The position of a movable element such as the end of a robot arm (10) which has several degrees of freedom, being mounted on a base (11) and including a wrist mechanism, is determined by installing a multiplicity of base targets (32, 74) around the base of the robot, and a multiplicity of arm targets (42, 74) around the base (14) of the wrist mechanism (15), and an optical means (90) that moves with the movable element to determine the positions of at least some of the base targets and of at least some of the arm targets. The optical means may be a laser tracker or a camera system (90), and it may be mounted on the part (13) of the robot arm to which the base (14) of the wrist mechanism (15) is connected. This enables existing robots (10) to achieve absolute positional accuracy relative to a fixed external frame of reference.