Task-Induced Reduction with Applications to Needle Steering

Vinutha Kallem
Mechanical Engineering Department
Johns Hopkins University

ABSTRACT:
What if sensitive organs prevents a physician from accessing a percutaneous target using a straight, rigid needle? One promising solution involves steering flexible bevel-tip needles. These needles introduce exciting robotics and control systems challenges because the needle tip evolves on a Lie group, and the system exhibits a high degree of nonholonomy.

In this work, we present image-guided controllers for steerable needles to improve the accuracy of needle insertions. We build upon a previously proposed needle steering model to develop nonlinear observer-based controllers to drive the needle tip to a desired subspace. These controllers are designed to work in conjunction with subspace planners for the needle tip to reach a desired location in human tissue. We show that the tasks of these controllers induces symmetry, thus resulting in a reduced system which greatly simplifies controller and observer design. We propose a method to perform such reductions for generic nonholonomic kinematic systems on Lie groups with left-invariant vector fields. This technique is used to develop controllers for curve-following of a unicycle and subspace-following in needle steering. We show that this "task-induced" reduction lifts to mechanical systems.