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Gramian-constrained optimization process for the stiffness model identification of industrial manipulators

Published online by Cambridge University Press:  23 December 2021

W. R. Oliveira Open the ORCID record for W. R. Oliveira [Opens in a new window]  and
L. G. Trabasso
W. R. Oliveira*
Affiliation:
Division of Mechanical Engineering, Aeronautics Institute of Technology (ITA), São José dos Campos, Brazil
L. G. Trabasso
Affiliation:
Division of Mechanical Engineering, Aeronautics Institute of Technology (ITA), São José dos Campos, Brazil SENAI Innovation Institute for Manufacturing Systems, Joinville, Brazil
*
*Corresponding author. E-mail: wesleyro@ccm-ita.org.br
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Abstract

This work deals with the elastostatic identification of industrial manipulators. By reviewing the basics of the physical elastic properties of both links and joints in the framework of the lumped stiffness modeling techniques, the Gramian nature of the stiffness matrices has been found out adequate to do so. Then, a novel optimization method has been developed, which incorporates the Gramian matrix formulation along a non-linear optimization process, acting as an intrinsic constraint for the conservativeness of the elastostatic modeling. Numerical and experimental analyses evince the effectiveness of the proposed method, as the elastostatic models obtained by means of the proposed technique predict more than 93.7% of the compliance deviations of a real industrial robot. The proposed method is simple enough to be jointly applicable to the most recent elastostatic model reduction techniques.

Keywords

elastostatic identificationGramian matrixrobot stiffnessrobot calibrationoptimization methods
Type
Research Article
Information
Robotica , Volume 40 , Issue 8 , August 2022 , pp. 2592 - 2609
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Villani, E., Suterio, R., Trabasso, L. G., Furtado, L. F. F., Alvarado, B. H. L. and Amorim, D. Y. K., “Metrological analysis of an industrial robot for aircraft fuselage assembly,” Revista SBA Controle & Automação 21(6), 634–646 (2010). doi: 10.1590/S0103-17592010000600009.CrossRefGoogle Scholar
Backer, J. and Bolmsjö, G., “Deflection model for robotic friction stir welding,” Indust. Robot Int. J. 41(4), 365–372 (2014). Emerald: 2014. doi: 10.1108/IR-01-2014-0301.CrossRefGoogle Scholar
Eguti, C. C. A. and Trabasso, L. G., “Design of a robotic orbital driller for assembling aircraft structures,” J. Mechatron. 24, 533–545 (2014). Elsevier: 2014. doi: 10.1016/j.mechatronics.2014.06.007.CrossRefGoogle Scholar
Mei, Z. and Maropoulos, P. G., “Review of the application of flexible, measurement-assisted assembly technology in aircraft manufacturing,” J. Eng. Manuf. 228(10), 1185–1197 (2014). SAGE: 2014. doi: 10.1177/095-4405413517387.CrossRefGoogle Scholar
Posada, J. R. D., Schneider, U., Pidan, S., Geravand, M., Stelzer, P. and Verl, A., “High Accurate Robotic Drilling with External Sensor and Compliance Model-Based Compensation,” Proceedings 2016 IEEE International Conference on Robotics and Automation (ICRA), May 2016, Stockholm-Sweden (2016) pp. 3901–3907.Google Scholar
Mosqueira, G., Apetz, J., Santos, K. M., Villani, E., Suterio, R. and Trabasso, L. G., “Analysis of the indoor GPS system as feedback for the robotic alignment of fuselages using laser radar measurements as comparison,” J. Rob. Comput. Integr. Manuf. 28, 700–709 (2012). Elsevier: 2012. doi: 10.1016/j.rcim.2012.03.004.CrossRefGoogle Scholar
Trabasso, L. G. and Mosqueira, G., “Light automation for aircraft fuselage assembly,” Aeronaut. J. 124(1272), 216–236 (2020). doi: 10.1017/aer.2019.117.CrossRefGoogle Scholar
Jamshidi, J., Kayani, A., Iravani, P., Maropoulos, P. G. and Summers, M. D., “Manufacturing and assembly automation by integrated metrology systems for aircraft wing fabrication,” J. Eng. Manuf. 224(1), 25–36 (2009). SAGE: 2009. doi: 10.1243/09544054JEM1280.CrossRefGoogle Scholar
Kayani, A. and Jamshidi, J., “Measurement Assisted Assembly for Large Volume Aircraft Wing Structures,” 4th International Conference on Digital Enterprise Technology. Proceedings, Bath, UK, 2007 (2007) pp. 426–434.Google Scholar
Klimchik, A. and Pashkevich, A., “Robotic Manipulators with Double Encoders: Accuracy Improvement Based on Advanced Stiffness Modeling and Intelligent Control,” IFAC Papers-Online, Vol. 51, Special Issue: Proceedings of 16th IFAC Symposium on Information Control Problems in Manufacturing (INCOM 2018), Bergamo-Italy, June-2018 (2018) pp. 740–745. doi: 10.1016/j.ifacol.2018.08.407.CrossRefGoogle Scholar
Devlieg, R. C., “Expanding the use of robotics in airframe assembly via accurate robot technology,” SAE Int. J. Aerospace, 3(1), 198–203 (2010), (SAE Technical Paper), Ref. 2010-01-1846. SAE, 2010. doi: 10.4271/2010-01-1846.CrossRefGoogle Scholar
Devlieg, R. C., Robotic manufacturing system with accurate control. USPTO Patent No. US 8,989,898 B2. United States, Issue Date: March 24th, 2015 (2015).Google Scholar
De Backer, J., Christiansson, A. K., Oqueka, J. and Bolmsjö, G., “Investigation of path compensation methods for robotic friction stir welding,” Indust. Robot Int. J. 39(6), 601–608 (2012). Emerald: 2012. doi: 10.1108/01439911211268813.Google Scholar
Li, R. and Zhao, Y., “Dynamic error compensation for industrial robot based on thermal effect model,” J. Meas. 88, 113–120 (2016). Elsevier: 2016. doi: 10.1016/j.measurement.2016.02.038.CrossRefGoogle Scholar
Bu, Y., Liao, W., Tian, W., Zhang, J. and Zhang, L., “Stiffness analysis and optimization in robotic drilling application,” J. Precision Eng. 49, 388–400 (2017). Elsevier: July 2017. doi: 10.1016/j.precisioneng.2017.04.001.CrossRefGoogle Scholar
Reinl, C., Friedmann, M., Bauer, J., Pischan, M., Abele, E. and Von Stryk, O., “Model-based Off-line Compensation of Path Deviation for Industrial Robots in Milling Applications,” Proceedings of the 2011 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2011), Budapest, Hungary, July 3–7 2011. (2011) pp. 367–372.Google Scholar
Klimchik, A., Bondarenko, D., Pashkevich, A., Briot, S. and Furet, B., “Compensation of tool deflection in robotic-based milling,” Proceedings of the ICINCO 2012 - 9th International Conference on Informatics in Control, Automation and Robotics, vol. 2 (2012) pp. 113–122. Scitepress: 2012. doi: 10.5220/0004040801130122.CrossRefGoogle Scholar
Roesch, O., “Model-based on-line compensation of path deviations for milling robots,” J. Adv. Mater. Res. 769, 255–262 (2013). TransTech Publications: Switzerland, 2013. doi: 10.4028/www.scientific.net/AMR.769.255.CrossRefGoogle Scholar
Wu, Y., Klimchik, A., Caro, S. and Pashkevich, A., “Optimality Criteria for Measurement Poses Selection in Calibration of Robot Stiffness Parameters,” Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, Jul 2012, Nantes (2012) pp. 1–10. doi: 10.1115/ESDA2012-82213ff.CrossRefGoogle Scholar
Dumas, C., Caro, S., Garnier, S. and Furet, B., “Joint stiffness identification of six-revolute industrial serial robots,” J. Robot Comput. Integr. Manuf. 27, 881–888 (2011). Elsevier: 2011. doi: 10.1016/j.rcim. 2011.02.003.CrossRefGoogle Scholar
Alici, G. and Shirinzadeh, B., “Enhanced stiffness modeling, identification and characterization for robot manipulators,” IEEE Trans. Rob. 21(4), 554–564 (2005). IEEE: Aug. 2005. doi: 10.1109/TRO.2004.842347.CrossRefGoogle Scholar
Pashkevich, A., D. Chablat and Ph. Wenger, “Stiffness analysis of overconstrained parallel manipulators,” Mech. Mach. Theory 44, 966–982 (2010). Elsevier, 2010. doi: 10.1016/j.mechmachtheory.2008.05.017.CrossRefGoogle Scholar
Pashkevich, A., Klimchik, A. and Chablat, D., “Enhanced stiffness modeling of manipulators with passive joints,” Mech. Mach. Theory 46(5), 662–679 (2010). Elsevier, 2010. doi: 10.1016/j.mechmachtheory.2010.12.008.CrossRefGoogle Scholar
Klimchik, A., Wu, Y., Caro, S., Furet, B. and Pashkevich, A., “Geometric and elastostatic calibration of robotic manipulator using partial pose measurements,” J. Adv. Rob. 28(21), 1419–1429 (2014). Taylor Francis: 2014. doi: 10.1080/01691864.2014.955824.CrossRefGoogle Scholar
Klimchik, A., Caro, S., Wu, Y., Chablat, D., Furet, B. and Pashkevich, A., “Stiffness Modeling of Robotic Manipulator with Gravity Compensator,” In: Computational Kinematics, Mechanisms and Machine Science (Thomas, F. and Pérez Gracia, A., eds.), vol. 15 (2014) pp. 185–192. Springer: 2014. doi: 10.1007/978-94-007-7214-4_21.CrossRefGoogle Scholar
Klimchik, A., Pashkevich, A. and Chablat, D., “Fundamentals of manipulator stiffness modeling using matrix structural analysis,” Mech. Mach. Theory 133, 365–394 (2019). doi: 10.1016/j.mechmachtheory.2018.11.023.Google Scholar
Klimchik, A. and Pashkevich, A., “Serial vs. quasi-serial manipulators: Comparison analysis of elastostatic behaviors,” J. Mech. Mach. Theory 107, 46–70 (2017). Elsevier: 2017. doi: 10.1016/j.mechmachtheory. 2016.09.019.CrossRefGoogle Scholar
Calafiore, G., Indri, M. and Bona, B., “Robot dynamic calibration: Optimal excitation trajectories and experimental parameter estimation,” J. Rob. Syst. 18(2), 55–68 (2001). John Wiley & Sons: 2001.3.0.CO;2-O>CrossRefGoogle Scholar
Daney, D., Papegay, Y. and Madeline, B., “Choosing measurement poses for robot calibration with the local convergence method and Tabu search,” Int. J. Rob. Res. 24, 501–518 (2005). SAGE: 2005. doi: 10.1177/0278364905053185.CrossRefGoogle Scholar
Swevers, J., Verdonck, W. and De Schutter, J., “Dynamic model identification for industrial robots,” IEEE Control Syst. Mag. 27(5), 58–71 (2007). IEEE, 2007. doi: 10.1109/MCS.2007.904659.Google Scholar
Wu, J., Wang, J. and You, Z., “An overview of dynamic parameter identification of robots,” J. Rob. Comput. Integr. Manuf. (JRCIM) 26, 414–419 (2010). Elsevier: 2010. doi: 10.1016/j.rcim.2 010.03.013.CrossRefGoogle Scholar
Khalil, W. and Gautier, M., “A Direct Determination of Minimum Inertial Parameters of Robots,” Proceedings. 1988 IEEE International Conference on Robotics and Automation, Philadelphia-USA (1988). doi: 10.1109/ROBOT.1988. 12308.CrossRefGoogle Scholar
Wu, Y., Klimchik, A., Caro, S., Furet, B. and Pashkevich, A., “Geometric calibration of industrial robots using enhanced partial pose measurements and design of experiments,” (JRCIM) Rob. Comput. Integr. Manuf. 35, 151–168 (2015). Elsevier: 2015. doi: 10.1016/j.rcim.2015.03.007.CrossRefGoogle Scholar
Klimchik, A., Wu, Y., Pashkevich, A., Caro, S. and Furet, B., “Optimal Selection of Measurement Configurations for Stiffness Model Calibration of Anthropomorphic Manipulators,” In: Applied Mechanical & Materials, vol. 162 (2012) pp. 161–170.CrossRefGoogle Scholar
Klimchik, A., Caro, S. and Pashkevich, A., “Practical Identifiability of the Manipulator Link Stiffness Parameters,” ASME 2013 International Mechanical Engineering Congress & Exposition, November 2013, San Diego, CA, USA (2013) pp. 1–10.Google Scholar
Klimchik, A., Furet, B., Caro, S. and Pashkevich, A., “Identification of the manipulator stiffness model parameters in industrial environment,” J. Mech. Mach. Theory 90, 1–22 (2015). Elsevier: 2015. doi: 10.1016/j.mechmachtheory.2015.03.002.CrossRefGoogle Scholar
Klimchik, A., Pashkevich, A. and Chablat, D., “CAD-based approach for identification of elasto-static parameters of robotic manipulators,” J. Finite Elements Anal. Des. 75, 19–30 (2013). Elsevier: 2013. doi: 10.1016/j.finel.2013.06.008.CrossRefGoogle Scholar
Horn, R. A. and Johnson, C. R., Matrix Analysis, 2nd ed. (Cambridge University Press, 2013). ISBN: 978-0-521-83940-2.Google Scholar
Sun, Z., Yu, C. and Anderson, B. D. O., “Distributed Optimization on Proximity Network Rigidity via Robotic Movements,” Proceedings of 2015 34th Chinese Control Conference (CCC), Hangzhou (China) (2015). doi: 10.1109/ChiCC.2015.7260739.CrossRefGoogle Scholar
Bianchin, G. and Pasqualetti, F., “Gramian-based optimization for the analysis and control of traffic networks,” IEEE Trans. Intell. Transp. Syst., 1–12 (2019), (Early Access–2019). doi: 10.1109/TITS.2019.2922900.CrossRefGoogle Scholar
Craig, J. J., Introduction to Robotics: Mechanics and Control, 3rd ed. 400f (Pearson/Prentice Hall, 2005). ISBN: 978-0201543612.Google Scholar
Salisbury, J. K., “Active Stiffness Control of a Manipulator in Cartesian Coordinates,” Proceedings 19th IEEE Conference on Decision Control (1980) pp. 87–97. doi: 10.1109/CDC.1980.272026.CrossRefGoogle Scholar
Timoshenko, S. and Goodier, J. N., Theory of Elasticity, 3d ed. (McGraw-Hill, New York, 1970).CrossRefGoogle Scholar
Chen, S. F. and Kao, I., “Conservative congruence transformation for joint and Cartesian stiffness matrices of robotic hands and fingers,” Int. J. Rob. Res. 19(9), 835–847 (2000). SAGE: Sept. 2000. doi: 10.1177/02783640022067201.CrossRefGoogle Scholar
Chen, S. F., “The 6/spl times/6 Stiffness Formulation and Transformation of Serial Manipulators via the CCT Theory,” Proceedings of the 2003 IEEE International Conference on Robotics and Automation (ICRA). Taipei-Taiwan, September 2003 (2003). doi: 10.1109/ROBOT.2003.1242218.CrossRefGoogle Scholar
Kao, I. and Ngo, C., “Properties of grasp stiffness matrix and conservative control strategy,” Int. J. Rob. Res. 18(2), 159–167 (1999). SAGE: 1999. doi: 10.1177/027836499901800204.CrossRefGoogle Scholar
Wu, Y., Optimal Pose Selection for the Identification of Geometric and Elastostatic Parameters of Machining Robots Ph.D. Thesis (Université Nantes Angers Le Mans, Nantes, France, 2014).Google Scholar
Rice, J., Mathematical Statistics and Data Analysis(Cengage Learning, n.l.,2006). ISBN 0534399428.Google Scholar
Goldberg, D. E., Genetic Algorithms in Search, Optimization & Machine Learning (Addison-Wesley, Reading, MA, 1989).Google Scholar
Ugray, Z., Lasdon, L., Plummer, J., Glover, F., Kelly, J. and Marti, R., “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput. 19(3), 328–340 (2007). doi: 10.2139/ssrn.886559.CrossRefGoogle Scholar
Lilliefors, H. W., “On the Kolmogorov-Smirnov test for normality with mean and variance unknown,” J. Am. Stat. Assoc. 62(318), 399–402 (1967).CrossRefGoogle Scholar