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

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)

Surrogate models for the design and control of soft mechanical systems

Soft mechanical systems constitute stretchable skins, tissue-like appendages, fibers and fluids, and utilize material deformation to transmit forces or motion to perform a mechanical task. These systems may possess infinite degrees of freedom with finite modes of actuation and sensing, and this creates challenges in modeling, design and controls. This thesis explores the use of surrogate models to approximate the complex physics between the inputs and outputs of a soft mechanical system composed of a ubiquitous soft building block known as Fiber Reinforced Elastomeric Enclosures (FREEs). Towards this the thesis is divided into two parts, with the first part investigating reduced order models for design and the other part investigating reinforcement learning (RL) framework for controls. The reduced order models for design is motivated by the need for repeated quick and accurate evaluation of the system performance. Two mechanics-based models are investigated: (a) A Pseudo Rigid Body model (PRB) with lumped spring and link elements, and (b) a Homogenized Strain Induced (HIS) model that can be implemented in a finite element framework. The parameters of the two models are fit either directly with experiments on FREE prototypes or with a high fidelity robust finite element model. These models capture fundamental insights on design by isolating a fundamental dyad building block of contracting FREEs that can be configured to either obtain large stroke (displacement) or large force. Furthermore, the thesis proposes a novel building block-based design framework where soft FREE actuators are systematically integrated in a compliant system to yield a given motion requirement. The design process is deemed useful in shape morphing adaptive structures such as airfoils, soft skins, and wearable devices for the upper extremities. Soft robotic systems such as manipulators are challenging to control because of their flexibility, ability to undergo large spatial deformations that are dependent on the external load. The second part of this work focuses on the control of a unique soft continuum arm known as the BR2 manipulator using reinforcement learning (RL). The BR2 manipulator has a unique parallel architecture with a combined bending mode and torsional modes, and its inherent asymmetric nature precludes well defined analytical models to capture its forward kinematics. Two RL-based frameworks are evaluated on the BR2 manipulator and their efficacy in carrying out position control using simple state feedback is reported in this work. The results highlight external load invariance of the learnt control policies which is a significant factor for deformable continuum arms for applications involving pick and place operations. The manipulator is deemed useful in berry harvesting and other agricultural applications

A continuum robotic platform for endoscopic non-contact laser surgery: design, control, and preclinical evaluation

The application of laser technologies in surgical interventions has been accepted in the clinical domain due to their atraumatic properties. In addition to manual application of fibre-guided lasers with tissue contact, non-contact transoral laser microsurgery (TLM) of laryngeal tumours has been prevailed in ENT surgery. However, TLM requires many years of surgical training for tumour resection in order to preserve the function of adjacent organs and thus preserve the patient’s quality of life. The positioning of the microscopic laser applicator outside the patient can also impede a direct line-of-sight to the target area due to anatomical variability and limit the working space. Further clinical challenges include positioning the laser focus on the tissue surface, imaging, planning and performing laser ablation, and motion of the target area during surgery. This dissertation aims to address the limitations of TLM through robotic approaches and intraoperative assistance. Although a trend towards minimally invasive surgery is apparent, no highly integrated platform for endoscopic delivery of focused laser radiation is available to date. Likewise, there are no known devices that incorporate scene information from endoscopic imaging into ablation planning and execution. For focusing of the laser beam close to the target tissue, this work first presents miniaturised focusing optics that can be integrated into endoscopic systems. Experimental trials characterise the optical properties and the ablation performance. A robotic platform is realised for manipulation of the focusing optics. This is based on a variable-length continuum manipulator. The latter enables movements of the endoscopic end effector in five degrees of freedom with a mechatronic actuation unit. The kinematic modelling and control of the robot are integrated into a modular framework that is evaluated experimentally. The manipulation of focused laser radiation also requires precise adjustment of the focal position on the tissue. For this purpose, visual, haptic and visual-haptic assistance functions are presented. These support the operator during teleoperation to set an optimal working distance. Advantages of visual-haptic assistance are demonstrated in a user study. The system performance and usability of the overall robotic system are assessed in an additional user study. Analogous to a clinical scenario, the subjects follow predefined target patterns with a laser spot. The mean positioning accuracy of the spot is 0.5 mm. Finally, methods of image-guided robot control are introduced to automate laser ablation. Experiments confirm a positive effect of proposed automation concepts on non-contact laser surgery.Die Anwendung von Lasertechnologien in chirurgischen Interventionen hat sich aufgrund der atraumatischen Eigenschaften in der Klinik etabliert. Neben manueller Applikation von fasergeführten Lasern mit Gewebekontakt hat sich die kontaktfreie transorale Lasermikrochirurgie (TLM) von Tumoren des Larynx in der HNO-Chirurgie durchgesetzt. Die TLM erfordert zur Tumorresektion jedoch ein langjähriges chirurgisches Training, um die Funktion der angrenzenden Organe zu sichern und damit die Lebensqualität der Patienten zu erhalten. Die Positionierung des mikroskopis chen Laserapplikators außerhalb des Patienten kann zudem die direkte Sicht auf das Zielgebiet durch anatomische Variabilität erschweren und den Arbeitsraum einschränken. Weitere klinische Herausforderungen betreffen die Positionierung des Laserfokus auf der Gewebeoberfläche, die Bildgebung, die Planung und Ausführung der Laserablation sowie intraoperative Bewegungen des Zielgebietes. Die vorliegende Dissertation zielt darauf ab, die Limitierungen der TLM durch robotische Ansätze und intraoperative Assistenz zu adressieren. Obwohl ein Trend zur minimal invasiven Chirurgie besteht, sind bislang keine hochintegrierten Plattformen für die endoskopische Applikation fokussierter Laserstrahlung verfügbar. Ebenfalls sind keine Systeme bekannt, die Szeneninformationen aus der endoskopischen Bildgebung in die Ablationsplanung und -ausführung einbeziehen. Für eine situsnahe Fokussierung des Laserstrahls wird in dieser Arbeit zunächst eine miniaturisierte Fokussieroptik zur Integration in endoskopische Systeme vorgestellt. Experimentelle Versuche charakterisieren die optischen Eigenschaften und das Ablationsverhalten. Zur Manipulation der Fokussieroptik wird eine robotische Plattform realisiert. Diese basiert auf einem längenveränderlichen Kontinuumsmanipulator. Letzterer ermöglicht in Kombination mit einer mechatronischen Aktuierungseinheit Bewegungen des Endoskopkopfes in fünf Freiheitsgraden. Die kinematische Modellierung und Regelung des Systems werden in ein modulares Framework eingebunden und evaluiert. Die Manipulation fokussierter Laserstrahlung erfordert zudem eine präzise Anpassung der Fokuslage auf das Gewebe. Dafür werden visuelle, haptische und visuell haptische Assistenzfunktionen eingeführt. Diese unterstützen den Anwender bei Teleoperation zur Einstellung eines optimalen Arbeitsabstandes. In einer Anwenderstudie werden Vorteile der visuell-haptischen Assistenz nachgewiesen. Die Systemperformanz und Gebrauchstauglichkeit des robotischen Gesamtsystems werden in einer weiteren Anwenderstudie untersucht. Analog zu einem klinischen Einsatz verfolgen die Probanden mit einem Laserspot vorgegebene Sollpfade. Die mittlere Positioniergenauigkeit des Spots beträgt dabei 0,5 mm. Zur Automatisierung der Ablation werden abschließend Methoden der bildgestützten Regelung vorgestellt. Experimente bestätigen einen positiven Effekt der Automationskonzepte für die kontaktfreie Laserchirurgie

Advances in Robot Kinematics : Proceedings of the 15th international conference on Advances in Robot Kinematics

International audienceThe motion of mechanisms, kinematics, is one of the most fundamental aspect of robot design, analysis and control but is also relevant to other scientific domains such as biome- chanics, molecular biology, . . . . The series of books on Advances in Robot Kinematics (ARK) report the latest achievement in this field. ARK has a long history as the first book was published in 1991 and since then new issues have been published every 2 years. Each book is the follow-up of a single-track symposium in which the participants exchange their results and opinions in a meeting that bring together the best of world’s researchers and scientists together with young students. Since 1992 the ARK symposia have come under the patronage of the International Federation for the Promotion of Machine Science-IFToMM.This book is the 13th in the series and is the result of peer-review process intended to select the newest and most original achievements in this field. For the first time the articles of this symposium will be published in a green open-access archive to favor free dissemination of the results. However the book will also be o↵ered as a on-demand printed book.The papers proposed in this book show that robot kinematics is an exciting domain with an immense number of research challenges that go well beyond the field of robotics.The last symposium related with this book was organized by the French National Re- search Institute in Computer Science and Control Theory (INRIA) in Grasse, France

컨센트릭 튜브 로봇: 안정성 분석, 최적 디자인, 자세 측정

학위논문 (박사)-- 서울대학교 대학원 : 기계항공공학부, 2015. 8. 박종우.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 manipulating the robots by rotating or translating the bases of the tubes. As the tubes rotate and translate with respect to each other, elastic potential energy associated with tube bending and twisting can accumulateif a configuration is not locally elastically stable, then a dangerous snapping motion may occur as energy is suddenly released. To enhance the elastic stability of the concentric tube robots, this paper presents two researches: i) optimal design of tube pair, ii) local stability test to avoid unstable configurations. While prior work has considered tubes of piecewise-constant pre-curvature, the first research in 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. The second research provide a local stability condition and test to determine if a configuration is a stable equilibrium or not. This condition applies to arbitrary robot designs with any external loads. The local stability test based on this condition is validated by comparison with known stability results, and its utility is demonstrated by application to stable path planning. Though those two researches address the elastic instability issue of concentric tube robots, they both are based on the theoretical kinematics of the robots. Robot control requires the rapid computation of this kinematics, which 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 the robot that provide measurements of local curvature, e.g., optical fiber Bragg gratings. In this point of view, the third research in this paper proposes a general framework for selecting the number and placement of such sensors with respect to arc length 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 solve for 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 shape accuracy.Contents Abstract 3 List of Tables 11 List of Figures 13 1 Introduction 1 1.1 Contributions of This Thesis . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Achieving Elastic Stability Through Precurvature Optimization 4 1.1.2 Optimizing Curvature Sensor Placement for Fast, Accurate Shape Sensing of Continuum Robots . . . . . . . . . . . . . 6 1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Achieving Elastic Stability Through Precurvature Optimization 11 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Kinematics of General Concentric-Tube Robot . . . . . . . . . . . . 14 2.3 Kinematics of Planar Tube Pair . . . . . . . . . . . . . . . . . . . . 16 2.4 Stability Condition for Planar Tube Pairs . . . . . . . . . . . . . . . 17 2.4.1 Ignoring Straight Transmission Length Inside Collar . . . . . 17 2.4.2 Considering Straight Transmission Length Inside Collar . . . 19 2.5 Evaluating Stability for Specific Pre-curvature Functions . . . . . . 22 2.5.1 Constant Pre-curvature . . . . . . . . . . . . . . . . . . . . . 23 2.5.2 Partially Constant Pre-curvature . . . . . . . . . . . . . . . . 23 2.5.3 Pre-curvature Function, û_y = b/(s+a). . . . . . . . . . . . . . . 25 2.6 Formulation as an Optimal Design Problem . . . . . . . . . . . . . 27 2.6.1 Numerical Solution of the Optimal Design Problem . . . . . 29 2.6.2 Analytic Solution of the Optimal Design Problem . . . . . . 31 2.6.3 Feasibility of Optimal Design Problem . . . . . . . . . . . . 36 2.7 Hardware Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 Elastic Stability of Concentric Tube Robots Subject to External Loads 51 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2 Concentric Tube Robot Modeling . . . . . . . . . . . . . . . . . . . 54 3.3 Elastostatic Kinematic Model . . . . . . . . . . . . . . . . . . . . . . 57 3.3.1 Concentric Tube Robot with No External Load . . . . . . . 58 3.3.2 Concentric Tube Robot with External Load . . . . . . . . . 59 3.3.3 Generalized Force Representation of External loads . . . . . 63 3.4 Evaluating Local Elastic Stability . . . . . . . . . . . . . . . . . . . 65 3.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.2 Jacobi Non-Conjugacy Test for Conservative External Loads 66 3.4.3 Physical Interpretation of Jacobi Non-Conjugacy Condition 68 3.4.4 Non-Conservative External Loads . . . . . . . . . . . . . . . 69 3.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.1 Example 1: Stability of an Unloaded Constant-precurvature Tube Pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.5.2 Example 2: Stability of a Constant Precurvature Tube Pair Subject to Elastic Forces . . . . . . . . . . . . . . . . . . . . 73 3.5.3 Example 3: Stability of a Constant-precurvature Tube Pair Subject to Constant World-frame Loads . . . . . . . . . . . . 77 3.5.4 Example 4: Application to Stable Path Planning . . . . . . . 80 4 Optimizing Curvature Sensor Placement for Shape Sensing 91 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.2 Shape Estimation for Continuum Robots . . . . . . . . . . . . . . . 94 4.2.1 Kinematics of Continuum Robots . . . . . . . . . . . . . . . 94 4.2.2 Shape Reconstruction Models . . . . . . . . . . . . . . . . . . 95 4.2.3 Optimal Sensor Location . . . . . . . . . . . . . . . . . . . . 98 4.3 Case Study: Concentric Tube Robots . . . . . . . . . . . . . . . . . 100 4.3.1 Kinematics of Concentric Tube Robots . . . . . . . . . . . . 101 4.3.2 Section-Based Principal Component Analysis Model . . . . . 102 4.3.3 Section-based Polynomial Regression Model . . . . . . . . . 104 4.4 Numerical Experiments for a Concentric Tube Robot . . . . . . . . 105 4.4.1 Selection of Basis Functions . . . . . . . . . . . . . . . . . . 107 4.4.2 Number and Location of Sensors . . . . . . . . . . . . . . . . 109 4.4.3 Comparison between Reconstruction Models . . . . . . . . . 109 5 Conclusion 115 Bibliography 118 국문초록 125Docto