AVOIDING HEAVY COMPUTATIONS IN INVERSE CALIBRATION PROCEDURE FOR 7 DOF ROBOT MANIPULATOR

Abstract

Procedure for determining commanded coordinates in machine space if desired coordinates are given is inverse calibration. A large amount of data is considered after measurement procedure and it is essential to locate desired point in the real space which is skewed due to measured geometric errors. The machine workspace is divided to cells using measurement points. It is depicted the importance of finding the proper cell in skewed 3D lattice, for calibration of translational axes of ATL machine with large workspace. To calibrate 7 DOF robot manipulator, this algorithm is extended. The problem of finding the proper cell in 7D skewed grid needs heavy computations and takes significant amount of computational time. Few ideas for avoiding these computations are described and the influence on the final precision of the calibration procedure is explored. Key words: inverse calibration; geometric errors; robot manipulator REFERENCES: [1] S. Zhu: An automated fabric layup machine for the manufacturing of fiber reinforced polymer composite, Graduate Theses and Dissertation – Paper 13170, Iowa State University, 2013. [2] A. Jordaens, T. Steensels: Formation of defects in flat laminates during automatic tape laying (framework of a master’s thesis), Faculty of Engineering Technology, Leuven, Belgium, 2015. [3] S. Samak, I. Dimovski, V. Dukovski, M. Trompeska: Volumetric calibration for improving accuracy of AFP/ATL machines, 7 th International Scientific Conference of Defensive Technologies, OTEH 2016, unpublished. [4] ISO 230-1:2012: Test code for machine tools – Part 1: Geometric accuracy of machines operating under no-lo-ad or quasi-static conditions. An International Standard, by International Standards Organization, 2012. [5] ISO 230-2:2014: Test code for machine tools – Part 2: Determination of accuracy and repeatability of positioning of numerically controlled axes. An International Standard, by International Standards Organization, 2014. [6] Technical report: Machine tools – numerical compensation of geometric errors, ISO/TR 16907:2015, ISO, 2015. [7] B. W. Mooring, Z. S. Roth, M. R. Driels: Fundamentals of Manipulator Calibration, John Wiley & Sons Inc., 1991. [8] J. S. Shamma, D. E. Whitney: A Method for Inverse Robot Calibration. Journal of Dynamic Systems, Measurement, and Control 109. 1, 36–43 (1987). [9] D. C. Lu, M. J. D. Hayes: Robot Calibration Using Relative Measurements, The 14th IFToMM World Congress, Taipei, Taiwan, October 25–30, 2015. [10] R. M. Murray, Z. Li, S. S. Sastry: A Mathematical Introduction to Robotic Manipulation. CRC Press; 1994. [11] S. Xiang, Y. Altintas: Modeling and compensation of volumetric errors for five-axis machine tools. International Journal of Machine Tools and Manufacture, 101, 65–78 (2016). [12] J. Yang, Y. Altintas: Generalized kinematics of five-axis serial machines with non-singular tool path generation. International Journal of Machine Tools and Manufacture 75, 119–132 (2013). [13] M. K. Agoston: Computer Graphics and Geometric Modeling – Mathematics, Springer, 2005. [14] M. K. Agoston: Computer Graphics and Geometric Modeling – Implementation and Algorithms, Springer, 2005. [15] R. A. Dwyer: Higher-dimensional Voronoi diagrams in linear expected time. Discrete & Computational Geometry 6. 3, 343–367 (1991). [16] C. B. Barber, D. P. Dobkin, H. Huhdanpaa: The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software (TOMS) 22, 4, 469–483 (1996).