Modeling, Sensorization and Control of Concentric-Tube Robots

Since the concept of the Concentric-Tube Robot (CTR) was proposed in 2006, CTRs have been a popular research topic in the field of surgical robotics. The unique mechanical design of this robot allows it to navigate through narrow channels in the human anatomy and operate in highly constrained environments. It is therefore likely to become the next generation of surgical robots to overcome the challenges that cannot be addressed by current technologies. In CSTAR, we have had ongoing work over the past several years aimed at developing novel techniques and technologies for CTRs. This thesis describes the contributions made in this context, focusing primarily on topics such as modeling, sensorization, and control of CTRs. Prior to this work, one of the main challenges in CTRs was to develop a kinematic model that achieves a balance between the numerical accuracy and computational efficiency for surgical applications. In this thesis, a fast kinematic model of CTRs is proposed, which can be solved at a comparatively fast rate (0.2 ms) with minimal loss of accuracy (0.1 mm) for a 3-tube CTR. A Jacobian matrix is derived based on this model, leading to the development of a real-time trajectory tracking controller for CTRs. For tissue-robot interactions, a force-rejection controller is proposed for position control of CTRs under time-varying force disturbances. In contrast to rigid-link robots, instability of position control could be caused by non-unique solutions to the forward kinematics of CTRs. This phenomenon is modeled and analyzed, resulting in design criteria that can ensure kinematic stability of a CTR in its entire workspace. Force sensing is another major difficulty for CTRs. To address this issue, commercial force/torque sensors (Nano43, ATI Industrial Automation, United States) are integrated into one of our CTR prototypes. These force/torque sensors are replaced by Fiber-Bragg Grating (FBG) sensors that are helically-wrapped and embedded in CTRs. A strain-force calculation algorithm is proposed, to convert the reflected wavelength of FBGs into force measurements with 0.1 N force resolution at 100 Hz sampling rate. In addition, this thesis reports on our innovations in prototyping drive units for CTRs. Three designs of CTR prototypes are proposed, the latest one being significantly more compact and cost efficient in comparison with most designs in the literature. All of these contributions have brought this technology a few steps closer to being used in operating rooms. Some of the techniques and technologies mentioned above are not merely limited to CTRs, but are also suitable for problems arising in other types of surgical robots, for example, for sensorizing da Vinci surgical instruments for force sensing (see Appendix A)

Design of a Robotic Instrument Manipulator for Endoscopic Deployment

This thesis describes the initial design process for an application of continuum robotics to endoscopic surgical procedures, specifically dissection of the colon. We first introduce the long-term vision for a benchtop dual-instrument endoscopic system with intuitive haptic controllers and then narrow our focus to the design and testing of the instrument manipulator itself, which must be actuated through the long, winding channel of a standard colonoscope. Based on design requirements for a target procedure, we analyze simulations of two types of continuum robots using recently established kinematic and mechanic modeling approaches: the concentric-tube robot (CTR) and the concentric agonist-antagonist robot (CAAR). In addition, we investigate solutions to the primary engineering challenge to this system, which is accurately transmitting joint motion through exible, hollow shafts. Based on our study of the manipulator simulations and transmission shafts, we select instrument designs for prototyping and testing. We present approaches for controlling the position of the robotic instrument in real-time using an input device, and demonstrate the degree of control we can achieve in various configurations by performing time trial experiments with our prototype robotic instruments. Our observations of the manipulator during testing inform us of sources of error, and we conclude this report with suggestions for future work, including shaft design and alternative continuum manipulator approaches

Study of Intrinsically Curved Elastic Rods Under External Loads with Applications to Concentric Tube Continuum Robots and their Control

Using variational principles, we investigate elastic rod structures under external loads that are clamped at one end and free at the other. Their stability properties are analyzed using second order conditions by generalizing the Jacobi theory of conjugate points. The notion of the index, which quantifies the dimension of the subspace of variations over which the second variation is negative, is also generalized to this class of problems. The variational structure of the parameter- dependent calculus of variations problems can be exploited to detect the changes in the index at the folds as the parameter is varied, with the assistance of distinguished bifurcation diagrams. We generalize these plots to cover our current case with fixed-free ends. Furthermore, we extend the investigation to the problems with discontinuous integrands by generalizing the concept of conjugate points, index, and distinguished bifurcation diagrams to them. For this purpose, second-order matching conditions are derived at the points of discontinuity. These techniques are developed with the aim of employing them in soft robotic applications, a field that is increasingly gaining popularity. Applications such as Concentric Tube Continuum Robots (CTCRs) employ intrinsically curved rods to generate flexible mechanisms. We emphasize the impact of intrinsic curvature, which is often a source of complex mechanics, on the equilibria of elastic rods and their stability. The interplay between geometric non-linearities, external load, and intrinsic curvature leads to intriguing and complex behavior such as snap-back instability. We study the influence of the parameters, such as intrinsic curvature, length, tip load, and lever arm of the load on this behavior. This study aids in their efficient utilization in practical applications. We extend this investigation to CTCRs, which resemble an intrinsically curved elastic rod with slightly different physics. These robots consist of multiple sections, and their properties change abruptly at the boundary of each section. This research has the potential to advance the design and control of robots for tackling more complex tasks. Finally, an open-loop gradient-based navigation is devised to model the robot maneuver using optimal control techniques. Through this approach, various tasks can be modelled in terms of objective functions that are subsequently optimized. We consider optimal control of CTCRs parameterized over pseudo-time, primarily focusing on minimizing the robot’s working volume during its motion. A numerical strategy to implement this optimization task is also discussed. This optimal control-based methodology can be adapted to any backbone-based continuum robots.Mithilfe von Variationsrechnung untersuchen wir das Verhalten elastischer Stabtragwerke unter äußeren Lasten, die an einem Ende eingespannt und am anderen Ende frei sind. Die Stabilitätseigenschaften der Gleichgewichte werden unter Verwendung von Bedingungen zweiter Ordnung durch Verallgemeinerung der Jacobi’sche Theorie der konjugierten Punkte analysiert. Der Indexbegriff, der die Dimension des Unterraums der Variationen quantifiziert, über dem die zweite Variation negativ-definit ist, wird auf diese Klasse von Problemen erweitert. Die Variationsstruktur der parameterabhängigen Variationsrechnung wird ausgenutzt, um die Änderungen des Index an den Falten in Spezielle Bifurkationsdiagramme vorherzusagen. Wir verallgemeinern diese Diagramme auf Probleme mit aktuellen feste-frei Enden. Außerdem untersuchen wir die Stabilität von Variationsproblemen mit diskontinuierlichen Integranden, indem wir das Konzept der konjugierten Punkte, des Index und der Spezielle Bifurkationsdiagramme auf diese erweitern. Zu diesem Zweck werden Anpassungsbedingungen zweiter Ordnung an den Unstetigkeitsstellen hergeleitet. Diese Techniken werden mit dem Ziel entwickelt, sie in Soft-Roboter-Anwendungen einzusetzen, einem Bereich, der zunehmend an Beliebtheit gewinnt. Einige Anwendungen wie Concentric Tube Continuum Robots (CTCRs), verwenden intrinsisch gekrümmte Stäbe, um flexible Mechanismen zu erzeugen. Das Zusammenspiel von geometrischen Nichtlinearitäten, externen Lasten und intrinsischer Krümmung führt zu faszinierendem und komplexem Verhalten, wie z.B. der Snap-Back-Instabilität. Die Untersuchung der Abhängigkeit dieses Verhaltens von Parametern wie Eigenkrümmung, Länge, Spitzenlast und Hebelarm der Last hilft bei der effizienten Nutzung in praktischen Anwendungen. Wir erweitern diese Untersuchung auf CTCRs, die einem in sich gekrümmten elastischen Stab ähneln, aber eine etwas andere Physik aufweisen. Diese Forschung hilft bei der Entwicklung und Steuerung von Robotern für komplexere Aufgaben. Diese Roboter bestehen aus mehreren Abschnitten und ihre Eigenschaften ändern sich abrupt an den Grenzen der einzelnen Abschnitte. Schließlich wird eine gradientenbasierte Navigation mit offenem Regelkreis eingesetzt, um das Robotermanöver mit optimalen Kontrollmethoden zu modellieren. Mit diesem Ansatz werden mehrere komplexe Aufgaben in Form von Zielfunktionen quantifiziert, die optimiert werden. Wir betrachten die optimale Steuerung von CTCRs, die über Pseudozeit parametrisiert sind, und konzentrieren uns dabei auf die Minimierung des Arbeitsvolumens des Roboters während seines Betriebs. Eine numerische Strategie zur Durchführung der resultierenden Optimierung wird ebenfalls vorgestellt

Design and Modeling of Multi-Arm Continuum Robots

Continuum robots are snake-like systems able to deliver optimal therapies to pathologies deep inside the human cavity by following 3D complex paths. They show promise when anatomical pathways need to be traversed thanks to their enhanced flexibility and dexterity and show advantages when deployed in the field of single-port surgery. This PhD thesis concerns the development and modelling of multi-arm and hybrid continuum robots for medical interventions. The flexibility and steerability of the robot’s end-effector are achieved through concentric tube technology and push/pull technology. Medical robotic prototypes have been designed as proof of concepts and testbeds of the proposed theoretical works.System design considers the limitations and constraints that occur in the surgical procedures for which the systems were proposed for. Specifically, two surgical applications are considered. Our first prototype was designed to deliver multiple tools to the eye cavity for deep orbital interventions focusing on a currently invasive intervention named Optic Nerve Sheath Fenestration (ONSF). This thesis presents the end-to-end design, engineering and modelling of the prototype. The developed prototype is the first suggested system to tackle the challenges (limited workspace, need for enhanced flexibility and dexterity, danger for harming tissue with rigid instruments, extensive manipulation of the eye) arising in ONSF. It was designed taking into account the clinical requirements and constraints while theoretical works employing the Cosserat rod theory predict the shape of the continuum end-effector. Experimental runs including ex vivo experimental evaluations, mock-up surgical scenarios and tests with and without loading conditions prove the concept of accessing the eye cavity. Moreover, a continuum robot for thoracic interventions employing push/pull technology was designed and manufactured. The developed system can reach deep seated pathologies in the lungs and access regions in the bronchial tree that are inaccessible with rigid and straight instruments either robotically or manually actuated. A geometrically exact model of the robot that considers both the geometry of the robot and mechanical properties of the backbones is presented. It can predict the shape of the bronchoscope without the constant curvature assumption. The proposed model can also predict the robot shape and micro-scale movements accurately in contrast to the classic geometric model which provides an accurate description of the robot’s differential kinematics for large scale movements

On the Statics, Dynamics, and Stability of Continuum Robots: Model Formulations and Efficient Computational Schemes

This dissertation presents advances in continuum-robotic mathematical-modeling techniques. Specifically, problems of statics, dynamics, and stability are studied for robots with slender elastic links. The general procedure within each topic is to develop a continuous theory describing robot behavior, develop a discretization strategy to enable simulation and control, and to validate simulation predictions against experimental results.Chapter 1 introduces the basic concept of continuum robotics and reviews progress in the field. It also introduces the mathematical modeling used to describe continuum robots and explains some notation used throughout the dissertation.The derivation of Cosserat rod statics, the coupling of rods to form a parallel continuum robot (PCR), and solution of the kinematics problem are reviewed in Chapter 2. With this foundation, soft real-time teleoperation of a PCR is demonstrated and a miniature prototype robot with a grasper is controlled.Chapter 3 reviews the derivation of Cosserat rod dynamics and presents a discretization strategy having several desirable features, such as generality, accuracy, and potential for good computational efficiency. The discretized rod model is validated experimentally using high speed camera footage of a cantilevered rod. The discretization strategy is then applied to simulate continuum robot dynamics for several classes of robot, including PCRs, tendon-driven robots, fluidic actuators, and concentric tube robots.In Chapter 4, the stability of a PCR is analyzed using optimal control theory. Conditions of stability are gradually developed starting from a single planar rod and finally arriving at a stability test for parallel continuum robots. The approach is experimentally validated using a camera tracking system.Chapter 5 provides closing discussion and proposes potential future work

Multi-objective particle swarm optimization for the structural design of concentric tube continuum robots for medical applications

Concentric tube robots belong to the class of continuum robotic systems whose morphology is described by continuous tangent curvature vectors. They are composed of multiple, interacting tubes nested inside one another and are characterized by their inherent flexibility. Concentric tube continuum robots equipped with tools at their distal end have high potential in minimally invasive surgery. Their morphology enables them to reach sites within the body that are inaccessible with commercial tools or that require large incisions. Further, they can be deployed through a tight lumen or follow a nonlinear path. Fundamental research has been the focus during the last years bringing them closer to the operating room. However, there remain challenges that require attention. The structural synthesis of concentric tube continuum robots is one of these challenges, as these types of robots are characterized by their large parameter space. On the one hand, this is advantageous, as they can be deployed in different patients, anatomies, or medical applications. On the other hand, the composition of the tubes and their design is not a straightforward task but one that requires intensive knowledge of anatomy and structural behavior. Prior to the utilization of such robots, the composition of tubes (i.e. the selection of design parameters and application-specific constraints) must be solved to determine a robotic design that is specifically targeted towards an application or patient. Kinematic models that describe the change in morphology and complex motion increase the complexity of this synthesis, as their mathematical description is highly nonlinear. Thus, the state of the art is concerned with the structural design of these types of robots and proposes optimization algorithms to solve for a composition of tubes for a specific patient case or application. However, existing approaches do not consider the overall parameter space, cannot handle the nonlinearity of the model, or multiple objectives that describe most medical applications and tasks. This work aims to solve these fundamental challenges by solving the parameter optimization problem by utilizing a multi-objective optimization algorithm. The main concern of this thesis is the general methodology to solve for patient- and application-specific design of concentric tube continuum robots and presents key parameters, objectives, and constraints. The proposed optimization method is based on evolutionary concepts that can handle multiple objectives, where the set of parameters is represented by a decision vector that can be of variable dimension in multidimensional space. Global optimization algorithms specifically target the constrained search space of concentric tube continuum robots and nonlinear optimization enables to handle the highly nonlinear elasticity modeling. The proposed methodology is then evaluated based on three examples that include cooperative task deployment of two robotic arms, structural stiffness optimization under the consideration of workspace constraints and external forces, and laser-induced thermal therapy in the brain using a concentric tube continuum robot. In summary, the main contributions are 1) the development of an optimization methodology that describes the key parameters, objectives, and constraints of the parameter optimization problem of concentric tube continuum robots, 2) the selection of an appropriate optimization algorithm that can handle the multidimensional search space and diversity of the optimization problem with multiple objectives, and 3) the evaluation of the proposed optimization methodology and structural synthesis based on three real applications

Modeling, Analysis, Force Sensing and Control of Continuum Robots for Minimally Invasive Surgery

This dissertation describes design, modeling and application of continuum robotics for surgical applications, specifically parallel continuum robots (PCRs) and concentric tube manipulators (CTMs). The introduction of robotics into surgical applications has allowed for a greater degree of precision, less invasive access to more remote surgical sites, and user-intuitive interfaces with enhanced vision systems. The most recent developments have been in the space of continuum robots, whose exible structure create an inherent safety factor when in contact with fragile tissues. The design challenges that exist involve balancing size and strength of the manipulators, controlling the manipulators over long transmission pathways, and incorporating force sensing and feedback from the manipulators to the user. Contributions presented in this work include: (1) prototyping, design, force sensing, and force control investigations of PCRs, and (2) prototyping of a concentric tube manipulator for use in a standard colonoscope. A general kinetostatic model is presented for PCRs along with identification of multiple physical constraints encountered in design and construction. Design considerations and manipulator capabilities are examined in the form of matrix metrics and ellipsoid representations. Finally, force sensing and control are explored and experimental results are provided showing the accuracy of force estimates based on actuation force measurements and control capabilities. An overview of the design requirements, manipulator construction, analysis and experimental results are provided for a CTM used as a tool manipulator in a traditional colonoscope. Currently, tools used in colonoscopic procedures are straight and exit the front of the scope with 1 DOF of operation (jaws of a grasper, tightening of a loop, etc.). This research shows that with a CTM deployed, the dexterity of these tools can be increased dramatically, increasing accuracy of tool operation, ease of use and safety of the overall procedure. The prototype investigated in this work allows for multiple tools to be used during a single procedure. Experimental results show the feasibility and advantages of the newly-designed manipulators

Design, Modeling and Control of Micro-scale and Meso-scale Tendon-Driven Surgical Robots

Manual manipulation of passive surgical tools is time consuming with uncertain results in cases of navigating tortuous anatomy, avoiding critical anatomical landmarks, and reaching targets not located in the linear range of these tools. For example, in many cardiovascular procedures, manual navigation of a micro-scale passive guidewire results in increased procedure times and radiation exposure. This thesis introduces the design of two steerable guidewires: 1) A two degree-of-freedom (2-DoF) robotic guidewire with orthogonally oriented joints to access points in a three dimensional workspace, and 2) a micro-scale coaxially aligned steerable (COAST) guidewire robot that demonstrates variable and independently controlled bending length and curvature of the distal end. The 2-DoF guidewire features two micromachined joints from a tube of superelastic nitinol of outer diameter 0.78 mm. Each joint is actuated with two nitinol tendons. The joints that are used in this robot are called bidirectional asymmetric notch (BAN) joints, and the advantages of these joints are explored and analyzed. The design of the COAST robotic guidewire involves three coaxially aligned tubes with a single tendon running centrally through the length of the robot. The outer tubes are made from micromachined nitinol allowing for tendon-driven bending of the robot at variable bending curvatures, while an inner stainless steel tube controls the bending length of the robot. By varying the lengths of the tubes as well as the tendon, and by insertion and retraction of the entire assembly, various joint lengths and curvatures may be achieved. Kinematic and static models, a compact actuation system, and a controller for this robot are presented. The capability of the robot to accurately navigate through phantom anatomical bifurcations and tortuous angles is also demonstrated in three dimensional phantom vasculature. At the meso-scale, manual navigation of passive pediatric neuroendoscopes for endoscopic third ventriculostomy may not reach target locations in the patient's ventricle. This work introduces the design, analysis and control of a meso-scale two degree-of-freedom robotic bipolar electrocautery tool that increases the workspace of the neurosurgeon. A static model is proposed for the robot joints that avoids problems arising from pure kinematic control. Using this model, a control system is developed that comprises of a disturbance observer to provide precise force control and compensate for joint hysteresis. A handheld controller is developed and demonstrated in this thesis. To allow the clinician to estimate the shape of the steerable tools within the anatomy for both micro-scale and meso-scale tools, a miniature tendon force sensor and a high deflection shape sensor are proposed and demonstrated. The force sensor features a compact design consisting of a single LED, dual-phototransistor, and a dual-screen arrangement to increase the linear range of sensor output and compensate for external disturbances, thereby allowing force measurement of up to 21 N with 99.58 % accuracy. The shape sensor uses fiber Bragg grating based optical cable mounted on a micromachined tube and is capable of measuring curvatures as high as 145 /m. These sensors were incorporated and tested in the guidewire and the neuroendoscope tool robots and can provide robust feedback for closed-loop control of these devices in the future.Ph.D

Novel Locomotion Methods in Magnetic Actuation and Pipe Inspection

There is much room for improvement in tube network inspections of jet aircraft. Often, these inspections are incomplete and inconsistent. In this paper, we develop a Modular Robotic Inspection System (MoRIS) for jet aircraft tube networks and a corresponding kinematic model. MoRIS consists of a Base Station for user control and communication, and robotic Vertebrae for accessing and inspecting the network. The presented and tested design of MoRIS can travel up to 9 feet in a tube network. The Vertebrae can navigate in all orientations, including smooth vertical tubes. The design is optimized for nominal 1.5 outside diameter tubes. We developed a model of the Locomotion Vertebra in a tube. We defined the model\u27s coordinate system and its generalized coordinates. We studied the configuration space of the robot, which includes all possible orientations of the Locomotion Vertebra. We derived the expression for the elastic potential energy of the Vertebra\u27s suspensions and minimized it to find the natural settling orientation of the robot. We further explore the effect of the tractive wheel\u27s velocity constraint on locomotion dynamics. Finally, we develop a general model for aircraft tube networks and for a taut tether. Stabilizing bipedal walkers is a engineering target throughout the research community. In this paper, we develop an impulsively actuated walking robot. Through the use of magnetic actuation, for the first time, pure impulsive actuation has been achieved in bipedal walkers. In studying this locomotion technique, we built the world\u27s smallest walker: Big Foot. A dynamical model was developed for Big Foot. A Heel Strike and a Constant Pulse Wave Actuation Schemes were selected for testing. The schemes were validated through simulations and experiments. We showed that there exists two regimes for impulsive actuation. There is a regime for impact-like actuation and a regime for longer duration impulsive actuation

Crossing Minimal Edge-Constrained Layout Planning using Benders Decomposition

We present a new crossing number problem, which we refer to as the edge-constrained weighted two-layer crossing number problem (ECW2CN). The ECW2CN arises in layout planning of hose coupling stations at BASF, where the challenge is to find a crossing minimal assignment of tube-connected units to given positions on two opposing layers. This allows the use of robots in an effort to reduce the probability of operational disruptions and to increase human safety. Physical limitations imply maximal length and maximal curvature conditions on the tubes as well as spatial constraints imposed by the surrounding walls. This is the major difference of ECW2CN to all known variants of the crossing number problem. Such as many variants of the crossing number problem, ECW2CN is NP-hard. Because the optimization model grows fast with respect to the input data, we face out-of-memory errors for the monolithic model. Therefore, we develop two solution methods. In the first method, we tailor Benders decomposition toward the problem. The Benders subproblems are solved analytically and the Benders master problem is strengthened by additional cuts. Furthermore, we combine this Benders decomposition with ideas borrowed from fix-and-relax heuristics to design the Dynamic Fix-and-Relax Pump (DFRP). Based on an initial solution, DFRP improves successively feasible points by solving dynamically sampled smaller problems with Benders decomposition. Because the optimization model is a surrogate model for its time-dependent formulation, we evaluate the obtained solutions for different choices of the objective function via a simulation model. All algorithms are implemented efficiently using advanced features of the GuRoBi-Python API, such as callback functions and lazy constraints. We present a case study for BASF using real data and make the real-world data openly available