A geometry deformation model for compound continuum manipulators with external loading

The complexity of soft continuum manipulators with hybrid and tuneable structures poses a challenging task to achieve an inverse kinematics model which is both precise and computationally efficient for control and optimization purposes. In this paper, a new method based on the principle of virtual work and a geometry deformation approach is presented for the inverse kinematics model of the STIFF-FLOP arm which is a pneumatically actuated continuum manipulator. We propose a novel simplified and computationally efficient yet accurate analytical solution to analyse the static behaviour of a compound soft manipulator in the presence of external and body forces which is verified against experimental data, showing promising agreement with 10% mean error for planar movements. In the process, we present a new modelling approach for braided soft extensor actuators with no braid-surface relative slip constraint. For the first time, our model predicts a simple analytical solution for the cross section deformation which is essential to control soft manipulators with regional tunable stiffness structure.