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

Improving Strength and Stability in Continuum Robots

Continuum robots, which are bio-inspired ’trunk-like’ robots, are characterized for their inherent compliance and range of motion. One of the key challenges in continuum robotics research is developing robots with sufficient strength and stability without adding additional weight or complexity to the design. The research conducted in this dissertation encompasses design and modeling strategies that address these challenges in strength and stability. This work improves three continuum robot actuation paradigms: (1) tendon-driven continuum robots (TDCR), (2) concentric tube robots (CTR), and (3) concentric push-pull robots (CPPR). The first chapter of contribution covers strategies for improving strength in TDCRs. The payload capacity and torsional stiffness of the robot can be improved by leveraging the geometry of the backbone design and tendon routing, with design choices experimentally validated on a robot prototype. The second chapter covers a new bending actuator, concentric precurved bellows (CPB), that are based upon CTR actuation. The high torsional stiffness of bellows geometry virtually eliminates the torsional compliance instability found in CTRs. Two bellows designs are developed for 3D printing and the mechanical properties of these designs are characterized through experiments on prototypes and in static finite element analysis. A torsionally rigid kinematic model is derived and validated on 3D printed prototypes. The third chapter of contribution covers the development and validation of a mechanics-based CPPR kinematics model. CPPRs are constructed from concentrically nested, asymmetrically patterned tubes that are fixed together at their distal tips. Relative translations between the tubes induces bending shapes from the robot. The model expands the possible design space of CPPRs by enabling the modeling of external loads, non-planar bending shapes, and CPPRs with more than two tubes. The model is validated on prototypes in loaded and unloaded experiments

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

Kinetostatic Path Planning for Continuum Robots By Sampling on Implicit Manifold

Continuum robots (CR) offer excellent dexterity and compliance in contrast to rigid-link robots, making them suitable for navigating through, and interacting with, confined environments. However, the study of path planning for CRs while considering external elastic contact is limited. The challenge lies in the fact that CRs can have multiple possible configurations when in contact, rendering the forward kinematics not well-defined, and characterizing the set of feasible robot configurations as non-trivial. In this paper, we propose to solve this problem by performing quasi-static path planning on an implicit manifold. We model elastic obstacles as external potential fields and formulate the robot statics in the potential field as the extremal trajectory of an optimal control problem obtained by the first-order variational principle. We show that the set of stable robot configurations is a smooth manifold diffeomorphic to a submanifold embedded in the product space of the CR actuation and base internal wrench. We then propose to perform path planning on this manifold using AtlasRRT*, a sampling-based planner dedicated to planning on implicit manifolds. Simulations in different operation scenarios were conducted and the results show that the proposed planner outperforms Euclidean space planners in terms of success rate and computational efficiency.Comment: 7 pages, 4 figures, submitted to IEEE ICRA 202

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 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, 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

Optically Sensorized Tendons for Articulate Robotic Needles

This study proposes an optically sensorized tendon composed of a 195 µm diameter, high strength, polarization maintaining (PM) fiber Bragg gratings (FBG) optical fiber which resolves the cross-sensitivity issue of conventional FBGs. The bare fiber tendon is locally reinforced with a 250 µm diameter Kevlar bundle enhancing the level of force transmission and enabling high curvature tendon routing. The performance of the sensorized tendons is explored in terms of strength (higher than 13N for the bare PM-FBG fiber tendon, up to 40N for the Kevlar-reinforced tendon under tensile loading), strain sensitivity (0.127 percent strain per newton for the bare PM-FBG fiber tendon, 0.04 percent strain per newton for the Kevlar-reinforced tendon), temperature stability, and friction-independent sensing behavior. Subsequently, the tendon is instrumented within an 18 Ga articulate NiTi cannula and evaluated under static and dynamic loading conditions, and within phantoms of varying stiffness for tissue-stiffness estimation. The results from this series of experiments serve to validate the effectiveness of the proposed tendon as a bi-modal sensing and actuation component for robot-assisted minimally invasive surgical instruments

Closed-loop control of soft continuum manipulators under tip follower actuation

Continuum manipulators, inspired by nature, have drawn significant interest within the robotics community. They can facilitate motion within complex environments where traditional rigid robots may be ineffective, while maintaining a reasonable degree of precision. Soft continuum manipulators have emerged as a growing subfield of continuum robotics, with promise for applications requiring high compliance, including certain medical procedures. This has driven demand for new control schemes designed to precisely control these highly flexible manipulators, whose kinematics may be sensitive to external loads, such as gravity. This article presents one such approach, utilizing a rapidly computed kinematic model based on Cosserat rod theory, coupled with sensor feedback to facilitate closed-loop control, for a soft continuum manipulator under tip follower actuation and external loading. This approach is suited to soft manipulators undergoing quasi-static deployment, where actuators apply a follower wrench (i.e., one that is in a constant body frame direction regardless of robot configuration) anywhere along the continuum structure, as can be done in water-jet propulsion. In this article we apply the framework specifically to a tip actuated soft continuum manipulator. The proposed control scheme employs both actuator feedback and pose feedback. The actuator feedback is utilized to both regulate the follower load and to compensate for non-linearities of the actuation system that can introduce kinematic model error. Pose feedback is required to maintain accurate path following. Experimental results demonstrate successful path following with the closed-loop control scheme, with significant performance improvements gained through the use of sensor feedback when compared with the open-loop case