A fast torsionally compliant kinematic model of concentric-tube robots

Real-Time Shape Estimation for Concentric Tube Continuum Robots with a Single Force/Torque Sensor

Shape-sensing in real-time is a key requirement for the development of advanced algorithms for concentric tube continuum robots when safe interaction with the environment is important e.g., for path planning, advanced control, and human-machine interaction. We propose a real-time shape-estimation algorithm for concentric tube continuum robots based on the force-torque information measured at the tubes' basis. It extends a shape estimation algorithm for elastic rods based on discrete Kirchhoff rod theory. For simplicity and efficiency of calculation, we combine it with a model under piece-wise constant curvature assumption, in which we model a concentric tube continuum robot as a combination of segments of planar constant curvatures lying on different equilibrium planes. We evaluate our approach for a single and two combined additively manufactured tubes and achieve an estimation frequency of 333 Hz for two combined tubes with a mean deviation along the backbone of the tubes of 1.91-5.22 mm.

Mechatronic Design of a Two-Arm Concentric Tube Robot System for Rigid Neuroendoscopy

Open surgical approaches are still often employed in neurosurgery, despite the availability of neuroendoscopic approaches that reduce invasiveness. The challenge of maneuvering instruments at the tip of the endoscope makes neuroendoscopy demanding for the physician. The only way to aim tools passed through endoscope ports is to tilt the entire endoscope; but, tilting compresses brain tissue through which the endoscope passes and can damage it. Concentric tube robots can provide necessary dexterity without endoscope tilting, while passing through existing ports in the endoscope and carrying surgical tools in their inner lumen. In this paper we describe the mechatronic design of a new concentric tube robot that can deploy two concentric tube manipulators through a standard neuroendoscope. The robot uses a compact differential drive and features embedded motor control electronics and redundant position sensors for safety. In addition to the mechatronic design of this system, this paper contributes experimental validation in the context of colloid cyst removal, comparing our new robotic system to standard manual endoscopy in a brain phantom. The robotic approach essentially eliminated endoscope tilt during the procedure (17.09° for the manual approach vs. 1.16° for the robotic system). The robotic system also enables a single surgeon to perform the procedure - typically in a manual approach one surgeon aims the endoscope and another operates the tools delivered through its ports.

Steerable catheters for minimally invasive surgery: a review and future directions

The steerable catheter refers to the catheter that is manipulated by a mechanism which may be driven by operators or by actuators. The steerable catheter for minimally invasive surgery has rapidly become a rich and diverse area of research. Many important achievements in design, application and analysis of the steerable catheter have been made in the past decade. This paper aims to provide an overview of the state of arts of steerable catheters. Steerable catheters are classified into four main groups based on the actuation principle: (1) tendon driven catheters, (2) magnetic navigation catheters, (3) soft material driven catheters (shape memory effect catheters, steerable needles, concentric tubes, conducting polymer driven catheters and hydraulic pressure driven catheters), and (4) hybrid actuation catheters. The advantages and limitations of each of them are commented and discussed in this paper. The future directions of research are summarized.

Designing Stable Concentric Tube Robots Using Piecewise Straight Tubes

Concentric tube robots experience elastic instability when the potential energy stored in torsional twisting of the tubes is suddenly released. To date, ensuring stability for all possible rotational configurations has involved constraining the precurvatures and/or precurved lengths of the tubes comprising the robot, which results in limitations on robot curvature and workspace. This paper presents a design approach that eliminates the constraints on tube precurvature and length for stable rotation. The idea is to compose designs in which, at every point along the length of a robot, a single tube is precurved and the others are straight. The resulting designs do not experience any precurvature-induced torsional tube twisting and so are stable regardless of precurvature and length. This design concept can be usefully employed at the tip of a robot to provide a large stable range of tip orientation angles. A stability analysis is provided for designs composed of an arbitrary number of tubes and design rules are provided for tube pairs that can produce tip angles varying from zero to a desired maximum value. The method is validated experimentally for a tube pair comprised of three sections.

Optimizing Tube Precurvature to Enhance Elastic Stability of Concentric Tube Robots

Robotic instruments based on concentric tube technology are well suited to minimally invasive surgery since they are slender, can navigate inside small cavities and can reach around sensitive tissues by taking on shapes of varying curvature. Elastic instabilities can arise, however, when rotating one precurved tube inside another. In contrast to prior work that considered only tubes of piecewise constant precurvature, we allow precurvature to vary along the tube's arc length. Stability conditions for a planar tube pair are derived and used to formulate an optimal design problem. An analytic formulation of the optimal precurvature function is derived that achieves a desired tip orientation range while maximizing stability and respecting bending strain limits. This formulation also includes straight transmission segments at the proximal ends of the tubes. The result, confirmed by both numerical and physical experiment, enables designs with enhanced stability in comparison to designs of constant precurvature.

Hand-held transendoscopic robotic manipulators: A transurethral laser prostate surgery case study

Natural orifice endoscopic surgery can enable incisionless approaches, but a major challenge is the lack of small and dexterous instrumentation. Surgical robots have the potential to meet this need yet often disrupt the clinical workflow. Hand-held robots that combine thin manipulators and endoscopes have the potential to address this by integrating seamlessly into the clinical workflow and enhancing dexterity. As a case study illustrating the potential of this approach, we describe a hand-held robotic system that passes two concentric tube manipulators through a 5 mm port in a rigid endoscope for transurethral laser prostate surgery. This system is intended to catalyze the use of a clinically superior, yet rarely attempted, procedure for benign prostatic hyperplasia. This paper describes system design and experiments to evaluate the surgeon's functional workspace and accuracy using the robot. Phantom and cadaver experiments demonstrate successful completion of the target procedure via prostate lobe resection.

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

Concentric tube robots are catheter-sized continuum robots that are well suited for minimally invasive surgery inside confined body cavities. These robots are constructed from sets of pre-curved superelastic tubes and are capable of assuming complex 3D curves. The family of 3D curves that the robot can assume depends on the number, curvatures, lengths and stiffnesses of the tubes in its tube set. The robot design problem involves solving for a tube set that will produce the family of curves necessary to perform a surgical procedure. At a minimum, these curves must enable the robot to smoothly extend into the body and to manipulate tools over the desired surgical workspace while respecting anatomical constraints. This paper introduces an optimization framework that utilizes procedureor patient-specific image-based anatomical models along with surgical workspace requirements to generate robot tube set designs. The algorithm searches for designs that minimize robot length and curvature and for which all paths required for the procedure consist of stable robot configurations. Two mechanics-based kinematic models are used. Initial designs are sought using a model assuming torsional rigidity. These designs are then refined using a torsionally-compliant model. The approach is illustrated with clinically relevant examples from neurosurgery and intracardiac surgery.