A refueling machine having relative positioning capability for refueling a nuclear reactor. The refueling machine includes a pair of articulated arms mounted on a refueling bridge. Each arm supports a respective telescoping mast. Each telescoping mast is designed to flex laterally in response to application of a lateral thrust on the end of the mast. A pendant mounted on the end of the mast carries an air-actuated grapple, television cameras, ultrasonic transducers and waterjet thrusters. The ultrasonic transducers are used to detect the gross position of the grapple relative to the bail of a nuclear fuel assembly in the fuel core. The television cameras acquire an image of the bail which is compared to a pre-stored image in computer memory. The pendant can be rotated until the television image and the pre-stored image match within a predetermined tolerance. Similarly, the waterjet thrusters can be used to apply lateral thrust to the end of the flexible mast to place the grapple in a fine position relative to the bail as a function of the discrepancy between the television and pre-stored images.