Paper:

# Calibration of Kinematic Parameters of Robot Arm Using Laser Tracking System: Compensation for Non-Geometric Errors by Neural Networks and Selection of Optimal Measuring Points by Genetic Algorithm

## Seiji Aoyagi^{*}, Masato Suzuki^{*}, Tomokazu Takahashi^{*},

Jun Fujioka^{**}, and Yoshitsugu Kamiya^{***}

^{*}Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan

^{**}Ishikawa National College of Technology, Ta-1, Kitatyujo, Tsubata-machi, Kahoku, Ishkawa 929-0392, Japan

^{***}Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan

Offline teaching based on high positioning accuracy of a robot arm is desired to take the place of manual teaching. In offline teaching, joint angles are calculated using a kinematic model of the robot arm. However, a nominal kinematic model does not consider the errors arising in manufacturing or assembly, not to mention the non-geometric errors arising in gear transmission, arm compliance, etc. Therefore, a method of precisely calibrating the parameters in a kinematic model is required. For this purpose, it is necessary to measure the three-dimensional (3-D) absolute position of the tip of a robot arm. In this paper, a laser tracking system is employed as the measurement apparatus. The geometric parameters in the robot kinematic model are calibrated by minimizing errors between the measured positions and the predicted ones based on the model. The residual errors caused by non-geometric parameters are further reduced by using neural networks, realizing high positioning accuracy of sub-millimeter order. To speed up the calibration process, a smaller number of measuring points is preferable. Optimal measuring points, which realize high positioning accuracy while remaining small in number, are selected using Genetic Algorithm (GA).

*Int. J. Automation Technol.*, Vol.6, No.1, pp. 29-37, 2012.

- [1] B. W. Mooring, Z. S. Roth, and M. R. Driels, “Fundamentals of Manipulator Calibration,” Wiley & Sons, New York, 1991.
- [2] B.W.Mooring and S. S. Padavala, “The Effect of Kinematic Model Complexity on Manipulator Accuracy,” in Proc. IEEE Int. Conf. Robotics and Automation, pp. 593-598, 1989.
- [3] D. E. Whitney, C. A. Lozinski, and J. M. Rourke, “Industrial Robot Forward Calibration Method and Results,” J. Dyn. Sdyst. Meas. Contr., Vol.108, No.1, pp. 1-8, 1986.
- [4] R. P. Judd and Al. B. Knasinski, “A Technique to Calibrate Industrial Robots with Experimental Verification,” IEEE Trans. Robotics and Automation, Vol.6, No.1, pp. 20-30, 1990.
- [5] H. W. Stone, “Kinematic Modeling, Identification, and Control of Robotic Manipulators,” Kluwer Academic Publishers, Norwell, Mass. 1987.
- [6] S. Komai and S. Aoyagi, “Calibration of Kinematic Parameters of a Robot Using Neural Networks by a Motion Capture System,” in Proc. Annual Spring Meeting The JSPE, pp. 1151-1152, 2007. (in Japanese)
- [7] Y. Koseki, T. Arai, K. Sugimoto, T. Takatsuji, and M. Goto, “Accuracy Evaluation of Parallel Mechanism Using Laser Tracking Coordinate Measuring System,” J. Society of Instrument and Control Engineers, Vol.34, No.7, pp. 726-733, 1998. (in Japanese)
- [8] J. Fujioka, S. Aoyagi, K. Ishii, H. Seki, and Y. Kamiya, “Study on Robot Calibration Using a Laser Tracking System (2nd Report) – Discussion on How to Select Parameters, Number of Measurement and Pose of Measurement in Multiple Positioning Method –,” J. The Japan Society for Precision Engineering, Vol.67, No.4, pp. 676-682, 2001. (in Japanese)
- [9] J. Fujioka, S. Aoyagi, H. Seki, and Y. Kamiya, “Development of Orientation Measuring System of a Robot Using a Gyroscope (2nd Report) – Proposal of Position and Orientation Calibration Method of a Robot Using Both Laser Tracking System and Gyroscope –,” J. The Japan Society for Precision Engineering, Vol.67, No.10, pp. 1657-1663, 2001. (in Japanese)
- [10] J. H. Jang, S. H. Kim, and Y. K. Kwak, “Calibration of Geometric and Non-Geometric Errors of an Industrial Robot,” Robotica, Vol.19, pp. 311-321, 2001.
- [11] K. Maekawa, “Calibration for High accuracy of Positioning by Neural Networks,” J. Robotics Society of Japan, Vol.13, No.7, pp. 35-36, 1995. (in Japanese)
- [12] W. Tanaka, T. Arai, K. Inoue, Y. Mae, and Y. Koseki, “Calibration Method with Simplified Measurement for Parallel Mechanism,” J. The Japan Society of Mechanical Engineers, Vol.71, No.701, pp. 206-213, 2005. (in Japanese)
- [13] J. Imoto, Y. Takeda, H. Saito, and K. Ichiryu, “Optimal Kinematic Calibration of Robots Based on the Maximum Positioning-Error Estimation,” J. The Japan Society of Mechanical Engineers, Vol.74, No.748, pp. 243-250, 2008. (in Japanese)
- [14] D. Daney, Y. Papegay, and B. Madeline, “Choosing Measurement Poses for Robot Calibration with the Local Convergence Method and Tabu Search,” The Int. J. Robotics Research, Vol.24, No.6, pp. 501-518, 2005.
- [15] J. Borm and C. Menq, “Determination of Optimal Measurement Configurations for Robot Calibration Based on Observability Measure,” The Int. J. Robotics Research, Vol.10, No.1, pp. 51-63, 1991.
- [16] M. Ishii, S. Sakane, M. Kakikura, and Y. Mikami, “Robot Manipulator Calibration for 3D Model Based Robot systems,” J. Robotics Society of Japan, Vol.7, No.2, pp. 74-83, 1988. (in Japanese).
- [17] K. Lau, R. J. Hocken, and W. C. Haight, “Automatic Laser Tracking Interferometer System for Robot Metrology,” Precision Engineering, Vol.8, No.1, pp. 3-8, 1986.
- [18] J. Denavit and R. S. Hartenberg, “A Kinematic Notation for Lower Pair Mechanism Based on Matrices,” ASME J. Applied Mechanics, pp. 215-212, 1955.
- [19] M. Riedmiller and H. Braun, “A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm,” in Proc. IEEE Int. Conf. Neural Networks, pp. 586-591, 1993.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.