Can concentric tube robots follow the leader?

Abstract

Ahstract-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-Ieader" 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-Ieader manner is not possible except in very special cases of tube precurvatures, combined with specific deployment sequences. We also show that follow-the-Ieader 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-Ieader 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-Ieader behavior, proposing a metric to quantify the similarity of a general deployment to a follow-the-Ieader deployment.

Sliding Mode Control of Steerable Needles

“…Concentric tube needle steering does not rely on the surrounding tissue medium to achieve a curved path and, because of this, can be used in both free space [6], [7] and tissue-embedded applications [12]. However, it requires a priori design of the component tubes [13], and so does not offer as much variability in the final trajectory within tissue. Tip steering has the advantage of typically traveling along a “follow the leader” trajectory, where the shaft follows the path of the tip, and steerability is largely unaffected by insertion depth.…”

Concentric Tube Robot Design and Optimization Based on Task and Anatomical Constraints

“…This result can be generalized if the robot design enables the trivial solution of (5) to be applied over m subintervals of s c ∈[0, L c ], each of which can be taken as constant curvature yielding an overall curve of piecewise constant curvature, $$u_{r}false(s_{r}false)=u_{c}false(s_{c}false)=\{\begin{array}{ll}{c}_1,& \forall s_c\in [0,s_{c1}]\\ c_2,& \forall s_c\in (s_{c1},s_{c2}]\\ c_3,& \forall s_c\in (s_{c2},s_{c3}]\\ \dots & \\ c_n,& \forall s_c\in (s_{c,m-1},L_c]\end{array}$$As shown below, applying these geometric results for follow-the-leader extension on concentric tube robots is straightforward. Follow-the-leader conditions are also considered in [24]. …”

“…This has been considered in detail for arcs in, e.g., [8] and initial results for helices appear in [24]. Without loss of generality and to further reduce the number of design parameters, only arcs are considered in the remainder of this paper.…”

Future robotic platforms in urologic surgery

“…Potential roles for steerable needles in Urologic Surgery include biopsy and ablation delivery to previously unreachable or inaccessible areas combined with precise control and non-linear path control. [36-38]…”