Exploiting flexible links in surgical applications: from interaction control to needle insertion

This thesis aims to contribute to the goal of improving autonomy in robotic surgery, focusing on the following challenges: (1) the development of accurate models for flexible surgical tools, (2) the investigation of properties for the real-time control of surgical instruments during the execution of minimally invasive robotic surgery. In the first part of the thesis, we investigate interaction control algorithms that take advantage of the inherent flexibility of commonly used surgical instruments. We leverage continuum mechanics theory and high-order approximants to model the surgical instrument and investigate passivity and stability properties. For the first time, this thesis theoretically demonstrates that force control based on a collocated feedback signal from a continuum flexible beam can be passive with respect to the environment port, meaning that stability can be guaranteed in any passive environment. On the other hand, when the feedback is non-collocated, passivity may be hampered, and these cases are analyzed using a high-order lumped approximant. An experimental validation using real-world surgical instruments is provided, showing coherence with theoretical expectations. In the second part, we focus on modelling the interaction between a bevel-tip biopsy needle and the surrounding tissue to enable automated needle insertion during a robotic prostate biopsy. In this context, the objective is to estimate the deflection of the tip during insertion and to plan the trajectory accordingly. An experimental comparison is conducted to assess the accuracy of existing models in predicting needle deflection.