Full Order High Gain Observer Design for Image-Guided Robotic Flexible Needle Steering

This paper represents a full state observer for the imaged guided robotic flexible needle. In many minimally invasive surgeries flexible needles are utilized, but because of the low accuracy of the imaging systems and needle tip size, the orientation of the needle cannot be measured directly. On the other hand, most of the proposed controllers need needle orientation in feedback law and thus, they are designed based on this fact that these states are directly available. According to the importance of this issue, in this paper a high-gain full observer is proposed and its stability is analyzed. Furthermore, it has been shown that the tracking error of any stable controller under some assumptions will remain bounded in case of utilizing observed states instead of the real states.

I. Introduction

Nowadays, robot-assisted surgery has significant influence on the minimally invasive surgeries. This comes from its precision, optimum and stunning performance. Using flexible needles in low-invasive surgical procedures is considered due to its advantages such as less postoperative pain, shorter hospital stay, faster recovery and so on. The effectiveness of such surgical operations relies on the precision of the measurement system as well as mathematical models. However, depending on the types of surgical sensors which are usually visual equipment, only the needle position can be determined and due to the small tip needle and the presence of measurement noise, it may not be possible to extract the orientation of the needle tip. It is notable that the medical autonomous systems are vulnerable to various disturbances [1] especially in flexible needle which is interacting with deformable tissue [2]. Based on these facts, to steer the needle it is necessary to estimate the states which are not available. From the control point of view, observers can be employed for unmeasurable states using the dynamic behavior of the system as well as measurable outputs. The only approach for steering needle on a straight path which does not need needle orientation is duty-cycled needle base rotation method [3], [4].