Shape sensing of medical continuum robots is important both for closed-loop control as well as for enabling the clinician to visualize the robot inside the body. There is a need for inexpensive, but accurate shape sensing technologies. This paper proposes the use of magnetic ball chains as a means of generating shape-specific magnetic fields that can be detected by an external array of Hall effect sensors. Such a ball chain, encased in a flexible polymer sleeve, could be inserted inside the lumen of any continuum robot to provide real-time shape feedback. The sleeve could be removed, as needed, during the procedure to enable use of the entire lumen. To investigate this approach, a shape-sensing model for a steerable catheter tip is derived and an observability and sensitivity analysis are presented. Experiments show maximum estimation errors of 7.1% and mean of 2.9% of the tip position with respect to total length.

This paper introduces a novel class of hyperredun-dant robots comprised of chains of permanently magnetized spheres enclosed in a cylindrical polymer skin. With their shape controlled using an externally-applied magnetic field, the spherical joints of these robots enable them to bend to very small radii of curvature. These robots can be used as steerable tips for endoluminal instruments. A kinematic model is derived based on minimizing magnetic and elastic potential energy. Simulation is used to demonstrate the enhanced steerability of these robots in comparison to magnetic soft continuum robots designed using either distributed or lumped magnetic material. Experiments are included to validate the model and to demonstrate the steering capability of ball chain robots in bifurcating channels.

A hybrid continuum robot design is introduced that combines a proximal tendon-actuated section with a distal telescoping section comprised of permanent-magnet spheres actuated using an external magnet. While, individually, each section can approach a point in its workspace from one or at most several orientations, the two-section combination possesses a dexterous workspace. The paper describes kinematic modeling of the hybrid design and provides a description of the dexterous workspace. We present experimental validation which shows that a simplified kinematic model produces tip position mean and maximum errors of 3% and 7% of total robot length, respectively.

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.

This paper presents a novel continuum robot sheath for use in single-port minimally invasive procedures such as neuroendoscopy in which the sheath is designed to deliver multiple robotic arms. Actuation of the sheath is achieved by using precurved superelastic tubes lining the working channels used for arm delivery. These tubes perform a similar role to push/pull tendons, but can accomplish shape change of the sheath via rotation. A kinematic model using Cosserat rod theory is derived which is based on modeling the system as a set of eccentrically aligned precurved tubes constrained along their length by an elastic backbone. The specific case of a two-arm sheath is considered in detail. Simulation and experiments are used to investigate the validate the concept and model.

This paper presents a novel continuum robot sheath for use in single-port minimally invasive procedures such as neuroendoscopy in which the sheath is designed to deliver multiple robotic arms. Articulation of the sheath is achieved by using precurved superelastic tubes lining the working channels used for arm delivery. These tubes perform a similar role to push/pull tendons, but can accomplish shape change of the sheath via rotation as well as translation. A kinematic model using Cosserat rod theory is derived which is based on modeling the system as a set of eccentrically aligned precurved tubes constrained along their length by an elastic backbone. The specific case of a two-arm sheath is considered in detail and its relationship to a concentric tube balanced pair is described. Simulation and experiment are used to investigate the concept, map its workspace and to evaluate the kinematic model.

The shape of a concentric tube robot depends not only on the relative rotations and translations of its constituent tubes, but also on the history of relative tube displacements. Existing mechanics-based models neglect all history-dependent phenomena with the result that when calibrated on experimental data collected over a robot's workspace, the maximum tip position error can exceed 8 mm for a 200-mm-long robot. In this paper, we develop a model that computes the bounding kinematic solutions in which Coulomb friction is acting either to maximize or minimize the relative twisting between each pair of contacting tubes. The path histories associated with these limiting cases correspond to first performing all tube translations and then performing relative tube rotations of sufficient angle so that the maximum Coulomb friction force is obtained along the interface of each contacting tube pair. The robot tip configurations produced by these path histories are shown experimentally to bound position error with respect to the estimated frictionless model compared to path histories comprised of translation or mixed translation and rotation. Intertube friction forces and torques are computed as proportional to the intertube contact forces. To compute these contact forces, the standard zero-clearance assumption that constrains the concentrically combined tubes to possess the same centerline is relaxed. The effects of clearance and friction are explored through numerical and physical experiments and it is shown that friction can explain much of the prediction error observed in existing models. This model is not intended for real-time control, but rather for path planning-to provide error bounds and to inform how the ordering of tube rotations and translations can be used to reduce the effect of friction.

Mechanics-based formulations of concentric tube robots incorporate tube bending and twisting, but do not include other phenomena that could model observed hysteretic behavior in which tube configurations reached by rotating tubes in different directions achieve different tip positions. As a step toward incorporating hysteretic tube-on-tube friction, this paper derives a model that enables computation of the contact forces applied by the tubes on each other along their lengths. To do so, it is necessary to include the small, but finite clearances between the tubes. Recasting the constrained energy minimization problem as its dual problem enables numerically efficient solution for the clearance-constrained centerlines of each tube as well as their contact forces. These variables are investigated through numerical examples and it is shown that, even without considering friction, the assumption of zero clearance can introduce tip position errors of several millimeters for clinically relevant robot lengths.

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.

Concentric tube robots comprise telescopic precurved elastic tubes. The robot's tip and shape are controlled via relative tube motions, i.e. tube rotations and translations. Non-linear interactions between the tubes, e.g. friction and torsion, as well as uncertainty in the physical properties of the tubes themselves, e.g. the Young's modulus, curvature, or stiffness, hinder accurate kinematic modelling. In this paper, we present a machine-learning-based methodology for kinematic modelling of concentric tube robots and in situ model adaptation. Our approach is based on Locally Weighted Projection Regression (LWPR). The model comprises an ensemble of linear models, each of which locally approximates the original complex kinematic relation. LWPR can accommodate for model deviations by adjusting the respective local models at run-time, resulting in an adaptive kinematics framework. We evaluated our approach on data gathered from a three-tube robot, and report high accuracy across the robot's configuration space.

Although existing mechanics-based models of concentric tube robots have been experimentally demonstrated to approximate the actual kinematics, determining accurate estimates of model parameters remains difficult due to the complex relationship between the parameters and available measurements. Further, because the mechanics-based models neglect some phenomena like friction, nonlinear elasticity, and cross section deformation, it is also not clear if model error is due to model simplification or to parameter estimation errors. The parameters of the superelastic materials used in these robots can be slowly time-varying, necessitating periodic re-estimation. This paper proposes a method for estimating the mechanics-based model parameters using an extended Kalman filter as a step toward on-line parameter estimation. Our methodology is validated through both simulation and experiments.

MRI-based navigation and propulsion of millirobots is a new and promising approach for minimally invasive therapies. The strong central field inside the scanner, however, precludes torque-based control. Consequently, prior propulsion techniques have been limited to gradient-based pulling through fluid-filled body lumens. This paper introduces a technique for generating large impulsive forces that can be used to penetrate tissue. The approach is based on navigating multiple robots to a desired location and using self-assembly to trigger the conversion of magnetic potential energy into sufficient kinetic energy to achieve penetration. The approach is illustrated through analytical modeling and experiments in a clinical MRI scanner.

The concept of navigating groups of magnetically propelled particles through the fluid-filled passageways of the body provides the potential to perform highly localized diagnostic and therapeutic procedures. The use of MRI scanners to both navigate and propel millimeter-scale robots has received recent attention. MRI-based motion planning and control laws have been proposed that can achieve independent position control of multiple robots despite the system being underactuated, i.e., the same magnetic gradients are experienced by all the robots. To date, however, these analyses have neglected the magnetic interaction forces and torques between these robots. Thus, the question of whether or not the relatively weak gradients can stabilize the particles as they approach each other has remained open. This paper investigates this question by analyzing interaction forces and torques experienced inside an MRI scanner. It is shown that interaction torques can be neglected in the presence of the strong central field of the scanner. Using the reduced force-based model, a lower bound on separation distance is derived and it is shown that this bound could be achieved if the system was fully actuated. Considering underactuation, simulation demonstrates that Model Predictive Control can stabilize pairs of robots at separation distances 2.5-3 times the lower bound on separation distance.

Kinematic models of concentric tube robots have matured from considering only tube bending to considering tube twisting as well as external loading. While these models have been demonstrated to approximate actual behavior, modeling error can be significant for medical applications that often call for positioning accuracy of 1-2mm. As an alternative to moving to more complex models, this paper proposes using sensing to adaptively update model parameters during robot operation. Advantages of this method are that the model is constantly tuning itself to provide high accuracy in the region of the workspace where it is currently operating. It also adapts automatically to changes in robot shape and compliance associated with the insertion and removal of tools through its lumen. As an initial exploration of this approach, a recursive on-line estimator is proposed and evaluated experimentally.

This paper presents a three dimensional ultrasound (3DUS)-based visual servoing technique for intraoperative tracking of the motion of both surgical instruments and tissue targets. In the proposed approach, visual servoing techniques are used to control the position of a virtual ultrasound probe so as to keep a target centered within the virtual probe's field-of-view. Multiple virtual probes can be servoed in parallel to provide simultaneous tracking of instruments and tissue. The technique is developed in the context of robotic beating-heart intracardiac surgery in which the goal of tracking is to both provide guidance to the operator as well as to provide the means to automate the surgical procedure. To deal with the low signal-to-noise ratio (SNR) of the 3DUS volumes, an intensity-based method is proposed that requires no primitive extraction or image segmentation since it directly utilizes the image intensity information as a visual feature. This approach is computationally efficient and can be applied to a wide range of tissue types and medical instruments. This paper presents the first validation of these techniques through offline robot and tissue tracking using actual in vivo cardiac volume sequences from a robotic beating-heart surgery.

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.

Actuators that are powered, imaged, and controlled by magnetic resonance (MR) scanners could inexpensively provide wireless control of MR-guided robots. Similar to traditional electric motors, the MR scanner acts as the stator and generates propulsive torques on an actuator rotor containing one or more ferrous particles. Generating maximum motor torque while avoiding instabilities and slippage requires closed-loop control of the electromagnetic field gradients, i.e., commutation. Accurately estimating the position and velocity of the rotor is essential for high-speed control, which is a challenge due to the low refresh rate and high latency associated with MR signal acquisition. This paper proposes and demonstrates a method for closed-loop commutation based on interleaving pulse sequences for rotor imaging and rotor propulsion. This approach is shown to increase motor torque and velocity, eliminate rotor slip, and enable regulation of rotor angle. Experiments with a closed-loop MR imaging actuator produced a maximum force of 9.4 N.

This paper introduces robotic implants as a novel class of medical robots in the context of treating esophageal atresia. The robotic implant is designed to apply traction forces to the two disconnected esophageal segments to induce sufficient growth so that the two ends can be joined together to form a functioning esophagus. In contrast to the current manual method of externally applying traction forces, the implant offers the potential to avoid prolonged patient sedation and to substantially reduce the number of X-rays required. A prototype design is presented along with evaluation experiments that demonstrate its capabilities to apply traction forces to ex vivo esophageal tissues.

Robot control requires the rapid computation of robot shape, which for continuum robots typically involves solving complex mechanics-based models. Furthermore, shape computation based on kinematic input variables can be inaccurate due to parameter errors and model simplification. An alternate approach is to compute the shape in real-time from a set of sensors positioned along the length of the robot that provide measurements of local curvature, e.g., optical fiber Bragg gratings. This paper proposes a general framework for selecting the number and placement of such sensors with respect to arclength so as to compute the forward kinematic solution accurately and quickly. The approach is based on defining numerically-efficient shape reconstruction models parameterized by sensor number and location. Optimization techniques are used to find the sensor locations that minimize shape and tip error between a reconstruction model and a mechanics-based model. As a specific example, several reconstruction models are proposed and compared for concentric tube robots. These results indicate that the choice of reconstruction model as well as sensor placement can have a substantial effect on robot shape estimation.

Fiber Bragg gratings (FBG)-based optical sensors are a promising real-time technique for sensing the 3D curvature of continuum robots. Existing implementations, however, have relied on embedding optical fibers in small-diameter metal wires or needles. This paper proposes polymer tubes as an alternative substrate for the fibers. This approach separates the sensors from the robot structural components while using a minimal amount of the robot's tool lumen and providing the potential of inexpensive fabrication. Since the fibers are stiffer than the polymer substrate, however, design challenges arise in modeling strain transfer between the fibers and the tube substrate. To investigate the potential of this approach, a strain transfer model is derived and validated through simulation and experiment.

Actuators that are powered, imaged, and controlled by Magnetic Resonance (MR) scanners offer the potential of inexpensively providing wireless control of MR-guided robots. Similar to traditional electric motors, the MR scanner acts as the stator and generates propulsive torques on an actuator rotor containing one or more ferrous particles. The MR scanner can control three orthogonal gradient fields. Prior work demonstrated control of a single actuator rotor. This paper proposes and demonstrates independent, simultaneous control of n rotors. The controller relies on inhomogeneity between rotors, such as ensuring no rotor axes are parallel. This paper provides easily-implemented velocity and position controllers with global asymptotic convergence, and optimization techniques for implementation. Code for simulations and control laws is available online.

Control of multiple magnetic particles inside the human body may have many potential applications, such as drug delivery in places where conventional procedures cannot reach. A natural candidate for powering as well as tracking these magnetic particles is the MRI scanner. Although it offers the means to control the particles, it also poses difficulties: the magnetic field is applied uniformly to the group, thus making the independent control of each particle a challenging issue, while the actuation and the tracking are interleaved which can result to delays in actuation and measurement. The closed-loop control of a group of millimeter-scale particles, immersed in fluid, driven by the MRI scanner is studied in this paper. More specifically, this problem is presented in a unified manner, handling such issues as delays, constraints, as well as disturbances, and results in a robustly stable controller. We also propose a condition that effectively answers when the system should be in tracking mode versus actuation mode. In addition to theoretical results, the capability of the proposed controller is illustrated through simulation results.

Minimally invasive surgery can involve navigating inside small cavities or reaching around sensitive tissues. Robotic instruments based on concentric tube technology are well suited to these tasks since they are slender and can be designed to take on shapes of high and varying curvature along their length. One limitation of these robots, however, is that elastic instabilities can arise when rotating one pre-curved tube inside another. While prior work has considered tubes of piecewise-constant pre-curvature, this paper proposes varying tube pre-curvature as a function of arc length as a means to enhance stability. Stability conditions for a planar tube pair are derived and used to define an optimal design problem. This framework enables solving for pre-curvature functions that achieve a desired tip orientation range while maximizing stability and respecting bending strain limits. Analytical and numerical examples of the approach are provided.

A novel robotic sensor is proposed to measure both the contact angle and the force acting between the tip of a surgical robot and soft tissue. The sensor is manufactured using a planar lithography process that generates microchannels that are subsequently filled with a conductive liquid. The planar geometry is then molded onto a hemispherical plastic scaffolding in a geometric configuration enabling estimation of the contact angle (angle between robot tip tangent and tissue surface normal) by the rotation of the sensor around its roll axis. Contact force can also be estimated by monitoring the changes in resistance in each microchannel. Bench top experimental results indicate that, on average, the sensor can estimate the angle of contact to within ±2° and the contact force to within ±5.3 g.

Actuators that are powered, imaged and controlled by Magnetic Resonance (MR) scanners offer the potential of inexpensively providing wireless control of MR-guided robots. Similar to traditional electric motors, the MR scanner acts as the stator and generates propulsive torques on an actuator rotor containing one or more ferrous particles. To generate maximum motor torque while avoiding instabilities and slippage, closed-loop control of the electromagnetic field gradients, i.e., commutation, is required. This paper proposes and demonstrates a method for commutation based on interleaving pulse sequences for rotor tracking and rotor propulsion. Fast rotor tracking is achieved by a new technique utilizing radio-frequency (RF) selective excitation of a properly located fiducial marker by the ferrous particle of the rotor. Optimal marker location is derived and demonstrated to provide accurate estimates of rotor angle. In addition, closed-loop commutation control is shown to increase motor torque and also to enable regulation of rotor angle.

Concentric tube robots are continuum robots that can navigate natural pathways to reach locations deep inside the human body. Their operation is based on rotating and telescopically actuating concentric tubes to achieve robot tip pose control. During tube manipulation, the elastic energy stored in the robot structure may give rise to unstable robot configurations and loss of control. This can occur, in particular, for highly curved and elongated tubes that are required for certain surgical interventions. This paper presents a path planning methodology that allows the utilization of such generally unstable concentric tube robots by ensuring that they operate in their stable configuration regions.

A novel robotic tool is proposed to enable the surgical removal of tissue from inside the beating heart. The tool is manufactured using a unique metal MEMS process that provides the means to fabricate fully assembled devices that incorporate micron-scale features in a millimeter scale tool. The tool is integrated with a steerable curved concentric tube robot that can enter the heart through the vasculature. Incorporating both irrigation and aspiration, the tissue removal system is capable of extracting substantial amounts of tissue under teleoperated control by first morselizing it and then transporting the debris out of the heart through the lumen of the robot. Tool design and robotic integration are described and ex vivo experimental results are presented.

Three dimensional ultrasound is a promising imaging modality for minimally invasive robotic surgery. As the robots are typically metallic, they interact strongly with the sound waves in ways that are not modeled by the ultrasound system's signal processing algorithms. Consequently, they produce substantial imaging artifacts that can make image guidance difficult, even for experienced surgeons. This paper introduces a new approach for detecting curved continuum robots in 3D ultrasound images. The proposed approach combines geodesic active contours with a speed function that is based on enhancing the "tubularity" of the continuum robot. In particular, it takes advantage of the known robot diameter along its length. It also takes advantage of the fact that the robot surface facing the ultrasound probe provides the most accurate image. This method, termed Tubular Enhanced Geodesic Active Contours (TEGAC), is demonstrated through ex vivo intracardiac experiments to offer superior performance compared to conventional active contours.

There are many examples of minimally invasive surgery in which tethered robots are incapable of accurately reaching target locations deep inside the body either because they are too large and result in tissue damage or because the tortuosity of the path leads to loss of tip control. In these situations, small untethered magnetically-powered robots may hold the potential to act as delivery vehicles for therapeutic agents. While MRI scanners provide a means to power, control and image such robots as they move throughout the body, a substantial challenge arises if the clinical application requires more than one such robot. The resulting system is underactuated and thus its controllability is in question. This paper presents a simple motion planning algorithm for two magnetic capsules and demonstrates through simulation and experiment that nonlinear fluid damping can be exploited to independently control the positions of the capsules.

Surgical robots are gaining favor in part due to their capacity to reach remote locations within the body. Continuum robots are especially well suited for accessing deep spaces such as cerebral ventricles within the brain. Due to the entry point constraints and complicated structure, current techniques do not allow surgeons to access the full volume of the ventricles. The ability to access the ventricles with a dexterous robot would have significant clinical implications. This paper presents a concentric tube manipulator mated to a robotically controlled flexible endoscope. The device adds three degrees of freedom to the standard neuroendoscope and roboticizes the entire package allowing the operator to conveniently manipulate the device. To demonstrate the improved functionality, we use an in-silica virtual model as well as an ex-vivo anatomic model of a patient with a treatable form of hydrocephalus. In these experiments we demonstrate that the augmented and roboticized endoscope can efficiently reach critical regions that a manual scope cannot.

A family of passive echogenic markers is presented by which the position and orientation of a surgical instrument can be determined in a 3-D ultrasound volume, using simple image processing. Markers are attached near the distal end of the instrument so that they appear in the ultrasound volume along with the instrument tip. They are detected and measured within the ultrasound image, thus requiring no external tracking device. This approach facilitates imaging instruments and tissue simultaneously in ultrasound-guided interventions. Marker-based estimates of instrument pose can be used in augmented reality displays or for image-based servoing. Design principles for marker shapes are presented that ensure imaging system and measurement uniqueness constraints are met. An error analysis is included that can be used to guide marker design and which also establishes a lower bound on measurement uncertainty. Finally, examples of marker measurement and tracking algorithms are presented along with experimental validation of the concepts.

We propose a novel systematic approach to optimizing the design of concentric tube robots for neurosurgical procedures. These procedures require that the robot approach specified target sites while navigating and operating within an anatomically constrained work space. The availability of preoperative imaging makes our approach particularly suited for neurosurgery, and we illustrate the method with the example of endoscopic choroid plexus ablation. A novel parameterization of the robot characteristics is used in conjunction with a global pattern search optimization method. The formulation returns the design of the least-complex robot capable of reaching single or multiple target points in a confined space with constrained optimization metrics. A particular advantage of this approach is that it identifies the need for either fixed-curvature versus variable-curvature sections. We demonstrate the performance of the method in four clinically relevant examples.

Concentric tube robots are a novel continuum robot technology that is well suited to minimally invasive surgeries inside small body cavities such as the heart. These robots are constructed of concentrically combined pre-curved elastic tubes to form 3D curves. Each telescopic section of the robot is either of fixed or variable curvature. One advantage of this approach is that the component tube curvatures, lengths and stiffnesses can easily be fabricated to be procedure- and patient-specific. This paper proposes an optimization framework for solving the robot design problem. Given a 3D description of the constraining anatomy, the number of fixed and variable curvature robot sections and a tip workspace description, the algorithm solves for the robot design that possesses the desired workspace, remains inside the anatomical constraints and minimizes the curvature and length of all sections. The approach is illustrated in the context of beating-heart closure of atrial septal defects.

Achieving superior outcomes through the use of robots in medical applications requires an integrated approach to the design of the robot, tooling and the procedure itself. In this paper, this approach is applied to develop a robotic technique for closing abnormal communication between the atria of the heart. The goal is to achieve the efficacy of surgical closure as performed on a stopped, open heart with the reduced risk and trauma of a beating-heart catheter-based procedure. In the proposed approach, a concentric tube robot is used to percutaneously access the right atrium and deploy a tissue approximation device. The device is constructed using a metal MEMS fabrication process and is designed to both fit the manipulation capabilities of the robot as well as to reproduce the beneficial features of surgical closure by suture. Experimental results demonstrate device efficacy through manual in-vivo deployment and bench-top robotic deployment.

Concentric tube robots are a novel class of continuum robots that are constructed by combining pre-curved elastic tubes such that the overall shape of the robot is a function of the relative rotations and translations of the constituent tubes. Frictionless kinematic and quasistatic force models for this class of robots have been developed that incorporate bending and twisting of the tubes. Experimental evaluation of these models has revealed, however, a directional dependence of tube rotation on robot shape that is not predicted by these models. To explain this behavior, this paper models the contributions of friction arising from two sources: the distributed forces of contact between the tubes along their length and the concentrated bending moments generated at discontinuities in curvature and at the boundaries. It is shown that while friction due to distributed forces is insufficient to explain the experimentally observed tube twisting, a simple model of frictional torque arising from concentrated moments provides a good match with the experimental data.

Three-dimensional ultrasound can be an effective imaging modality for image-guided interventions since it enables visualization of both the instruments and the tissue. For robotic applications, its realtime frame rates create the potential for image-based instrument tracking and servoing. These capabilities can enable improved instrument visualization, compensation for tissue motion as well as surgical task automation. Continuum robots, whose shape comprises a smooth curve along their length, are well suited for minimally invasive procedures. Existing techniques for ultrasound tracking, however, are limited to straight, laparoscopic-type instruments and thus are not applicable to continuum robot tracking. Toward the goal of developing tracking algorithms for continuum robots, this paper presents a method for detecting a robot comprised of a single constant curvature in a 3D ultrasound volume. Computational efficiency is achieved by decomposing the six-dimensional circle estimation problem into two sequential three-dimensional estimation problems. Simulation and experiment are used to evaluate the proposed method.

This paper presents a novel actuation technology for robotically assisted MRI-guided interventional procedures. Compact and wireless, the actuators are both powered and controlled by the MRI scanner. The design concept and performance limits are described and derived analytically. Simulation and experiments in a clinical MR scanner are used to validate the analysis and to demonstrate the capability of the approach for needle biopsies. The concepts of actuator locking mechanisms and multi-axis control are also introduced.

This paper introduces the first stiffness controller for continuum robots. The control law is based on an accurate approximation of a continuum robot's coupled kinematic and static force model. To implement a desired tip stiffness, the controller drives the actuators to positions corresponding to a deflected robot configuration that produces the required tip force for the measured tip position. This approach provides several important advantages. First, it enables the use of robot deflection sensing as a means to both sense and control tip forces. Second, it enables stiffness control to be implemented by modification of existing continuum robot position controllers. The proposed controller is demonstrated experimentally in the context of a concentric tube robot. Results show that the stiffness controller achieves the desired stiffness in steady state, provides good dynamic performance, and exhibits stability during contact transitions.

A novel approach to constructing robots is based on concentrically combining pre-curved elastic tubes. By rotating and extending the tubes with respect to each other, their curvatures interact elastically to position and orient the robot's tip, as well as to control the robot's shape along its length. Since these robots form slender curves, they are well suited for minimally invasive medical procedures. A substantial challenge to their practical use is the real-time solution of their kinematics that are described by differential equations with split boundary equations. This paper proposes a numerically efficient approach to real-time position control. It is shown that the forward kinematics are smooth functions that can be pre-computed and accurately approximated using Fourier series. The inverse kinematics can be solved in real time using root finding applied to the functional approximation. Experimental demonstration of real-time position control using this approach is also described.

Concentric tube robots are a subset of continuum robots constructed by combining pre-curved elastic tubes. As the tubes are rotated and translated with respect to each other, their curvatures interact elastically, enabling control of the robot's tip configuration as well as the curvature along its length. This technology is projected to be useful in many types of minimally invasive medical procedures. Because these robots are flexible by design, they deflect considerably when applying forces to the external environment. Thus, in contrast to rigid-link robots, their kinematic and static force models are coupled. This paper derives a multi-tube quasistatic model that relates tube rotations and translations together with externally applied loads to robot shape and tip configuration. The model can be applied in robot design, procedure planning as well as control. For validation, the multi-tube model is compared experimentally to a computationally-efficient single-tube approximate model.

Stiffness control of a continuum robot can prevent excessive contact forces during robot navigation inside delicate, uncertain and confined environments. Furthermore, it enables the selection of tip stiffnesses that match varying task requirements. This paper introduces a computationally-efficient approach to continuum-robot stiffness control that is based on writing the forward kinematic model as the product of two transformations. The first transformation calculates the non-contact kinematics of the robot and can be formulated based on the specific type of continuum robot under consideration. The second transformation calculates the tip deflection due to applied forces and is efficiently computed using the special Cosserat rod model. To implement a desired tip stiffness, the two transformations are used to solve for the actuator positions that deform the manipulator so as to generate the required tip force at the measured tip position. The efficacy of the proposed controller is demonstrated experimentally on a concentric-tube continuum robot.

A novel approach toward construction of robots is based on a concentric combination of precurved elastic tubes. By rotation and extension of the tubes with respect to each other, their curvatures interact elastically to position and orient the robot's tip, as well as to control the robot's shape along its length. In this approach, the flexible tubes comprise both the links and the joints of the robot. Since the actuators attach to the tubes at their proximal ends, the robot itself forms a slender curve that is well suited for minimally invasive medical procedures. This paper demonstrates the potential of this technology. Design principles are presented and a general kinematic model incorporating tube bending and torsion is derived. Experimental demonstration of real-time position control using this model is also described.

A recent approach to steerable needle design is based on combining pre-curved tubes concentrically. By rotating and extending the tubes with respect to each other, the position and orientation of the needle tip, as well as the shape of the inserted length, can be controlled. Prior models neglected torsional twisting in the curved portions of the tubes. This paper presents a mechanics model that includes torsion, applies to any number of tubes and allows curvature and stiffness to vary with arc length. While the general model is comprised of differential equations, an analytic solution is given for two tubes of constant curvature. This solution enables analytic prediction of "snap through" instability based on a single dimensionless parameter. Simulation and experiments are used to illustrate the results.

During needle-based procedures, transitions between tissue layers often involve puncture events that produce substantial deformation and tend to drive the needle off course. In this paper, we analyze the mechanics of these rupture events corresponding to unstable crack propagation during the insertion of a sharp needle in an inhomogeneous tissue. The force-deflection curve of the needle prior to a rupture event is modeled by a nonlinear viscoelastic Kelvin model and a stress analysis is used to predict the relationship between rupture force and needle velocity. The model predicts that the force-deflection response of the needle is steeper and the tissue absorbs less energy when the needle moves faster. The force of rupture also decreases for faster insertion under certain conditions. The observed properties are sufficient to show that maximizing needle velocity minimizes tissue deformation and damage, and consequently, results in less needle insertion position error. The model predicts that tissue deformation and absorbed energy asymptotically approach lower bounds as velocity increases. Experiments with porcine cardiac tissue confirm the analytical predictions.

This paper presents a robotic system capable of using three-dimensional ultrasound to guide a surgical instrument to a tracked target location. Tracking of both the surgical instrument and target was done using image based algorithms on the real-time 3D ultrasound data. The tracking techniques are shown to be especially amenable for execution on powerful graphics processor units. By harnessing a graphics card, it was possible to detect both a surgical instrument and a surgical target at a rate of 25 Hz. The high update rate permits the use of tracked instrument and target locations for controlling a robot. Validation of the system was done in a water tank, where the robot moved the instrument to the target site with a mean error of 1.2 mm

Prior papers have introduced steerable needles composed of precurved concentric tubes. The curvature and extent of these needles can be controlled by the relative rotation and translation of the individual tubes. Under certain assumptions on the geometry and design of these needles, the forward kinematics problem can be solved in closed form by means of algebraic equations. The inverse kinematics problem, however, is not as straightforward owing to the nonlinear map between relative tube displacements and needle tip configuration as well as to the multiplicity of solutions as the number of tubes increases. This paper presents a general approach to solving the inverse kinematics problem using a pseudoinverse solution together with gradients of nullspace potential functions to enforce geometric and mechanical constraints.

This paper presents a real-time 3D ultrasoundguided robotic system, designed to autonomously navigate a surgical instrument to surgeon-specified target points. The system tracks the instrument in real-time (2 Hz) using image processing. Thus, it does not require tracking of the ultrasound scan head. It makes use of a line detection algorithm and a passive instrument marker, which together report the instrument's position and orientation (6 d.o.f.) from a single ultrasound image. Validation experiments are presented. The system controlled instrument position in a variety of image locations with a mean error of 0.8 mm

A new approach to steerable needle design is proposed for use in minimally invasive surgery. The technology is based on sets of curved concentric tubes. By rotating and extending the tubes with respect to each other, the position and orientation of the needle tip, as well as the shape of the inserted length, can be controlled. A mechanics model is presented for computing the shape of the needle. Forward and inverse kinematic equations are also derived. In addition, experimental results are presented as validation of the approach

Needle based intervention procedures are a common minimally invasive surgical technique. In many of these procedures, the needle can be considered rigid and the tissue deforms and displaces substantially as the needle is advanced to its target. An energy based, fracture mechanics approach is presented to show that the velocity dependence of tissue properties can reduce tissue motion with increased needle velocities. In-vitro test results on porcine heart samples show that the force required to initiate cutting reduces with increasing needle velocity up to a critical speed, above which, the rate independent cutting force of the underlying tissue becomes the limiting factor. In-vivo tests show increased needle speed results in reduced force and displacement for needle insertion into the heart. Results indicate that automated insertion could substantially improve performance in some applications.

Robots are useful tools in minimally invasive surgery, providing benefits such as reduction in hand tremor, navigation, and workspace scaling. Unfortunately, minimally invasive configurations result in two likely sources of kinematic error: port displacement and instrument shaft flexion. For a quasistatic system, a measure is presented that relates the errors in the robot Jacobian to the angular difference between desired motions and actual motions. Simulations and experimental data demonstrate this measure for a laboratory system. One potential use for the presented measure is, for bounded errors, determining whether the system monotonically converges for all initial and desired positions in the workspace. In addition, the measure is useful for path planning, determining less error-prone paths.

An important component of machine perception is the estimation of contact states during task execution. This paper addresses two fundamental questions that must be answered when formulating mathematical descriptions of the contact states: Are two contact states distinguishable from each other? Can the unknown or imprecisely known parameters in these descriptions be identified? A technique is presented to answer these questions, which is based on a Taylor series expansion of the contact state's constraint equations. The approach is illustrated through several examples.

Properly selected port sites for robot-assisted coronary artery bypass graft (CABG) improve the efficiency and quality of these procedures. In clinical practice, surgeons select port locations using external anatomic landmarks to estimate a patient's internal anatomy. This paper proposes an automated approach to port selection based on a preoperative image of the patient, thus avoiding the need to estimate internal anatomy. Using this image as input, port sites are chosen from a grid of surgeon-approved options by defining a performance measure for each possible port triad. This measure seeks to minimize the weighted squared deviation of the instrument and endoscope angles from their optimal orientations at each internal surgical site. This performance measure proves insensitive to perturbations in both its weighting factors and moderate intraoperative displacements of the patient's internal anatomy. A validation study of this port site selection was performed. cardiac algorithm also Six surgeons dissected model vessels using the port triad selected by this algorithm with performance compared to dissection using a surgeon-selected port triad and a port triad template described by Tabaie et al., 1999. With the algorithm-selected ports, dissection speed increased by up to 43% (p = 0.046) with less overall vessel trauma. Thus, this algorithmic approach to port site selection has important clinical implications for robot-assisted CABG which warrant further investigation.

Presents the design and testing of a multi-channel vibrotactile display. It is composed of a cylindrical handle with four embedded vibrating elements driven by piezoelectric beams. Vibrations are transmitted to the hands through arrays of pins. The device was tested in sensory substitution for conveying force information during a teleoperated peg insertion. Results show that the device is effective in reducing peak forces during the insertion task.

During teleoperation, a human operator often receives only 2D visual feedback from the remote environment. While a variety of kinematic sensors exist on the remote manipulator for control purposes, the information inherent in these signals is rarely extracted and presented to the operator in a useful form. This paper investigates the extraction of such information through the development of an algorithm that estimates the geometric properties of a manipulated object and its environment using the remote robot sensors and knowledge of the task being performed. The focus of the paper is the development of contact constraint equations parametrized by the desired geometric properties and the automatic segmentation of the data stream according to the set of active contacts. The approach is validated for 3D peg-in-hole insertion using a desktop teleoperator system.

During teleoperation, the automatic identification of remote environment properties has the potential of improving performance by providing task-specific feedback to the operator. Similarly, virtual training systems can be calibrated using such an automatic identification procedure. For those properties which ran be described by parametrized constraint equations, this paper provides a method by which the active constraints can be determined during each portion of the remote manipulator's data stream. The parametrized properties can then be estimated from the appropriate data stream segments. The approach is validated for peg-in-hole insertion using a desktop teleoperator system. The proposed segmentation procedure is compared with manual segmentation to estimate the geometric properties of the peg and hole.

This paper proposes techniques for automatically identifying and modeling the kinematic constraints of manipulated objects. The existence of constraints is established by examination of the forces and torques normal and tangential to the object's motion. Constraints are modeled as joints with configuration and history dependent forces. To illustrate these concepts, several experimental examples are presented.

The use of rigid-body models during frictional contact is often justified by proving the existence of a unique solution to the forward dynamic equations. The implicit assumption here is that the contact forces so obtained are stable. In this paper, the rigid-body assumption is relaxed and body-to-body contacts are modeled using springs and dampers. A singular perturbation analysis reveals additional necessary conditions to ensure contact force stability in the reduced rigid-body model. Furthermore, the analysis indicates that stability depends on a damping ratio associated with the rigid contacts.

The use of rigid body models during frictional contact is often justified by proving the existence of a unique solution to the forward dynamic equations. The implicit assumption here is that the contact forces so obtained are stable. In this paper, the rigid-body assumption is relaxed and body-to-body contacts are modelled using springs and dampers. A singular perturbation analysis reveals additional necessary conditions to ensure contact force stability in the reduced rigid-body model. Furthermore, the analysis indicates that stability depends on a damping ratio associated with the rigid contacts.

It is well known that the introduction of Coulomb friction in rigid-body dynamics can lead to problems of existence and uniqueness in the forward equations. In this paper, it is shown that these problems relate to jamming and wedging. Separate conditions for jamming and wedging are provided in the three common formulations of constrained systems. These conditions are illustrated with examples.>

When Coulomb friction is added to rigid-body dynamics equations, the forward dynamic solution may not exist. and if it exists it is not necessarily unique. The author studies the existence and uniqueness properties of the forward solution of these equations. It is shown that existence and uniqueness problems arise even for a single degree-of-freedom system and conditions are derived under which such problems occur. A graphical method which clearly shows the number of solutions associated with each value of input torque is presented. A transmission element is used as an example of such a system.>

The avoidance of stick-slip motion at low velocities through feedback control is discussed. Simplified single-joint robot models are derived for position and force control. It is shown that both models can be represented by the same differential equation. Most prior work in control used friction models which depend only on the current value of velocity. This type of analysis indicates that stick-slip can be avoided only through velocity feedback. The tribology literature, however, indicates that friction also depends on the past history of motion. To include this dependence, a state variable friction model is used in conjunction with the position and force control models. Analysis reveals the existence of a second regime of stable, low-velocity motion associated with position feedback gains above a critical value. This is an important result because the accuracy of position data is typically much better than that of velocity data at these speeds.>

The importance of appropriately modeling friction for the simulation and control of high-performance robot systems is discussed. Incorporating Coulomb-type friction in the dynamic equations introduces two difficulties in the forward dynamic solution. It is shown that the differential equations become discontinuous in the highest-order derivative terms. In addition, the load dependency of this type of friction generally causes the equations to be implicit in the joint accelerations. For the important case of load-dependent transmission friction, the equations are shown to be explicit. Techniques for the forward solution are described through the example of a roller screw transmission. Experimental and simulation results are used to show the importance of load-dependent friction in a particular robot. Implementational issues are discussed as well as implications for robot control.>