Design of Concentric Tube Robots Using Tube Patterning for Follow-The-Leader Deployment

Concentric tube robots (CTRs) have a great potential for use in medical applications. Coupled with a follow-the-leader (FTL) deployment, they allow navigation in constrained environments. However, they are subject to instabilities if one makes use of high curvatures for the tubes, long overlapping lengths of their curved sections, or long transmission lengths. One approach to improve their stability is to pattern the tubes of which they are composed by local removals of material along their lengths. Applying patterns on tubes was proved to be of interest for given deployed lengths of a CTR. In this article, we present a method to enlarge the application field of CTRs that deploy in a follow-the-leader manner, by integrating tube patterning in the design process, with a stability criterion. Our method allows the designer to determine a custom pattern geometry to theoretically ensure the stability of CTRs made of any number of constant curvature tubes, for a complete FTL deployment sequence, and while respecting a desired shape during deployment.