Linear Robust Control in Indirect Deformable Object Manipulation

Abstract

<p>Robotic platforms have several characteristics such as speed and precision that make them enticing for use in medical procedures. Companies such as Intuitive Medical and Titan Medical have taken advantage of these features to introduce surgical robots for minimally invasive procedures. Such robots aim to reduce procedure and patient recovery times. Current technology requires platforms to be master-slave manipulators controlled by a surgeon, effectively converting the robot into an expensive surgical tool. Research into the interaction between robotic platforms and deformable objects such as human tissue is necessary in the development of autonomous and semi-autonomous surgical systems. This thesis investigates a class of robust linear controllers based on a worst case performance measure known as the $H_{\infty}$ norm, for the purpose of performing so called Indirect Deformable Object Manipulation (IDOM). This task allows positional regulation of regions of interest in a deformable object without directly interacting with them, enabling tasks such as stabilization of tumors during biopsies or automatic suturing. A complete approach to generating linear $H_{\infty}$ based controllers is presented, from derivation of a plant model to the actual synthesis of the controller. The introduction of model uncertainty requires $\mu$ synthesis techniques, which extend $H_{\infty}$ designs to produce highly robust controller solutions. In addition to $H_{\infty}$ and $\mu$ synthesis designs, the thesis presents an approach to design an optimal PID controller with gains that minimize the $H_{\infty}$ norm of a weighted plant. The three control approaches are simulated performing set point regulation in $\text{MATLAB}^{TM}$'s $simulink$. Simulations included disturbance inputs and noises to test stability and robustness of the approaches. $H_{\infty}$ controllers had the best robust performance of the controllers simulated, although all controllers simulated were stable. The $H_{\infty}$ and PID controllers were validated in an experimental setting, with experiments performed on two different deformable synthetic materials. It was found that $H_{\infty}$ techniques were highly robust and provided good tracking performance for a material that behaved in a relatively elastic manner, but failed to track well when applied to a highly nonlinear rubber compound. PID based control was outperformed by $H_{\infty}$ control in experiments performed on the elastic material, but proved to be superior when faced with the nonlinear material. These experimental findings are discussed and a linear $H_{\infty}$ control design approach is proposed.</p>