Parallel-distributed model in three-dimensional soft-fingered grasping and manipulation

This paper focuses on three-dimensional grasping and manipulation by robotic fingers with soft fingertips. The authors have proposed two-dimensional parallel-distributed model of a soft fingertip to describe the dependency of its potential energy to the relative orientation between the fingertip and the object. Here we extend the previous two-dimensional model to three-dimensional model, incorporating the rotation in three-dimensional space. We formulate the elastic potential energy stored in a soft fingertip due to the contact with the planar surface in three-dimensional space. We sketch the Lagrangian of the system consisting of a rigid prism grasped by three fingers with soft fingertips.