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Needle insertion is a critical aspect of many medical treatments, diagnostic methods, and scientific studies, and is considered to be one of the simplest and most minimally invasive medical procedures. Robot-assisted needle steering has the potential to improve the effectiveness of existing medical procedures and enable new ones by allowing increased accuracy through more dexterous control of the needle-tip path and acquisition of targets not accessible by straight-line trajectories. In this article, we describe a robot-assisted needle-steering system that uses three integrated controllers: a motion planner concerned with guiding the needle around obstacles to a target in a desired plane, a planar controller that maintains the needle in the desired plane, and a torsion compensator that controls the needle-tip orientation about the axis of the needle shaft.