Concentric tube robots are catheter-sized robots that are ideally suited for navigating along natural anatomical pathways and treating deep-seated pathologies. Their telemanipulation in dynamic environments requires on-line computation of inverse kinematics with simultaneous avoidance of anatomical obstacles. Moreover, unstable configurations, which arise for elongated curved robots that navigate extremely tortuous paths, must be avoided. To achieve on-line computations, existing work has investigated Jacobian approximations and configuration-space precomputation. This paper leverages the state-of-the-art multi-core computer architectures to deliver real-time local inverse kinematics solutions using the established concentric tube robot mechanics models while avoiding both instabilities and anatomical collisions. Furthermore, it considers frictional active constraints for concentric tube robots, i.e. viscoelastic force fields that guide the operator away from obstacles and towards safe configurations. The value of the proposed framework is demonstrated on realistic clinical scenarios.