Closed-Form Inverse Kinematics for Continuum Manipulators

This paper presents a novel, analytical approach to solving inverse kinematics for multi-section continuum robots, defined as robots composed of a continuously bendable backbone. The problem is decomposed into several simpler subproblems. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming endpoints for all sections of a multi-section trunk are known, this paper then details applying single-section inverse kinematics to each section of the multi-section trunk by compensating for the resulting changes in orientation. Finally, an approach which computes per-section endpoints given only a final-section endpoint provides a complete solution to the multi-section inverse kinematics problem. The results of implementing these algorithms in simulation and on a prototype continuum robot are presented and possible applications discussed.