Path Planning for Concentric Tube Robots: a Toolchain with Application to Stereotactic Neurosurgery

Abstract: We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clouds. Then, the nonlinear and highly nonconvex optimal control problem is solved by introducing a homotopy on the obstacle positions where at one extreme of the parameter the obstacles are removed from the operating space, and at the other extreme they are located at their intended positions. We present a detailed example (with more than a thousand obstacles) from stereotactic neurosurgery with real-world data obtained from labelled MPRI scans. Keywords: optimal control, non-linear programming, homotopy methods, optimal path planning, concentric tube robots, stereotactic neurosurgery 1. INTRODUCTION by finding paths of connected voxels that the robot can traverse, subject to constraints on its curvature.