IJAT Vol.15 No.5 pp. 590-598
doi: 10.20965/ijat.2021.p0590


Quasi-Static Compliance Calibration of Serial Articulated Industrial Manipulators

Nikolas Alexander Theissen*,†, Monica Katherine Gonzalez*, Asier Barrios**, and Andreas Archenti*,***

*Manufacturing and Metrology Systems Division, Department of Production Engineering, KTH Royal Institute of Technology
68 Brinellvägen, Stockholm 10044, Sweden

Corresponding author

**IDEKO S.COOP, Elgoibar, Spain

***Industrial Dependability Division, Department of Sustainable Production Development, KTH Royal Institute of Technology, Södertälje, Sweden

February 22, 2021
April 26, 2021
September 5, 2021
manipulator calibration, contact applications, quasi-statics

This article presents a procedure for the quasi-static compliance calibration of serial articulated industrial manipulators. Quasi-static compliance refers to the apparent stiffness displayed by manipulators at low-velocity movements, i.e., from 50 to 250 mm/s. The novelty of the quasi-static compliance calibration procedure lies in the measurement phase, in which the quasi-static deflections of the manipulator’s end effector are measured under movement along a circular trajectory. The quasi-static stiffness might be a more applicable model parameter, i.e., representing the actual manipulator more accurately, for manipulators at low-velocity movements. This indicates that the quasi-static robot model may yield more accurate estimates for the trajectory optimization compared with static stiffness in the implementation phase. This study compares the static and apparent quasi-static compliance. The static deflections were measured at discretized static configurations along circular trajectories, whereas the quasi-static deflections were measured under circular motion along the same trajectories. Loads of different magnitudes were induced using the Loaded Double Ball Bar. The static and quasi-static displacements were measured using a linear variable differential transformer embedded in the Loaded Double Ball Bar and a Leica AT901 laser tracker. These measurement procedures are implemented in a case study on a large serial articulated industrial manipulator in five different positions of its workspace. This study shows that the measured quasi-static deflections are bigger than the measured static deflections. This, in turn, indicates a significant difference between the static and apparent quasi-static compliance. Finally, the implementation of the model parameters to improve the accuracy of robots and the challenges in realizing cost-efficient compliance calibration are discussed.

Cite this article as:
Nikolas Alexander Theissen, Monica Katherine Gonzalez, Asier Barrios, and Andreas Archenti, “Quasi-Static Compliance Calibration of Serial Articulated Industrial Manipulators,” Int. J. Automation Technol., Vol.15, No.5, pp. 590-598, 2021.
Data files:
  1. [1] International Federation of Robotics, “Executive Summary World Robotics 2020 Industrial Robots,” 2020.
  2. [2] International Federation of Robotics, “History,” 2018.
  3. [3] A. Verl, A. Valente, S. Melkote, C. Brecher, E. Ozturk, and L. T. Tunc, “Robots in machining,” CIRP Annals – Manufacturing Technology, Vol.68, No.2, pp. 799-822, 2019.
  4. [4] B. Siciliano and O. Khatib, “Springer Handbook of Robotics,” Springer-Verlag, Berlin, Heidelberg, 2007.
  5. [5] H. Zhang, J. Wang, G. Zhang, and Z. Gan, “Machining with Flexible Manipulator: Toward Improving Robotic Machining Performance,” Proc. of the 2005 IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics Monterey, CA, July 24-28, 2005.
  6. [6] International Federation of Robotics, “World Robotics Industrial Robots 2017,” 2017.
  7. [7] F. C. Park, “Optimal Robot Design and Differential Geometry,” J. of Mechanical Design, Vol.117, No.B, 87, 1995.
  8. [8] A. Blomdell, G. Bolmsjo, T. Brogardh, P. Cederberg, M. Isaksson, R. Johansson, M. Haage, K. Nilsson, M. Olsson, T. Olsson, A. Robertsson, and J. Wang, “Extending an industrial robot controller,” IEEE Robotics & Automation Magazine, Vol.12, No.3, pp. 85-94, 2005.
  9. [9] U. Schneider, J. Diaz Posada, and A. Verl, “Automatic Pose Optimization for Robotic Processes,” Proc. of the 2015 IEEE Int. Conf. on Robotics and Automation (ICRA), pp. 2054-2059, 2015.
  10. [10] S. Caro, C. Dumas, S. Garnier, and B. Furet, “Workpiece Placement Optimization Robotic-based Manufacturing,” IFAC Proc. Volumes, Vol.46, No.9, pp. 819-824, 2013.
  11. [11] S. Bachche and K. Oka, “Design, Modeling and Performance Testing of End-Effector for Sweet Pepper Harvesting Robot Hand,” J. Robot. Mechatron., Vol.25, No.4, pp. 705-717, 2013.
  12. [12] A. Nubiola and I. A. Bonev, “Absolute calibration of an ABB IRB 1600 robot using a laser tracker,” Robotics and Computer-Integrated Manufacturing, Vol.29, No.1, pp. 236-245, 2013.
  13. [13] B. Mooring, Z. S. Roth, and M. R. Driels, “Fundamentals of manipulator calibration,” Wiley, New York, 1991.
  14. [14] International Organization for Standardization, “ISO 9283:1998 Manipulating industrial robots – Performance criteria and related test methods,” 1998.
  15. [15] S. Aoyagi, M. Suzuki, T. Takahashi, J. Fujioka, and Y. Kamiya, “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,” Int. J. Automation Technol., Vol.6, No.1, pp. 29-37, 2012.
  16. [16] H. P. Jawale and H. T. Thorat, “Positional Error Estimation in Serial Link Manipulator Under Joint Clearances and Backlash,” J. of Mechanisms and Robotics, Vol.5, No.2, 2013.
  17. [17] A. Klimchik, B. Furet, S. Caro, and A. Pashkevich, “Identification of the manipulator stiffness model parameters in industrial environment,” Mechanism and Machine Theory, Vol.90, pp. 1-22, 2015.
  18. [18] N. A. Theissen, A. Mohammed, and A. Archenti, “Articulated industrial robots: An approach to thermal compensation based on joint power consumption,” L. Blunt and W. Knapp (Eds.), “Laser Metrology and Machine Performance XIII,” pp. 81-90, 2019.
  19. [19] C. Dumas, S. Caro, S. Garnier, and B. Furet, “Joint stiffness identification of six-revolute industrial serial robots,” Robotics and Computer-Integrated Manufacturing, Vol.27, No.4, pp. 881-888, 2011.
  20. [20] K. Kamali, A. Joubair, I. A. Bonev, and P. Bigras, “Elasto-geometrical Calibration of an Industrial Robot under Multidirectional External Loads Using a Laser Tracker,” Proc. of the 2016 IEEE Int. Conf. on Robotics and Automation (ICRA), pp. 4320-4327, 2016.
  21. [21] A. Joubair and I. A. Bonev, “Non-kinematic calibration of a six-axis serial robot using planar constraints,” Precision Engineering, Vol.40, pp. 325-333, 2015.
  22. [22] P. Corke, “Robotics, Vision and Control: Fundamental Algorithms In MATLAB◦ledR Second, Completely Revised, Extended And Updated Edition,” Springer, 2017.
  23. [23] K. M. Lynch and F. C. Park, “Modern Robotics: Mechanics, Planning, and Control,” Cambridge University Press, 2017.
  24. [24] A. Klimchik, Y. Wu, C. Dumas, S. Caro, B. Furet, and A. Pashkevich, “Identification of geometrical and elastostatic parameters of heavy industrial robots,” May 6-10 2013, Karlsruhe, Germany, 2013.
  25. [25] A. Pashkevich, A. Klimchik, and D. Chablat, “Enhanced stiffness modeling of serial manipulators with passive joints,” E. Hall (Ed.), “Advances in Robot Manipulators,” pp. 331-360, IntechOpen, 2011.
  26. [26] I. Tyapin, G. Hovland, and T. Brogårdh, “Method for Estimating Combined Controller, Joint and Link Stiffnesses of an Industrial Robot,” Proc. of the 2014 IEEE Int. Symp. on Robotic and Sensors Environments (ROSE), pp. 1-6, 2014.
  27. [27] E. Abele, M. Weigold, and S. Rothenbücher, “Modeling and Identification of an Industrial Robot for Machining Applications,” CIRP Annals – Manufacturing Technology, Vol.56, No.1, pp. 387-390, 2007.
  28. [28] P. Schellekens, N. Rosielle, H. Vermeulen, M. Vermeulen, S. Wetzels, and W. Pril, “Design for Precision: Current Status and Trends,” CIRP Annals, Vol.47, No.2, pp. 557-586, 1998.
  29. [29] R. Hooke and J. Martyn, “Lectiones Cutlerianae, or a collection of lectures,” John Martyn Printer, 1679.
  30. [30] S.-F. Chen and I. Kao, “Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers,” The Int. J. of Robotics Research, Vol.19, No.9, pp. 835-847, 2000.
  31. [31] Leica Geosystems, “User Manual AbsoluteTracker AT901,” 2009.
  32. [32] A. Archenti, “A Computational Framework for Control of Machining System Capability: From Formulation to Implementation,” Doctoral thesis, KTH Royal Institute of Technology, 2011.
  33. [33] Mirco-Epsilon USA, “Linear inductive displacement sensors,” 2017.
  34. [34] M. Gonzalez, A. Hosseini, N. A. Theissen, and A. Archenti, “Quasi-static loaded circular testing of serial articulated industrial manipulators,” Proc. of the 52th Int. Symp. on Robotics, pp. 1-6, 2020.
  35. [35] International Organization for Standardization, “ISO 230-4:2005 Test code for machine tools – Part 4: Circular tests for numerically controlled machine tools,” 2005.
  36. [36] J. K. Salisbury, “Active stiffness control of a manipulator in cartesian coordinates,” Proc. of the 19th IEEE Conf. on Decision and Control including the Symp. on Adaptive Processes, pp. 95-100, 1980.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Sep. 19, 2021