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)

Deep Reinforcement Learning for Concentric Tube Robot Path Planning

As surgical interventions trend towards minimally invasive approaches, Concentric Tube Robots (CTRs) have been explored for various interventions such as brain, eye, fetoscopic, lung, cardiac and prostate surgeries. Arranged concentrically, each tube is rotated and translated independently to move the robot end-effector position, making kinematics and control challenging. Classical model-based approaches have been previously investigated with developments in deep learning based approaches outperforming more classical approaches in both forward kinematics and shape estimation. We propose a deep reinforcement learning approach to control where we generalise across two to four systems, an element not yet achieved in any other deep learning approach for CTRs. In this way we explore the likely robustness of the control approach. Also investigated is the impact of rotational constraints applied on tube actuation and the effects on error metrics. We evaluate inverse kinematics errors and tracking error for path following tasks and compare the results to those achieved using state of the art methods. Additionally, as current results are performed in simulation, we also investigate a domain transfer approach known as domain randomization and evaluate error metrics as an initial step towards hardware implementation. Finally, we compare our method to a Jacobian approach found in literature.Comment: 13 pages, 13 figures. Accepted to IEEE Transactions on Medical Robotics and Bionics Symposium Special Issu

Deep Reinforcement Learning for Concentric Tube Robot Control with a Goal-Based Curriculum

Concentric Tube Robots (CTRs), a type of continuum robot, are a collection of concentric, pre-curved tubes composed of super elastic nickel titanium alloy. CTRs can bend and twist from the interactions between neighboring tubes causing the kinematics and therefore control of the end-effector to be very challenging to model. In this paper, we develop a control scheme for a CTR end-effector in Cartesian space with no prior kinematic model using a deep reinforcement learning (DRL) approach with a goal-based curriculum reward strategy. We explore the use of curricula by changing the goal tolerance through training with constant, linear and exponential decay functions. Also, relative and absolute joint representations as a way of improving training convergence are explored. Quantitative comparisons for combinations of curricula and joint representations are performed and the exponential decay relative approach is used for training a robust policy in a noise-induced simulation environment. Compared to a previous DRL approach, our new method reduces training time and employs a more complex simulation environment. We report mean Cartesian errors of 1.29 mm and a success rate of 0.93 with a relative decay curriculum. In path following, we report mean errors of 1.37 mm in a noise-induced path following task. Albeit in simulation, these results indicate the promise of using DRL in model free control of continuum robots and CTRs in particular

Deep Reinforcement Learning for Concentric Tube Robot Path Following

As surgical interventions trend towards minimally invasive approaches, Concentric Tube Robots (CTRs) have been explored for various interventions such as brain, eye, fetoscopic, lung, cardiac, and prostate surgeries. Arranged concentrically, each tube is rotated and translated independently to move the robot end-effector position, making kinematics and control challenging. Classical model-based approaches have been previously investigated with developments in deep learning-based approaches outperforming more classical approaches in both forward kinematics and shape estimation. We propose a deep reinforcement learning approach to control where we generalize across two to four systems, an element not yet achieved in any other deep learning approach for CTRs. In this way, we explore the likely robustness of the control approach. Also investigated is the impact of rotational constraints applied on tube actuation and the effects on error metrics. We evaluate inverse kinematics errors and tracking errors for path-following tasks and compare the results to those achieved using state-of-the-art methods. Additionally, as current results are performed in simulation, we also investigate a domain transfer approach known as domain randomization and evaluate error metrics as an initial step toward hardware implementation. Finally, we compare our method to a Jacobian approach found in the literature

Data-efficient Non-parametric Modelling and Control of an Extensible Soft Manipulator

Data-driven approaches have shown promising results in modeling and controlling robots, specifically soft and flexible robots where developing physics-based models are more challenging. However, these methods often require a large number of real data, and gathering such data is time-consuming and can damage the robot as well. This paper proposed a novel data-efficient and non-parametric approach to develop a continuous model using a small dataset of real robot demonstrations (only 25 points). To the best of our knowledge, the proposed approach is the most sample-efficient method for soft continuum robot. Furthermore, we employed this model to develop a controller to track arbitrary trajectories in the feasible kinematic space. To show the performance of the proposed approach, a set of trajectory-tracking experiments has been conducted. The results showed that the robot was able to track the references precisely even in presence of external loads (up to 25 grams). Moreover, fine object manipulation experiments were performed to demonstrate the effectiveness of the proposed method in real-world tasks. Finally, we compared its performance with common data-driven approaches in seen/useen-before trajectory tracking scenarios. The results validated that the proposed approach significantly outperformed the existing approaches in unseen-before scenarios and offered similar performance in seen-before scenarios

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