Concentric Tube Robots as Steerable Needles: Achieving Follow-the-Leader Deployment

Concentric tube robots can enable new clinical interventions if they are able to pass through soft tissue, deploy along desired paths through open cavities, or travel along winding lumens. These behaviors require the robot to deploy in such a way that the curved shape of its shaft remains unchanged as the tip progresses forward (i.e., "follow-the-leader" deployment). Follow-the-leader deployment is challenging for concentric tube robots due to elastic (and particularly torsional) coupling between the tubes that form the robot. However, as we show in this paper, follow-the-leader deployment is possible, provided that tube precurvatures and deployment sequences are appropriately selected. We begin by defining follow-the-leader deployment and providing conditions that must be satisfied for a concentric tube robot to achieve it. We then examine several useful special cases of follow-the-leader deployment, showing that both circular and helical precurvatures can be employed, and provide an experimental illustration of the helical case. We also explore approximate follow-the-leader behavior and provide a metric for the similarity of a general deployment to a follow-the-leader deployment. Finally, we consider access to the hippocampus in the brain to treat epilepsy, as a motivating clinical example for follow-the-leader deployment.