Kinematic Modeling of an MRI-Compatible Concentric Steerable Needle Robot based on Screw Theory

Magnetic resonance imaging (MRI) technology provides high resolution stereotactic information for surgeons, which enables minimally invasive surgical operations. However, conventional straight needles cannot access target tissues without penetrating certain healthy ones. An MRI-compatible system deploying a so-called concentric tube needle which consists of a straight outer cannula, a helical shaped tube and a straight inner needle is proposed in this paper to tackle the aforementioned issue. A mechanism ensuring the required corkscrew-like motion of the concentric needle is designed and modeled first. Detailed models including forward and inverse kinematics, velocity kinematics, and quasi-static dynamics for the steerable needle are mathematically derived based on modern screw theory, which reveals the geometric relationships of robot motions simply and elegantly. Finally, a neurosurgical example is given to demonstrate the application scenario of the proposed system and derived kinematic models.