Model study on the traceability of the accuracy of an industrial manipulator to an external measurement system based on the Banach fixed-point theorem

Industrial manipulators have good repeatability but poor accuracy. To improve the accuracy of an industrial manipulator, using an external large-scale measurement system to provide the accurate positioning information is another good selection in addition to the error mapping and other calibration methods. In this paper, we present the model explaining how the accuracy of a manipulator is traced back to an external measurement system. The model analyzes the traceability problem in two parts: the position and the attitude. In both parts, movement sequences of the manipulator are constructed. The accuracy of the manipulator can be traced back to the external measurement system as long as the sequences of movements are convergent. However, the sequences of movements are not always convergent unless we provide a reasonable condition. In this paper, we find a conservative estimate of the condition by the Banach fixed-point theorem. Then, we set up an experiment to verify the accuracy traceability model. The results indicate that the proposed model exists, and is very effective in improving the positioning accuracy of a manipulator compared to conventional methods.