Equilibrium Manipulation Planning for a Soft Elastic Rod Considering an External Distributed Force and Intrinsic Curvature

Abstract

Previous work has shown that the set of equilibrium shapes of a rod is a smooth 6-dimensional manifold. We develop the Kirchhoff rod model in a differential equation form using Darboux vector that easily adds distributed force and intrinsic curvature. It can be seen that in this letter, the manifold of the equilibrium set is the same. Furthermore, we address the rod manipulation planning problem which has the certain point on rod following a predefined spatial track. We propose a novel rod manipulation planning algorithm that considers the spatial configuration distance between the current and the goal, and follows its quickest descent direction in each planning step. The experiments show that it has a much higher successful rate than straight-line path planning in the Euclidean space of the gripper and significantly less planning time than the commonly used sampling method. The hardware experiments are also conducted on a platform that consists of a manipulator, an F/T sensor and two cameras. We choose soft rubber rods in the experiments, and the results validate the proposed model and methods.