Nonholonomic Modeling of Needle Steering

As a flexible needle with a bevel tip is pushed through soft tissue, the asymmetry of the tip causes the needle to bend. We propose that, by using nonholonomic kinematics, control and path planning, an appropriately designed needle can be steered through tissue to reach a specified 3D target. Such steering capability will enhance targeting accuracy and markedly improve outcomes for percutaneous therapies, facilitate research on therapy effectiveness, and enable new minimally invasive techniques. In this paper, we consider a first step toward active needle steering: design and experimental validation of a nonholonomic model for steering flexible needles with bevel tips. The model generalizes the standard three degree-of-freedom (DOF) nonholonomic bicycle model to 6 DOF using Lie group theory. Model parameters were fit using experimental data, which were acquired via a robotic device designed for the specific purpose of inserting a flexible needle. The resulting parametric fit quantitatively validates the bevel tip needle steering model, enabling future research in flexible needle path planning, control and simulation.