Designing Stable Concentric Tube Robots Using Piecewise Straight Tubes

Concentric tube robots experience elastic instability when the potential energy stored in torsional twisting of the tubes is suddenly released. To date, ensuring stability for all possible rotational configurations has involved constraining the precurvatures and / or precurved lengths of the tubes comprising the robot, which results in limitations on robot curvature and workspace. This paper presents a design approach that eliminates the constraints on tube precurvature and length for stable rotation. The idea is to compose designs in which, at every point along the length of a robot, a single tube is precurved and the others are straight. The resulting designs do not experience any precurvature-induced torsional tube twisting and so are stable regardless of precurvature and length. This design concept can be usefully employed at the tip of a robot to provide a large stable range of tip orientation angles. A stability analysis is provided for designs composed of an arbitrary number of tubes and design rules are provided for tube pairs that can produce tip angles varying from zero to a desired maximum value. The method is validated experimentally for a tube pair comprised of three sections.