  The compliance of soft robotic arms renders the development of accurate
kinematic & dynamical models especially challenging. The most widely used model
in soft robotic kinematics assumes Piecewise Constant Curvature (PCC). However,
PCC fails to effectively handle external forces, or even the influence of
gravity, since the robot does not deform with a constant curvature under these
conditions. In this paper, we establish three-dimensional (3D) modeling of a
multi-segment soft robotic arm under the less restrictive assumption that each
segment of the arm is deformed on a plane without twisting. We devise a
kinematic and dynamical model for the soft arm by deriving equivalence to a
serial universal joint robot. Numerous experiments on the real robot platform
along with simulations attest to the modeling accuracy of our approach in 3D
motion with load. The maximum position/rotation error of the proposed model is
verified 6.7x/4.6x lower than the PCC model considering gravity and external
forces.
