Abstract-Concentric tube robots are catheter-sized robots that can navigate natural pathways to reach deep anatomical locations. Their intraoperative telemanipulation in dynamic environments requires on-line computation of inverse kinematics with simultaneous avoidance of anatomical collisions. Moreover, unstable configurations, which arise for elongated curved robots that navigate extremely tortuous paths, must be avoided. This paper leverages state-of-the-art multi-core computer architectures to deliver real-time inverse kinematics solutions that avoid robot instabilities and anatomical collisions. Furthermore, it introduces frictional active constraints to concentric tube robots for intraoperative assistance in navigation. Our framework is evaluated in silico through clinical scenarios from heart surgery and neurosurgery.