A geometrical approach to inverse kinematics for continuum manipulators

We present a new geometrical approach to solving inverse kinematics for continuous backbone (continuum) robot manipulators. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming end-points 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 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 physical continuum robot are presented and possible applications are discussed.