This letter presents the development and evaluation of concurrent control of a robotic system for less-invasive treatment of osteolytic lesions behind an acetabular implant. This system implements safety constraints including a remote center of motion, virtual walls, and joint limits while operating through the screw holes of the acetabular implant. The formulated linear constrained optimization problem ensures these constraints are satisfied while maintaining precise control of the tip of a Continuum Dexterous Manipulator attached to a positioning robot. Experiments evaluated the performance of the tip control method within an acetabular cup. The controller reliably reached a series of goal points with a mean error of 0.42 mm and a worst-case error of straying 1.0 mm from our path.