Image-Guided Observer-Based Control For Needle Steering

In robot-assisted needle insertion procedures, in order to steer a beveled-tip needle toward a target location, the needle tip pose is required to be used as feedback. Mathematically, the needle tip pose can be expressed as a position vector and a rotation matrix that represents the orientation of the needle. Using the traditional two dimensional (2D) ultrasound imaging modality, since the images are low in resolution and the needles are small in diameter, only the position of the needle tip can be measured, and the orientation information cannot be directly extracted. This paper presents a nonlinear observer for estimating the needle tip orientation based on needle three dimensional (3D) kinematic equations and the position data measured from ultrasound images. Assuming bounded inputs for the needle model, it is shown that the observation error remains bounded. The performance of the observer is shown in an observer/ controller feedback loop. The stability and convergence of the observer/controller combination are shown by solving Linear Matrix Inequality (LMI) optimizations. Experiments performed for different tissue types and different needle insertion goals verify the effectiveness of our method.