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

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

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

Implicit active constraints for safe and effective guidance of unstable concentric tube robots

Safe and effective telemanipulation of concentric tube robots is hindered by their complex, non-intuitive kinematics. In order for clinicians to operate these robots naturally, guidance schemes in the form of attractive and repulsive constraints can simplify task execution. The real-time seamless calculation and application of guidance, however, requires computationally efficient algorithms that solve the non-linear inverse kinematics of the robot and guarantee that the commanded robot configuration is stable and sufficiently away from the anatomy. This paper presents a multi-processor framework that allows on-the-fly calculation of optimal safe paths based on rapid workspace and roadmap precomputation. The realtime nature of the developed software enables complex guidance constraints to be implemented with minimal computational overhead. A clinically challenging user study demonstrates that the incorporated guiding constraints are highly beneficial for fast and accurate navigation with concentric tube robots

Data-driven modelling and control of concentric tube robots with application in distal lung sampling

This research aims to explore the use of Concentric Tube Robots (CTRs) as a novel alternative to needle-based interventions in order to make these procedures more accurate and repeatable. CTRs due to their small footprint, compliance, and dexterity have been proposed for several minimally-invasive robotic surgeries. As a novel flexible robot, it has the potential to reach distal parts of the human lung that are difficult or impossible to reach with conventional needle-based interventions. There are, however, still significant challenges associated with the motion and position control of CTRs. Commonly used model-based control approaches are computationally expensive to solve and often employ simplified geometric/dynamic assumptions, which could be inaccurate in the presence of unmodelled disturbances and external interaction forces. Consequently, this work explores different control strategies to overcome these limitation. This is achieved by first building a simulation environment based on a computationally improved kinematic model that enables real-time control. Then, data-driven control approaches are investigated in order to provide accurate position control in the presence of uncertainties in the system. Finally, a three-phase affordance-aware motion planner is proposed to demonstrate the feasibility of using CTRs for percutaneous lung biopsy. According to this, the first part of this work concentrates on computationally efficient real-time modelling and simulation of CTRs. In order to achieve this, two approaches are taken. The first one introduces a method that can rapidly estimate the solution of the kinematic model, while the second approach focuses on implementing the existing model in a computationally efficient way in Robot Operating System (ROS) using C++. Second, this work explores data-driven solutions to control the robot without relying on the kinematic model. Consequently, two data-driven solutions are proposed, namely the Hybrid Dual Jacobian approach and the Extended Dynamic Mode Decomposition (EDMD) algorithm. The hybrid controller combines the advantages of model-based and data-driven control approaches, while the EDMD provides a completely model-free solution to control the robot. Both controllers are capable of rapidly predicting the robot’s nonlinear dynamics from a limited data set and offer consistent control under external loading and in the presence of obstacles. The third part of the thesis explores the use of CTRs in the context of distal lung sampling. This work demonstrates that CTRs are suitable for Needle-Based Optical Endomicroscopy where a CTR steers a fluorescent imaging probe with cellular and bacterial imaging capability inside soft tissue. Then, it is also demonstrated that a CTR can be used as a Steerable Needle to reach a target deep inside the tissue. To achieve these tasks, a motion planner is essential due to the fact that a CTR is only capable of reaching specific points in its workspace and there are a number of configurations where the robot becomes unstable. Based on this, a threeii phase affordance-aware motion planner algorithm is developed. The motion planner selects the best entry point for a specific task. Based on the selected entry point it first generates a stable trajectory from the robot’s initial configuration to the selected entry point. Then, a feasible trajectory is generated from the entry point to the target. Finally, the proposed datadriven control algorithm is applied to autonomously steer the robot on the generated trajectory toward the target region for endomicroscopic imaging