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 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 how stable a given robot configuration is 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.

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.

Concentric tube robots are thin, tentacle-like devices that can move along curved paths and can potentially enable new, less invasive surgical procedures. Safe and effective operation of this type of robot requires that the robot's shaft avoid sensitive anatomical structures (e.g., critical vessels and organs) while the surgeon teleoperates the robot's tip. However, the robot's unintuitive kinematics makes it difficult for a human user to manually ensure obstacle avoidance along the entire tentacle-like shape of the robot's shaft. We present a motion planning approach for concentric tube robot teleoperation that enables the robot to interactively maneuver its tip to points selected by a user while automatically avoiding obstacles along its shaft. We achieve automatic collision avoidance by precomputing a roadmap of collision-free robot configurations based on a description of the anatomical obstacles, which are attainable via volumetric medical imaging. We also mitigate the effects of kinematic modeling error in reaching the goal positions by adjusting motions based on robot tip position sensing. We evaluate our motion planner on a teleoperated concentric tube robot and demonstrate its obstacle avoidance and accuracy in environments with tubular obstacles.

Benign prostatic hyperplasia is the most common symptomatic disease in men. A new transurethral surgical intervention is available that has been shown to reduce bleeding, catheterization time, and hospitalization time in comparison to traditional Transurethral Resection of the Prostate (TURP). However, this new procedure, Holmium Laser Enucleation of the Prostate (HoLEP), is so challenging to accomplish that only a small number of expert surgeons are able to offer it. Toward facilitating broader use of HoLEP, we propose a new hand-held robotic system for the purpose of making the surgery easier to perform. In current HoLEP, the only way to aim the laser and/or manipulate tissue is to move the entire endoscope, stretching a large quantity of tissue. In contrast, our new robotic approach provides the surgeon with two concentric tube manipulators that can aim the laser and manipulate tissue simultaneously. The manipulators are deployed through a 5 mm working channel in a 26 French (8.66 mm) endoscope clinically used for transurethral procedures. This paper describes the design of the robot and experiments illustrating its ability to perform the motions expected to be useful in HoLEP.