Robot-Assisted Needle Steering Using a Control Theoretic Approach

Abstract

This paper presents a new 2D motion planner for steering flexible needles inside relatively rigid tissue. This approach uses a nonholonomic system approach, which models tissue-needle interaction, and formulates the problem as a Markov Decision Process that is solvable using infinite horizon Dynamic Programming. Unlike conventional numerical solvers such as the value iterator which inherently suffers from the curse of dimensionality for processing large-scale models, partitioned-based solvers show promising numerical performance. Given the locations of the obstacles and the targeted area, the proposed solver provides a descent solution where high spatial or angular resolution is required. As theoretically expected, it is shown how prioritized partitioning increases computational performance compared to the generic value iteration which has been used in an existing steering approach. Starting from any initial condition in the workspace, this method enables the needle to reach its target and avoid collisions with obstacles through selecting the shortest path with the least number of turning points thereby causing less trauma. In this paper, emphasis is given to the control aspects of the problem rather than to biomedical issues. Experimental results using an artificial phantom show that the method is capable of positioning the needle tip at the targeted area with an acceptable level of accuracy.