Partial estimation of needle tip orientation in generalized coordinates in ultrasound image-guided needle insertion

In many subcutaneous needle insertion procedures, measuring needle deflection is necessary in order to accurately guide the needle towards inner body targets. Typically, needle deflection measurement are obtained from 2D ultrasound images, which can only provide the needle tip position, however, having knowledge about the needle tip heading (orientation) is very valuable in predicting the needle's future path for planning and needle steering reasons. Due to the small diameter of the needles and the low resolution of ultrasound imaging, the direct measurement of the needle tip orientation is not a trivial task. This paper represents a model-based non linear observer for partial estimating the needle tip orientation during needle insertion procedures using image-based position measurements. The proposed method employs a 3D kinematic unicycle model expressed in generalized coordinates. Applying nonlinear transformations on system states, the linearized transformed system equations are utilized in the observer design procedure. However, due to the singularities imposed by these transformations, certain assumptions are made for the convergence proof of the observer. The proposed observer is tested in simulations and experiments. In experiments, the observer is fed by the needle tip position measurements, which are obtained from real-time ultrasound images.