Motion Planning for Concentric Tube Robots Using Mechanics-based Models

Continuum Robots for Medical Interventions

Continuum robots are not constructed with discrete joints but, instead, change shape and position their tip by flexing along their entire length. Their narrow curvilinear shape makes them well suited to passing through body lumens, natural orifices, or small surgical incisions to perform minimally invasive procedures. Modeling and controlling these robots are, however, substantially more complex than traditional robots comprised of rigid links connected by discrete joints. Furthermore, there are many approaches to achieving robot flexure. Each presents its own design and modeling challenges, and to date, each has been pursued largely independently of the others. This article attempts to provide a unified summary of the state of the art of continuum robot architectures with respect to design for specific clinical applications. It also describes a unifying framework for modeling and controlling these systems while additionally explaining the elements unique to each architecture. The major research accomplishments are described for each topic and directions for the future progress needed to achieve widespread clinical use are identified.

Learning the Complete Shape of Concentric Tube Robots

Concentric tube robots, composed of nested pre-curved tubes, have the potential to perform minimally invasive surgery at difficult-to-reach sites in the human body. In order to plan motions that safely perform surgeries in constrained spaces that require avoiding sensitive structures, the ability to accurately estimate the entire shape of the robot is needed. Many state-of-the-art physics-based shape models are unable to account for complex physical phenomena and subsequently are less accurate than is required for safe surgery. In this work, we present a learned model that can estimate the entire shape of a concentric tube robot. The learned model is based on a deep neural network that is trained using a mixture of simulated and physical data. We evaluate multiple network architectures and demonstrate the model's ability to compute the full shape of a concentric tube robot with high accuracy.

Design, implementation, and control of a deformable manipulator robot based on a compliant spine

This article presents the conception, the numerical modeling, and the control of a dexterous, deformable manipulator bio-inspired by the skeletal spine found in vertebrate animals. Through the implementation of this new manipulator, we show a methodology based on numerical models and simulations, that goes from design to control of continuum and soft robots. The manipulator is modeled using a finite element method (FEM), using a set of beam elements that reproduce the lattice structure of the robot. The model is computed and inverted in real-time using optimization methods. A closed-loop control strategy is implemented to account for the disparities between the model and the robot. This control strategy allows for accurate positioning, not only of the tip of the manipulator, but also the positioning of selected middle points along its backbone. In a scenario where the robot is piloted by a human operator, the command of the robot is enhanced by a haptic loop that renders the boundaries of its task space as well as the contact with its environment. The experimental validation of the model and control strategies is also presented in the form of an inspection task use case.

Planning High-Quality Motions for Concentric Tube Robots in Point Clouds via Parallel Sampling and Optimization

We present a method that plans motions for a concentric tube robot to automatically reach surgical targets inside the body while avoiding obstacles, where the patient's anatomy is represented by point clouds. Point clouds can be generated intra-operatively via endoscopic instruments, enabling the system to update obstacle representations over time as the patient anatomy changes during surgery. Our new motion planning method uses a combination of sampling-based motion planning methods and local optimization to efficiently handle point cloud data and quickly compute high quality plans. The local optimization step uses an interior point optimization method, ensuring that the computed plan is feasible and avoids obstacles at every iteration. This enables the motion planner to run in an anytime fashion, i.e., the method can be stopped at any time and the best solution found up until that point is returned. We demonstrate the method's efficacy in three anatomical scenarios, including two generated from endoscopic videos of real patient anatomy.

Surgeon Design Interface for Patient-Specific Concentric Tube Robots

Concentric tube robots have potential for use in a wide variety of surgical procedures due to their small size, dexterity, and ability to move in highly curved paths. Unlike most existing clinical robots, the design of these robots can be developed and manufactured on a patient- and procedure-specific basis. The design of concentric tube robots typically requires significant computation and optimization, and it remains unclear how the surgeon should be involved. We propose to use a virtual reality-based design environment for surgeons to easily and intuitively visualize and design a set of concentric tube robots for a specific patient and procedure. In this paper, we describe a novel patient-specific design process in the context of the virtual reality interface. We also show a resulting concentric tube robot design, created by a pediatric urologist to access a kidney stone in a pediatric patient.

Elastic Stability of Concentric Tube Robots: A Stability Measure and Design Test

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.

Elastic Stability of Concentric Tube Robots Subject to External Loads

Concentric tube robots, which are comprised of precurved elastic tubes that are concentrically arranged, are being developed for many medical interventions. The shape of the robot is determined by the rotation and translation of the tubes relative to each other, and also by any external forces applied by the environment. As the tubes rotate and translate relative to each other, elastic potential energy caused by tube bending and twisting can accumulate; if a configuration is not locally elastically stable, then a dangerous snapping motion may occur as energy is suddenly released. External loads on the robot also influence elastic stability. In this paper, we provide a second-order sufficient condition, and also a separate necessary condition, for elastic stability. Using methods of optimal control theory, we show that these conditions apply to general concentric tube robot designs subject to arbitrary conservative external loads. They can be used to assess the stability of candidate robot configurations. Our results are validated via comparison with other known stability criteria, and their utility is demonstrated by an application to stable path planning.

Optimizing Design Parameters for Sets of Concentric Tube Robots using Sampling-based Motion Planning

Concentric tube robots are tentacle-like medical robots that can bend around anatomical obstacles to access hard-to-reach clinical targets. The component tubes of these robots can be swapped prior to performing a task in order to customize the robot's behavior and reachable workspace. Optimizing a robot's design by appropriately selecting tube parameters can improve the robot's effectiveness on a procedure-and patient-specific basis. In this paper, we present an algorithm that generates sets of concentric tube robot designs that can collectively maximize the reachable percentage of a given goal region in the human body. Our algorithm combines a search in the design space of a concentric tube robot using a global optimization method with a sampling-based motion planner in the robot's configuration space in order to find sets of designs that enable motions to goal regions while avoiding contact with anatomical obstacles. We demonstrate the effectiveness of our algorithm in a simulated scenario based on lung anatomy.

A Motion Planning Approach to Automatic Obstacle Avoidance during Concentric Tube Robot Teleoperation

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.

Concentric Tube Robots as Steerable Needles: Achieving Follow-the-Leader Deployment

Concentric tube robots can enable new clinical interventions if they are able to pass through soft tissue, deploy along desired paths through open cavities, or travel along winding lumens. These behaviors require the robot to deploy in such a way that the curved shape of its shaft remains unchanged as the tip progresses forward (i.e., "follow-the-leader" deployment). Follow-the-leader deployment is challenging for concentric tube robots due to elastic (and particularly torsional) coupling between the tubes that form the robot. However, as we show in this paper, follow-the-leader deployment is possible, provided that tube precurvatures and deployment sequences are appropriately selected. We begin by defining follow-the-leader deployment and providing conditions that must be satisfied for a concentric tube robot to achieve it. We then examine several useful special cases of follow-the-leader deployment, showing that both circular and helical precurvatures can be employed, and provide an experimental illustration of the helical case. We also explore approximate follow-the-leader behavior and provide a metric for the similarity of a general deployment to a follow-the-leader deployment. Finally, we consider access to the hippocampus in the brain to treat epilepsy, as a motivating clinical example for follow-the-leader deployment.

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.

Interactive-rate Motion Planning for Concentric Tube Robots

Concentric tube robots may enable new, safer minimally invasive surgical procedures by moving along curved paths to reach difficult-to-reach sites in a patient's anatomy. Operating these devices is challenging due to their complex, unintuitive kinematics and the need to avoid sensitive structures in the anatomy. In this paper, we present a motion planning method that computes collision-free motion plans for concentric tube robots at interactive rates. Our method's high speed enables a user to continuously and freely move the robot's tip while the motion planner ensures that the robot's shaft does not collide with any anatomical obstacles. Our approach uses a highly accurate mechanical model of tube interactions, which is important since small movements of the tip position may require large changes in the shape of the device's shaft. Our motion planner achieves its high speed and accuracy by combining offline precomputation of a collision-free roadmap with online position control. We demonstrate our interactive planner in a simulated neurosurgical scenario where a user guides the robot's tip through the environment while the robot automatically avoids collisions with the anatomical obstacles.

Continuous Shape Estimation of Continuum Robots Using X-ray Images

We present a new method for continuously and accurately estimating the shape of a continuum robot during a medical procedure using a small number of X-ray projection images (e.g., radiographs or fluoroscopy images). Continuum robots have curvilinear structure, enabling them to maneuver through constrained spaces by bending around obstacles. Accurately estimating the robot's shape continuously over time is crucial for the success of procedures that require avoidance of anatomical obstacles and sensitive tissues. Online shape estimation of a continuum robot is complicated by uncertainty in its kinematic model, movement of the robot during the procedure, noise in X-ray images, and the clinical need to minimize the number of X-ray images acquired. Our new method integrates kinematics models of the robot with data extracted from an optimally selected set of X-ray projection images. Our method represents the shape of the continuum robot over time as a deformable surface which can be described as a linear combination of time and space basis functions. We take advantage of probabilistic priors and numeric optimization to select optimal camera configurations, thus minimizing the expected shape estimation error. We evaluate our method using simulated concentric tube robot procedures and demonstrate that obtaining between 3 and 10 images from viewpoints selected by our method enables online shape estimation with errors significantly lower than using the kinematic model alone or using randomly spaced viewpoints.

The Importance of Continuous and Discrete Elements in Continuum Robots

In this paper, we examine key issues underlying the design and operation of robots featuring continuous body (“continuum”) elements. We contrast continuum and continuum-like robots created to date with their counterparts in the natural world. It is observed that natural continuum locomotors or manipulators almost invariably rely on hard or discrete elements (in their structure or operation) in their interactions with their environment. We suggest innovations in continuum robot design and operation motivated by this observation, supported by experiments using the “Tendril” continuum robot. The results suggest new ways in which continuum robot operations could be significantly enhanced. In particular, the exploitation of “hard” and “discrete” environmental features can greatly enhance stability in continuum robot operations, compensating for inherent backbone compliance. Additionally, the incorporation of discrete behaviours (sweeping and striking with the backbone) can both compensate for imprecision in continuum robot control and enable new impulsive manipulation modes. We discuss the implications for the creation and potential application of novel hybrid continuum and discrete robots.