Inverse Kinematics and Dexterous Workspace Formulation for 2-Segment Continuum Robots with Inextensible Segments

TL;DR

This paper introduces an efficient inverse kinematics solution for 2-segment continuum robots with inextensible segments, including a novel dexterous workspace formulation that enhances target pose reachability analysis.

Contribution

It presents a new variable separation approach for IK of inextensible continuum robots and derives the first dexterous workspace formulation considering configuration limits and singularities.

Findings

The proposed method solves 100% of IK problems in simulations.

It significantly outperforms Jacobian-based methods in computational efficiency.

The workspace formulation aids in finding the closest feasible orientation to a target pose.

Abstract

The inverse kinematics (IK) problem of continuum robots has been investigated in depth in the past decades. Under the constant-curvature bending assumption, closed-form IK solution has been obtained for continuum robots with variable segment lengths. Attempting to close the gap towards a complete solution, this paper presents an efficient solution for the IK problem of 2-segment continuum robots with one or two inextensible segments (a.k.a, constant segment lengths). Via representing the robot's shape as piecewise line segments, the configuration variables are separated from the IK formulation such that solving a one-variable nonlinear equation leads to the solution of the entire IK problem. Furthermore, an in-depth investigation of the boundaries of the dexterous workspace of the end effector caused by the configuration variables limits as well as the angular velocity singularities of the continuum robots was established. This dexterous workspace formulation, which is derived for the first time to the best of the authors' knowledge, is particularly useful to find the closest orientation to a target pose when the target orientation is out of the dexterous workspace. In the comparative simulation studies between the proposed method and the Jacobian-based IK method involving 500,000 cases, the proposed variable separation method solved 100% of the IK problems with much higher computational efficiency.