An Integrator-Backstepping Control Approach for Three-Dimensional Needle Steering

In this paper, we design a set of two-dimensional (2-D) needle steering controllers used to minimize the 3-D deflection of a flexible, bevel-tipped needle. The controllers are based on a nonlinear design tool known as integrator-backstepping. The needle's deflection is split into its two 2-D planar problems, each of which is then governed by its own, separate controller. One controller, called vertical deflection control (VDC), steers the needle so that it deflects primarily along the vertical plane. The second controller, called horizontal deflection control (HDC), steers the needle so that it deflects primarily along the horizontal plane. Our 3-D steering algorithm combines the effect of these two controllers based on the current magnitude of the deflection along each plane. Using an 18 gauge brachytherapy needle, we tested our proposed method on a phantom tissue composed of liquid plastic, and a two-layer biological tissue formed of gelatin and ex vivo beef. Without needle steering, the average needle deflection was 11.2 mm. Using the proposed 3-D needle steering technique, the deflection decreased to an average of 0.5 mm.