Real-time adaptive kinematic model estimation of concentric tube robots

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

Design Optimization Algorithms for Concentric Tube Robots

Concentric tube robots are tentacle-like surgical robots that can bend around anatomical obstacles to access hard-to-reach surgical targets. These robots have potential to enable minimally invasive surgical procedures by allowing physicians to access clinical regions that were previously unreachable using traditional instruments. Concentric tube robots are composed of nested, customizable tubes which undergo complicated mechanical interactions that generate tentacle-like motion. As a consequence of this intricate kinematic mechanism, the physical specifications of each of the robots tubes, i.e. the robot’s design, significantly affect the shapes that the robot can undertake and the regions it can reach. Customizing the design of these robots can potentially facilitate successful surgical procedures on a variety of patients. In this thesis, we present design optimization algorithms to generate appropriate design parameters on an application- and patient-specific basis. We consider three design optimization problems. First, we present a design optimization algorithm that generates a concentric tube robot design under which the robot can maximize the reachable volume of a given goal region in the human body. We provide analysis establishing that our design optimization algorithm for generating a single design is asymptotically optimal. Second, we present an algorithm that computes sets of concentric tube robot designs that can collectively maximize the reachable volume of a given goal region in the human body. Third, we introduce an algorithm that generates the set of designs of minimal size such that the designs in the set can collectively reach a physician-specified percentage of the goal region. Each of our algorithms combines a search in the design space of a concentric tube robot using Adaptive Simulated Annealing with a sampling-based motion planner in the robot’s configuration space in order to find a single or sets of designs that enable paths to the goal regions while avoiding contact with anatomical obstacles. We demonstrate the effectiveness of each of our algorithms in a simulated scenario based on lung anatomy and compare our algorithms’ performance with that of current state-of-the-art design optimization algorithms.Bachelor of Scienc

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

A Novel Fiber Jamming Theory and Experimental Verification

This thesis developed a novel theory of fiber jamming and experimentally verified it. The theory relates the performance, which is the ratio between the stiff and soft states of a fiber jamming chamber, to three relative design parameters: the ratio of the wall thickness to the membrane inner diameter, the ratio of the fiber diameter to membrane inner diameter, and the number of fibers. These three parameters, when held constant across different chamber sizes, hold the performance constant. To test the theory, three different types of fiber jamming chambers were built in three different sizes. Each chamber was set up as a cantilever beam and deflected 10mm in both the un-jammed (soft) and jammed (stiff) states. When the three design parameters were held constant, the performance of the chamber was consistent within 10\%. In contrast, when the parameters were altered, there was a statistically significant $p \u3c .0001$ and noticeable effect on chamber performance. These two results can be used in tandem to design miniaturized fiber jamming chambers. These results also have a direct application in soft robots designed for minimally invasive surgery

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

Ein Beitrag zur Berücksichtigung von pseudoelastischem Werkstoffverhalten in der Modellierung tubulärer Kontinuumsroboter

Die Arbeit widmet sich der elastokinematischen Modellierung tubulärer Kontinuumsroboter aus Nickel-Titan-Röhrchen. Besonderes Augenmerk liegt dabei auf der Berücksichtigung des nichtlinearen und hysteresebehafteten Werkstoffverhaltens der Nickel-Titan-Legierung und dessen Einfluss auf das mechanische Verhalten tubulärer Kontinuumsmechanismen. Einleitend erfolgt eine Motivation zur potentiellen Anwendung tubulärer Kontinuumsroboter in der Medizin, eine Gegenüberstellung unterschiedlicher Kanülen zur aktiven Trajektorienverfolgung sowie die Darlegung des Standes der Forschung von tubulären Kontinuumsrobotern. Die Modellierung wird dann in mehreren Stufen, aus zum Teil verschachtelten, Teilmodellen aufgebaut. Zunächst wird die Werkstoffcharakteristik der Nickel-Titan-Legierung durch ein nichtlineares Werkstoffmodell mit Hystereseberücksichtigung abgebildet und mit Messungen verglichen. Darauf aufbauend wird ein Bauteilmodell hergeleitet, welches einzelne Nickel-Titan-Röhrchen unter reiner Biegung abbilden kann. Anschließend erfolgt die Betrachtung der Auswirkung der Werkstoffhysterese auf die Gleichgewichtslage tubulärer Kontinuumsmechanismen sowie die Bestimmung von Gleichgewichtskrümmungen und Übergangswinkeln. Diese Teilmodelle werden aus einer numerischen Kontaktsimulation einer einfachen Röhrchenkombination mit linearelastischem Werkstoffverhalten abgeleitet. Eine Gesamtkinematik führt die, aus den Teilmodellen gewonnenen, kinematischen Zustände zu einer Beschreibung des Bewegungsverhaltens des gesamten Kontinuumsmechanismus zusammen. Zur Beurteilung der Modellqualität erfolgen Messungen der Trajektorie der Röhrchenenden eines tubulären Kontinuumsmechanismus aus zwei Röhrchen. Es wird gezeigt, dass es mit der Modellierungsweise möglich ist, die gesamte Trajektorie für eine maximale Kanülenlänge von 70 mm mit einer maximalen euklidischen Abweichung von etwa 2 mm abzubilden. Die Kalibrierung der kinematischen Zustände reduziert die maximale euklidische Abweichung deutlich unter 1 mm. Basierend auf dem nichtlinearen Bauteilmodell und der berechneten Gleichgewichtslage erfolgt eine modellbasierte Bestimmung der erforderlichen Antriebskräfte zum Verschieben der Röhrchen und der Vergleich dieser mit Messungen. Die Arbeit schließt mit der Beschreibung aller verwendeten Experimentalaufbauten ab. Dazu gehören die Antriebseinheit zur Verschiebung der Röhrchen, eine schwenkbare Austrittsbuchse zur Erhöhung der Bewegungsfreiheit tubulärer Kontinuumsmechanismen, ein Stereokamera-Messsystem zur Trajektorienmessung und ein Kraftmesssystem zur Bestimmung der erforderlichen Antriebskräfte.This thesis addresses the elastokinematic modeling of tubular continuum robots comprised of nickel-titanium tubes. Particular attention is paid to the nonlinear and hysteretic material behaviour of nickel-titanium and its influence on the mechanical behaviour of tubular continuum mechanisms. Initially, a potential application of tubular continuum robots in medicine is motivated. It is followed by a comparison of different cannulas for active following of trajectories and a statement of the state of the research on tubular continuum robots. The modelling is then built up in several stages of partially nested submodels. First, the material characteristic of the nickel-titanium alloy is represented by a nonlinear material constitutive law with hysteresis. Based on this, a structural element constitutive law is derived, which represents single nickel-titanium tubes under pure bending. Subsequently, the effect of the material hysteresis on the equilibrium conformation of tubular continuum mechanisms and the determination of equilibrium curvatures and transition angles is considered. These submodels are derived from a numerical contact simulation of a simple tube combination with linear elastic material behaviour. The kinematic states, obtained from the submodels, are then combined into an overall kinematic formulation of the entire continuum mechanisms motion behaviour. Trajectory measurements of the tube ends of a tubular continuum mechanism made of two tubes are conducted to assess the model quality. The measurements show that the modelling method is able to map the entire trajectory for a maximum cannula length of 70 mm, with a maximum euclidean deviation of approximately 2 mm. The calibration of the kinematic states reduces the maximum euclidean deviation to well below 1 mm. Finally, based on the non-linear structural element constitutive law and the calculated equilibrium conformation, a model-based determination of the required driving forces for moving the tubes is presented and compared to measurements. The work concludes with a description of all employed experimental setups. These include the drive unit for displacing the tubes, a pivotable outlet bushing to increase the freedom of movement of tubular continuum mechanisms, a stereo camera measurement system for trajectory measurement and a force measurement system for determining the required driving forces