Elastic Stability of Concentric Tube Robots: A Stability Measure and Design Test

Concentric tube robots are needle-sized manipulators which have been investigated for use in minimally invasive surgeries. It was noted early in the development of these devices that elastic energy storage can lead to a rapid snapping motion for designs with moderate to high tube curvatures. Substantial progress has recently been made in the concentric tube robot community in designing snap-free robots, planning stable paths, and characterizing conditions that result in snapping for specific classes of concentric tube robots. However, a general measure for determining the stability of a given robot configuration has yet to be proposed. In this paper, we use bifurcation and elastic stability theory to provide such a measure, as well as to produce a test for determining whether a given design is snap-free (i.e., whether snapping can occur anywhere in the unloaded robot's workspace). These results are useful in designing, planning motions for, and controlling concentric tube robots with high curvatures.