Concentric Tube Robots: Design, Deployment, and Stability

Abstract

Concentric tube robots are needle-diameter robots consisting of multiple precurved, nested, superelastic tubes. They can be made to controllably elongate and bend by grasping the tubes at their bases and applying axial rotation and translation to each tube independently. This causes the tubes to bend and twist one another. This dissertation presents modeling, analysis, and design of these robots for medical uses as both robotic manipulators and steerable needles. The design of a robotic system for endoscopic endonasal surgery is presented, and a novel electrical technique for creating custom tube curvatures is described. The elastic stability of concentric tube robots is modeled and analyzed to provide design conditions for stability and a stability indicator that characterizes the relative stability of the robot based on its configuration. When used as a needle, the shaft of the robot must always remain along the path traced by the tip, as the robot elongates. Necessary and sufficient design and actuation conditions are presented that result in this behavior, and approximations of it are also considered. Lastly, a method is developed and experimentally characterized for mechanics-based force sensing using knowledge of the robot stiffness and position and/or orientation measurements along the shaft of the robot.