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Identifying the Kinematic Parameters of Hexapod Machine Tool

Authors: M. M. Agheli, M. J. Nategh


Hexapod Machine Tool (HMT) is a parallel robot mostly based on Stewart platform. Identification of kinematic parameters of HMT is an important step of calibration procedure. In this paper an algorithm is presented for identifying the kinematic parameters of HMT using inverse kinematics error model. Based on this algorithm, the calibration procedure is simulated. Measurement configurations with maximum observability are decided as the first step of this algorithm for a robust calibration. The errors occurring in various configurations are illustrated graphically. It has been shown that the boundaries of the workspace should be searched for the maximum observability of errors. The importance of using configurations with sufficient observability in calibrating hexapod machine tools is verified by trial calibration with two different groups of randomly selected configurations. One group is selected to have sufficient observability and the other is in disregard of the observability criterion. Simulation results confirm the validity of the proposed identification algorithm.

Keywords: Observability, Calibration, parallel robot, Hexapod Machine Tool (HMT), InverseKinematics Error Model, ParameterIdentification

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[1] Benjamin W.Mooring and Zvi S. Roth and Morris R. Driels, "Fundamentals of Manipulator Calibration", John Wiely & Sons, New York, 1991.
[2] H. Zhuang, Y. Jiahua, and O. Masory, "Calibration of Stewart platforms and other parallel manipulators by minimizing inverse kinematics residuals," Journal of Robotic Systems, vol. 15, pp. 395-405, 1998.
[3] Yu-jen Chiu,Ming-Hwei Perng, "Self-calibration of a general hexapod manipulator with enhanced precision in 5-DOF motions", Mechanism and Machine Theory, vol. pp. 1-23, 2004.
[4] K. T. Sung, W. Park, and Y K. Lee, "Study on Observability of Paralleltyped Machining Centre Using a Single Planar Table and Digital Indicators," Mechanism and Machine Theory, vol. 41, pp. 1147-1156, 2006.
[5] H. Zhuang, K. Wang, and Z. S. Roth, "Optimal selection of measurement Configurations for robot calibration using simulated annealing," Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Diego, CA, pp. 393-398, 1994.
[6] T,Anderson, M.J.Thurley, O.Marklund, "Pellet Size Estimation Using Spherical Fitting", Instrumentation and Measurement Technology Conference Proceedings IEEE, Location: Warsaw, ISSN: 1091-5281, ISBN: 1-4244-0588-, pp. 1-5, 2007.
[7] David Daney, Ioannis Z. Emiris, "Calibration of parallel robots : on the Elimination of Pose-Dependent Parameters", Proceedings of EUCOMES, the first European Conference on Mechanism Science , Obergurgl (Austria), February 21-26, 2006.
[8] David Daney, Yves Papegay, "Choosing Measurement Poses for Robot Calibration with the Local Convergence Method andTabu Search", International Journal of Robotic Research, Sage publications, vol. 24, pp. 501-518, 2005.
[9] Bernhard Jokiel Jr. , John C. Ziegert , and Lothar Bieg, "Uncertainty propagation in calibration of parallel kinematics machines," Precision Engineering, vol. 25, pp. 48-55, 2001.
[10] A. Nahvi, J. M. Hollerbach, and V. Hayward, "Calibration of a parallel robot using multiple kinematics closed loops," Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Diego, CA, pp. 407-412, 1994.
[11] A. Nahvi, and J. M. Hollerbach, "The noise amplification index for optimal pose selection in robot calibration," Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Minneapolis, MN, pp. 647-654, 1996.
[12] J. H. Borm, and C. H. Menq, "Determination of optimal measurement Configurations for robot calibration based on observabililty measure," Journal of Robotic Systems , vol. 10, pp. 51-63, 1991.
[13] C.H. Meng, J.H. Borm, "Identification and observability measure of a basis set of error parameters in robot calibration", J. Mechanism, Transmissions and automation in design, vol. 111, pp. 513-518, 1989.
[14] Shannon C. Ridgeway , Carl D. Crane , "Optimized Kinematics of a 6-6 Parallel Mechanism Considering Position and Orientation Errors", FCRAR 2003, The 16th Florida Conference on the Recent Advances in Robotics, Florida Atlantic University, Boca Raton, FL, May 2003.
[15] szabolcs szatmári , "geometrical errors of parallel robots", periodica polytechnica ser. mech. eng., vol. 43, no. 2, pp. 155-162, 1999.
[16] GAO Meng, LI Tiemin, TANG Xiaoqiang, DUAN Guanghong, "Estimates of Identification Result Disturbances in Parallel Mechanism Calibration", Tsinghua Science and Technology , vol. 11, pp. 80-87, 2006.
[17] Hai Wang, Kuang-Chao Fan ," Identification of strut and assembly errors of a 3- PRS serial-parallel machine tool", International Journal of Machine Tools & Manufacture, vol. 44, pp. 1171-1178, 2004.
[18] Han Sung Kim, "Kinematics Calibration of a Cartesian Parallel Manipulator", International Journal of Control, Automation, and Systems, vol. 3, pp. 453-460, 2005.
[19] Yung Ting , Ho-Chin Jar, Chun-Chung Li, "Measurement and calibration for Stewart micromanipulation system", Precision Engineering, vol., pp. 226-233, 2007.
[20] Haomin Lin, John E. McInroy, "Disturbance attenuation in precise hexapod pointing using positive force feedback", Control Engineering Practice, vol. 14, pp. 1377-1386, 2006.
[21] Rocco Vertechy, Vincenzo Parenti Castelli, " Accurate and fast body pose estimation by three point position data," Mechanism and machine theory, vol. 42, pp.1170-1183, 2007.
[22] Tae-Young Lee, Jae-Kyung Shim, "Improved dialytic elimination algorithm for the forward kinematics of the general Stewart-Gough platform", Mechanism and Machine Theory, vol. 38, 563-577, 2003.
[23] E. Castillo-Castaneda, Y. Takeda, "Improving path accuracy of a cranktype 6-dof parallel mechanism by stiction compensation", Mechanism and Machine Theory, vol. 43, pp.104-114, 2008.
[24] J. Gao, P. Webb and N. Gindy, "Error reduction for an inertial-sensorbased dynamic parallel kinematics machine positioning system", Meas. Sci. Technol., vol. 14, pp. 543-550, 2003.
[25] Takaaki OIWA, "Study on Accuracy Improvement of Parallel Kinematics Machine-Compensation Methods for Thermal Expansion of Link and Machine Frame-", 1st Korea Japan Conf Positioning Technol, pp. 189-194, 2002.
[26] Seung Reung Lim, Woo Chun Choi, Jae-Bok Song and Daehie Hong, "Error Model and Accuracy Analysis of a Cubic Parallel Device", International Journal of the Korean Society of Precision Engineering, vol. 2, 2001.