Designing snap-free concentric tube robots: A local bifurcation approach

In designing concentric tube robots, it is often desirable to use curvatures that are as high as possible. However, with high curvatures comes the potential for elastic instabilities. This can be addressed by motion planning or by designing the robot to preclude the possibility of instability. In this paper, we pursue the latter. Our primary contribution is to show that local bifurcation theory can be used to predict the existence of elastic instability anywhere in the workspace of robots with arbitrarily many tubes, with straight transmissions. We show how to use these results to design robots that are guaranteed to remain elastically stable at all times.