  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.
