System Design and Elastic Stability Modeling of Transendoscopic Continuum Robots
Hendrick, Richard Joseph
The motivation for this dissertation is to provide surgeons with more capable tools during minimally invasive surgery. Specifically, this work is focused on the design of robotic systems that provide flexible, multi-arm robotic manipulation through rigid endoscopes. Two custom systems are designed, optimized, and experimentally evaluated: one for laser-based prostate surgery, and one for removal of cysts from the center of the brain. These designs are heavily motivated by the idea that these robotic systems should be small, compact, hand-held devices to have minimal impact on the surgical workflow and be more easily integrated into the operating room. A challenge with these flexible manipulators is that they are susceptible to elastic instability, which means they can jump in an uncontrolled way from one location to another. This dissertation explores this phenomenon in detail from a modeling perspective and derives (1) a technique, based on bifurcation theory, to guarantee instability avoidance throughout the manipulator's workspace, and (2) a relative stability measure which can be used to predict when the manipulator will lose elastic stability. This analysis also provides insights into how stability affects the design, control, stiffness, and dexterity of these flexible manipulators. This work also examines control strategies that use 'extra', or redundant, degrees of freedom to accomplish secondary objectives with these flexible manipulators. In addition to following a desired trajectory, we investigate avoiding instability and maximizing stiffness or compliance. We show stabilization of trajectories that would have otherwise been unstable, and show that designs that were previously considered off-limits because of stability concerns, may still be very useful when controlled by a stability-aware controller.