Geometric control of 3D needle steering in soft-tissue

In this paper, a 3D automated needle steering system is presented that can enhance the performance of needle-based procedures. The system comprises a nonholonomic needle steering model and a nonlinear controller for 3D needle steering. First, a reduced-order needle steering model is presented. Next, a geometric reduction procedure is carried out to present the nonlinear control system in a transformed format. Finally, the transformed model is used to design a two-step controller. The controller first stabilizes the system on an equilibrium manifold of the system and later employs a switching law to stabilize it on an equilibrium point in the manifold. The former performs insertion of the needle up to a desired depth and the latter performs retraction/insertion motion that guides the needle toward a desired point at the given depth. Validation experiments are performed on a phantom and ex-vivo animal tissues and the results are compared with manual needle insertions performed by skilled surgeons. The mean error of our 3D needle steering system is 60% less than manual needle insertions.