Robust H∞ Image-Based Control of Flexible Tip-Steerable Needles with Time-Varying Delays

This paper investigates the image guidance control of flexible tip-steerable needles subject to random time delay of control input. The aim of the bevel-tip needle guidance in this paper is to steer the needle tip to a planar plane. Therefore, the 6-degree-of-freedom (DOF) model is reduced to a 3-DOF one. Furthermore, the reduced order model is transformed to a linear system by feedback linearization. In the setup of the needle guidance task, the states of the needle tip are estimated from the captured image. As the processing of the image and estimation of needle states are time consuming and the feedback controller using the estimated states. These delays are modeled as random delays and considered in a closed loop system. To address the random time delay, a robust $\mathcal{H}_{\infty}$ is proposed for the needle tip guidance task, which is novel in the bevel-tip needle guidance problem. Moreover, simulation results are provided to verify the effectiveness of the proposed time-delayed robust controller by comparing with the commonly used $\mathcal{H}_{\infty}$ controller without considering time delay.