D. Caleb Rucker

A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots

Continuum robots, which are composed of multiple concentric, precurved elastic tubes, can provide dexterity at diameters equivalent to standard surgical needles. Recent mechanics-based models of these “active cannulas” are able to accurately describe the curve of the robot in free space, given the preformed tube curves and the linear and angular positions of the tube bases. However, in practical applications, where the active cannula must interact with its environment or apply controlled forces, a model that accounts for deformation under external loading is required. In this paper, we apply geometrically exact rod theory to produce a forward kinematic model that accurately describes large deflections due to a general collection of externally applied point and/or distributed wrench loads. This model accommodates arbitrarily many tubes, with each having a general preshaped curve. It also describes the independent torsional deformation of the individual tubes. Experimental results are provided for both point and distributed loads. Average tip error under load was 2.91 mm (1.5% - 3% of total robot length), which is similar to the accuracy of existing free-space models.

Equilibrium Conformations of Concentric-tube Continuum Robots

Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these “active cannulas” assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that previously reported models are special cases of our formulation, and then explore in detail the implications of torsional flexibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models1 it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments.

Continuum Robots for Medical Applications: A Survey

In this paper, we describe the state of the art in continuum robot manipulators and systems intended for application to interventional medicine. Inspired by biological trunks, tentacles, and snakes, continuum robot designs can traverse confined spaces, manipulate objects in complex environments, and conform to curvilinear paths in space. In addition, many designs offer inherent structural compliance and ease of miniaturization. After decades of pioneering research, a host of designs have now been investigated and have demonstrated capabilities beyond the scope of conventional rigid-link robots. Recently, we have seen increasing efforts aimed at leveraging these qualities to improve the frontiers of minimally invasive surgical interventions. Several concepts have now been commercialized, which are inspiring and enabling a current paradigm shift in surgical approaches toward flexible access routes, e.g., through natural orifices such as the nose. In this paper, we provide an overview of the current state of this field from the perspectives of both robotics science and medical applications. We discuss relevant research in design, modeling, control, and sensing for continuum manipulators, and we highlight how this work is being used to build robotic systems for specific surgical procedures. We provide perspective for the future by discussing current limitations, open questions, and challenges.

A Telerobotic System for Transnasal Surgery

Mechanics-based models of concentric tube continuum robots have recently achieved a level of sophistication that makes it possible to begin to apply these robots to a variety of real-world clinical scenarios. Endonasal skull base surgery is one such application, where their small diameter and tentacle-like dexterity are particularly advantageous. In this paper, we provide the medical motivation for an endonasal surgical robot featuring concentric tube manipulators, and describe our model-based design and teleoperation methods, as well as a complete system incorporating image guidance. Experimental demonstrations using a laparoscopic training task, a cadaver reachability study, and a phantom tumor resection experiment illustrate that both novice and expert users can effectively teleoperate the system, and that skull base surgeons can use the robot to achieve their objectives in a realistic surgical scenario.

A MRI-guided concentric tube continuum robot with piezoelectric actuation: A feasibility study

This paper presents a versatile magnetic resonance imaging (MRI) compatible concentric tube continuum robotic system. The system enables MR image-guided placement of a curved, steerable active cannula. It is suitable for a variety of clinical applications including image-guided neurosurgery and percutaneous interventions, along with procedures that involve accessing a desired image target, through a curved trajectory. This 6 degree-of-freedom (DOF) robotic device is piezoelectrically actuated to provide precision motion with joint-level precision of better than 0.03mm, and is fully MRI-compatible allowing simultaneous robotic motion and imaging with no image quality degradation. The MRI compatibility of the robot has been evaluated under 3 Tesla MRI using standard prostate imaging sequences, with an average signal to noise ratio loss of less than 2% during actuator motion. The accuracy of active cannula control was evaluated in benchtop trials using an external optical tracking system with RMS error in tip placement of 1.00mm. Preliminary phantom trials of three active cannula placements in the MRI scanner showed cannula trajectories that agree with our kinematic model, with a RMS tip placement error of 0.61 - 2.24 mm.

A bimanual teleoperated system for endonasal skull base surgery

We describe transnasal skull base surgery, including the current clinical procedure and the ways in which a robotic system has the potential to enhance the current standard of care. The available workspace is characterized by segmenting medical images and reconstructing the available 3D geometry. We then describe thin, “tentacle-like” robotic tools with shafts constructed from concentric tube robots, and an actuation unit designed to robotically control them in a teleoperated setting. Lastly, we discuss the results of a proof-of-concept study in a cadaveric specimen, illustrating the ability of the robot to access clinically relevant skull base targets.

Sliding Mode Control of Steerable Needles

Steerable needles can potentially increase the accuracy of needle-based diagnosis and therapy delivery, provided they can be adequately controlled based on medical image information. We propose a novel sliding mode control law that can be used to deliver the tip of a flexible asymmetric-tipped needle to a desired point, or to track a desired trajectory within tissue. The proposed control strategy requires no a priori knowledge of model parameters, has bounded input speeds, and requires little computational resources. We show that if the standard nonholonomic model for tip-steered needles holds, then the control law will converge to desired targets in a reachable workspace, within a tolerance that can be defined by the control parameters. Experimental results validate the control law for target points and trajectory following in phantom tissue and ex vivo liver. Experiments with targets that move during insertion illustrate robustness to disturbances caused by tissue deformation.

Deflection-based force sensing for continuum robots: A probabilistic approach

The inherent flexibility of continuum robots allows them to interact with objects in a safe and compliant way. This flexibility also makes it possible to use robot deflection to estimate external forces applied to the robot. This “intrinsic force sensing” concept is particularly useful for thin continuum robots where application constraints preclude the use of traditional force sensors. This paper describes an Extended Kalman Filter approach to estimate forces applied at the tip of a continuum robot using only uncertain pose measurements and a kinematic-static model of the robot with uncertainty.

A Mechanics-Based Nonrigid Registration Method for Liver Surgery Using Sparse Intraoperative Data

In open abdominal image-guided liver surgery, sparse measurements of the organ surface can be taken intraoperatively via a laser-range scanning device or a tracked stylus with relatively little impact on surgical workflow. We propose a novel nonrigid registration method which uses sparse surface data to reconstruct a mapping between the preoperative CT volume and the intraoperative patient space. The mapping is generated using a tissue mechanics model subject to boundary conditions consistent with surgical supportive packing during liver resection therapy. Our approach iteratively chooses parameters which define these boundary conditions such that the deformed tissue model best fits the intraoperative surface data. Using two liver phantoms, we gathered a total of five deformation datasets with conditions comparable to open surgery. The proposed nonrigid method achieved a mean target registration error (TRE) of 3.3 mm for targets dispersed throughout the phantom volume, using a limited region of surface data to drive the nonrigid registration algorithm, while rigid registration resulted in a mean TRE of 9.5 mm. In addition, we studied the effect of surface data extent, the inclusion of subsurface data, the trade-offs of using a nonlinear tissue model, robustness to rigid misalignments, and the feasibility in five clinical datasets.

Visual sensing of continuum robot shape using self-organizing maps

Shape control of continuum robots requires a means of sensing the the curved shape of the robot. Since continuum robots are deformable, they take on shapes that are general curves in space, which are not fully defined by actuator positions. Vision-based shape-estimation provides a promising avenue for shape-sensing. While this is often facilitated by fiducial markers, sometimes fiducials are not feasible due to either the robots application or its size. To address this, we present a robust and efficient stereo-vision-based, shape-sensing algorithm for continuum robots that does not rely on fiducials or assume orthogonal camera placement. The algorithm employs self-organizing maps to triangulate three-dimensional backbone curves. Experiments with an object with a known shape demonstrate an average accuracy of 1.53 mm on a 239 mm arc length curve.