3D motion planning algorithms for steerable needles using inverse kinematics

Abstract

Steerable needles can be used in medical applications to reach targets behind sensitive or impenetrable areas. The kinematics of a steerable needle are nonholonomic and, in 2D, equivalent to a Dubins car with constant radius of curvature. In 3D, the needle can be interpreted as an airplane with constant speed and pitch rate, zero yaw, and controllable roll angle. We present a constant-time motion planning algorithm for steerable needles based on explicit geometric inverse kinematics similar to the classic Paden-Kahan subproblems. Reachability and path competitivity are analyzed using analytic comparisons with shortest path solutions for the Dubins car (for 2D) and numerical simulations (for 3D). We also present an algorithm for local path adaptation using null-space results from redundant manipulator theory. The inverse kinematics algorithm can be used as a fast local planner for global motion planning in environments with obstacles, either fully autonomously or in a computer-assisted setting. © 2009 Springer-Verlag.