A medical examination and treatment apparatus includes a robot operable to control a tool, and an internal position-determination system to measure a position of the tool by determining a setting of adjusting elements of the robot. The apparatus further includes an external position-determination system to measure the position of the tool, and a position monitoring system to compare the position of the tool determined by the internal position-determination system with the position of the tool determined by the external position-determination system. A mobility of the tool is restricted if an adjustable threshold relating to deviations between position measurements is exceeded.