Accurate estimation of the position and shape of the rolling joint in hyper-redundant manipulators

Hyper-redundant manipulators driven by cables are used in minimally invasive surgery because of their flexibility and small diameters. In particular, manipulators composed of many rigid links and joints have the advantages of high stiffness and payload. However, these manipulators have difficulty in estimating their positions and shapes using calculations based only on the kinematics model that assumes all joint angles are equal. In this paper, we present a method for estimating the position and shape of the rolling joint in hyper-redundant manipulators by minimizing the joint moments. This allows the determination the equilibrium position of all segments of the rolling joint, and therefore an estimation of its shape. We experimentally determine the position and shape of a prototype of the rolling joint and compare them to a simulation of our method. The maximum error between the simulation and the experimental results is 4.13 mm, which is a 77.22% improvement over the kinematic model that calculates the same joint angle. This verifies that our method accurately estimates the position and shape of the rolling joint.