cosserat rods: the mechanics-based perspective used to describe the kinematics and statics allows including into the model the large deformations due to axial, shear, torsion and bending effects. The position fields of the manipulators' shapes are analytically integrated and validated with respect to exact solutions and experiments.