An apparatus includes a reference fixture. The reference fixture includes a joint, and a joint tracker to track motion of the joint. The apparatus also includes a surgical instrument. A tether is connected between the joint and the surgical instrument. A shape sensor extends from the reference fixture through the joint, through the tether, and into the surgical instrument. The shape sensor is substantially free of twist. The joint tracker measures the motion of the joint. Information from the shape sensor in combination with information from the joint tracker provides absolute three-dimensional information relative to the reference fixture, i.e., provides absolute three-dimensional information in a fixed world reference frame.