Robert J . Webster III

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 could enhance targeting accuracy and may improve outcomes for percutaneous therapies, facilitate research on therapy effectiveness, and eventually 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 unicycle and bicycle models to 6 DOF using Lie group theory. Model parameters are fit using experimental data, acquired via a robotic device designed for the specific purpose of inserting and steering a flexible needle. The experiments quantitatively validate the bevel-tip needle steering model, enabling future research in flexible needle path planning, control, and simulation. KEY WORDS—nonholonomic system, steerable needle, surgical robot, medical robot, path planning, Lie group, Lie algebra