Compliance Characterization and Specification for Surgical Continuum Robots via Modeling, Control, and Design
The goal of this dissertation is to develop tools for surgeons that provide better access, dexterity, and performance during minimally invasive surgery. This work focuses on a class of thin, flexible devices called continuum robots. Continuum robots have garnered significant interest as medical devices due to their small size, end effector dexterity, and ability to navigate narrow, curved lumens. Kinematic and mechanics-based models are essential for capturing their shape and behavior, which can be complex due to their flexible nature and elastic materials. In this dissertation, models are developed and employed to solve design, compliance, and control problems for surgical continuum robots. This work seeks to characterize compliance behavior and utilize this understanding in the design process and during real-time control. Parallel continuum robots seek to enhance the stiffness of serial continuum robots by using multiple elastic backbones. Chapter 2 describes a new class of parallel continuum robot made up of multiple flexible needles that incorporates the ability to reconfigure the arrangement of its elastic elements for changing task requirements. A mechanics-based model and sensing framework are developed and experimentally validated to enable control and shape sensing of multi-needle robots. This model is a key contribution for future research on this new class of robot, as it provides the tools necessary for analyzing and designing the dexterity and compliance of the system, and for controlling physical hardware. This dissertation also describes a control algorithm for continuum robots that resolves redundancy (extra degrees of freedom compared to the primary task) to simultaneously accomplish secondary goals during position control. In Chapter 3, the algorithm is applied to concentric tube robots, whose nested, precurved tubes can store up torsional energy and undesirably "snap" from one configuration to another. This controller avoids unstable configurations during position control and is implemented with a simple resolved rates approach. We demonstrate that an otherwise-unstable, high-curvature robot can be safely controlled. In addition, the algorithm can incorporate compliance secondary objectives such as tip compliance optimization. Tool triangulation is a major challenge during endoscopic surgery. Standard tools extend straight out from the endoscope rather than angling towards the center of the workspace. Chapter 4 presents a design method for steerable sheaths, made from flexible tubes with asymmetric stiffness, for contact-aided tool triangulation. We design a serpentine material removal pattern and leverage self-contact of the resulting slots to create a multi-sheath robot. The proximal sheaths have a contact-aided triangulation pose and enable independent control of the nested distal sheaths. Robotic control handles are designed for controlling this bimanual system during endoscopic submucosal dissection.