Constrained motion control of robotic end-effectors is essential for safe operation in confined spaces such as the urinary bladder. This paper presents the clinical motivation for the development of new control algorithms for robotic-assisted transurethral bladder resection and surveillance using multisegment continuum robots. The anatomy, workspace, and access constraints for this procedure are identified and used as a guideline for the design of the telesurgical system and its control architecture. Constraints are mapped into the configuration space of the robot rather than in task space simplifying the modeling and the enforcement of virtual fixtures. The redundancy resolution is autonomously modified in order to exploit the remaining degrees of freedom using task priority. These methods are validated on a glass model of urinary bladder.