Can concentric tube robots follow the leader?

Continuum robots have opened a broad array of applications to robotics in general, and the concentric tube continuum robots promise many benefits in medicine. Many people intuitively assume that these robots can deploy along a curved trajectory, in such a way that the curved shape of the robot's shaft remains unchanged as the tip progresses forward (i.e. “follow-the-leader” deployment). This capability would be useful in advancing along winding lumens (e.g. blood vessels, lung bronchi, etc.), as well as when the device is embedded in soft tissue and used as a steerable needle. However, in this paper we show that deploying in a follow-the-leader manner is not possible except in very special cases of tube precurvatures, combined with specific deployment sequences. We also show that follow-the-leader deployment is not possible even for many of the “simple” cases where one might intuitively expect it to be. Fortunately, useful special cases of perfect follow-the-leader behavior do exist, and we provide examples and describe the conditions that must be satisfied for this to be possible. We also study approximate follow-the-leader behavior, proposing a metric to quantify the similarity of a general deployment to a follow-the-leader deployment.