The method of high accuracy calculation of robot trajectory for the complex curves

• Autorzy: Lozhkin Alexander , Bozek Pavol , Maiorov Konstantin

Identyfikatory

DOI

10.2478/mspe-2020-0035

• Języki publikacji: EN

Abstrakty

EN

The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.

Słowa kluczowe

EN

analytical method; linear transformations; planar complex curves; symmetries

• Wydawca: STE GROUP
• Czasopismo: Management Systems in Production Engineering
• Rocznik: 2020
• Tom: nr 4 (28)
• Strony: 247--252
• Opis fizyczny: Bibliogr. 48 poz., rys., tab.

Twórcy

autor

Lozhkin Alexander

• Kalashnikov Izhevsk State Technical University Institute of Informatics and Hardware Software department 30 let Pobedy, 5, Izhevsk, Russian Federation

autor

Bozek Pavol

• Slovak University of Technology in Bratislava Faculty of Materials Science and Technology Institute of Production Technologies Jana Bottu, 2781/25, 917 24 Trnava, Slovak Republic

autor

Maiorov Konstantin

• Kalashnikov Izhevsk State Technical University Institute of Informatics and Hardware Software department 30 let Pobedy, 5, Izhevsk, Russian Federation

Bibliografia

• [1] J. Stillwell. Mathematics and its History. Springer-Verlag, New York. 2010.
• [2] Ryaben'kii, V., Tsynkov, S.: A Theoretical Introduction to Numerical Analysis. CRC Press, (2006).
• [3] Trefethen, L. N.: Approximation Theory and Approximation Practice (Applied Mathematics). Society for Industrial and Applied Mathematics Philadelphia, PA, (2012).
• [4] Iske. A.: Approximation Theory and Algorithms for Data Analysis (Texts in Applied Mathematics). Springer, New York, (2018).
• [5] Powell. M.; Approximation Theory and Methods. Cambridge. CUP, (2015).
• [6] Anastassiou, G. A., Kester, M.: Discrete Approximation Theory. WSPC, (2016).
• [7] Duong, X. T., Li, J., Song, L., Yan, L.: Frame decomposition and radial maximal semigroup characterization of Hardy spaces associated to operators, Journal of Approximation Theory, 243, pp. 45-85, (2019).
• [8] O. Ciaurri, et all. "Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions". Journal of Approximation Theory, vol. 235, 2018, pp. 20-45.
• [9] K. Schiefermayr. "The growth of polynomials outside of a compact set-The Bernstein-Walsh inequality revisited". Journal of Approximation Theory, vol. 223, 2017, pp. 9-18.
• [10] F. E. Cobos,et all. "Approximation and Entropy Numbers of Embeddings Between Approximation Spaces". Constructive Approximation, vol. 47(3), 2018 pp. 453-486.
• [11] MX. Yuan, Z. Chen, B. Yao, XC. Zhu. "Time Optimal Contouring Control of Industrial Biaxial Gantry: A Highly Efficient Analytical Solution of Trajectory Planning". In Proc. of the IEEEASME Transactions On Mechatronics, 2017, pp. 247-257.
• [12] M. Baranov, P. Bozek, V. Prajova, T. Ivanova, D. Novokshonov, A. Korshunov. “Constructing and calculating of multistage sucker rod string according to reduced stress.:” Acta Montanistica Slovaca, vol. 22, pp. 107-115, Feb. 2017.
• [13] T. Vopat, J. Peterka, V. Šimna. “The influence of different types of copy milling on the surface roughness and tool life of end mills.”25th DAAAM international symposium on intelligent manufacturing and automation, 2014. Procedia engineering, vol 100, pp. 868-876, 2015.
• [14] J. Peterka. “A new approach to calculating the arithmetical mean deviation of a profile during copy milling.” Strojniskivestnik-journal of mechanical engineering2004. vol 50, pp. 594-597, Dec. 2004.
• [15] K. Sentyakov, J. Peterka, V. Smirnov, P. Bozek and V. Sviatskii. ”Modeling of boring mandrel working proces with vibration damper.” Materials, 13, pp. 1-13, Apr. 2020
• [16] S. Vaclav, J. Peterka, P. Pokorny, P. “Objective method for assembly.” in Annals of DAAAM for 2007 & Proceeding of the 18th Inter. DAAAM Symp.: Intelligent Manufacturing & Automation: Focus on Creativity, Responsibility, and Ethics of Engineering, 2007, pp. 797-798.
• [17] S. Vaclav, J. Jurko, S. Lecky. “Allowance treatment static designed couple and repeatable precision in assembly.” in MTEM, 2017, vol. 137, Art. Numb. UNSP 04007.
• [18] M. Nemeth, A. Nemethova and G. Michalconok. “Determination Issues of Data Mining Process of Failures in the Production Systems.” in 8 th Comp. Scien. On-Line Conf. (CSOC). Artificial Intelligence Methods in Intelligent Algorithms Book Series: Advance in Intelligent Systems and Computing. 2019, vol. 985, pp. 200-207.
• [19] A. Nemethova, M. Nemeth, G. Michalconok and A. Bohm. “Identification of KDD Problems from Medical Data.” in 8 th Computer Science On-Line Conference (CSOC). Artificial Intelligence Methods in Intelligent Algorithms Book Series: Advance in Intelligent Systems and Computing. 2019, vol. 985, pp. 191-199
• [20] T. Martinec, J. Mlýnek, M. Petru. “Calculation of the robot trajectory for the optimum directional orientation of fibre placement in the manufacture of composite profile frames.” Rob. And Comp-Integr. Man., vol. 35, pp. 42-54, Oct. 2015.
• [21] Zhang Zhiyong, He Dongjian, Tang Jing Lei, Meng Lingshuai. “Picking Robot Arm Trajectory Planning Method.” Sensors & Transducers, vol. 162, pp. 11-20, Jan. 2014.
• [22] B. Siciliano et al. Robotics (Modeling, planning and control), Springer, Berlin, 2009, chapter 4: Trajectory planning, pp. 161-189.
• [23] A. Gaspareto, P. Boscariol, A. Lanzutti, R. Vidoni. “Trajectory Planning in Robotics.” Math. Comput. Sci, vol. 6, pp. 269- 279, Aug. 2012.
• [24] R. Benotsman, S. E. Kacemi, M. Redhabennachenhou. “Calculation methodology for trajectory planning of a 6-axis manipulator arm.” in Annals of faculty engineering Hunedoara – Inter. Journal of Eengin. Tome xvi, vol. XVI, pp. 27-32, Aug. 2018.
• [25] P. Bozek, P. Pokorny, J. Svetik, A. Lozhkin, I. Arkhipov. “The calculations of Jordan curves trajectory of robot movement.” IJARS, vol. 7, doi:10.11.77/1729881416663665, 2016.
• [26] P. Bozek, Z. Ivandic and others. “Solutions to the characteristic equation for industrial robot's elliptic trajectories.” Tehniheski vjesnik - Technical Gazette, vol. 23, pp. 1017- 1023, 2016.
• [27] K. Joonyoung. “Trajectory Generation of a Two-Wheeled Mobile Robot in an Uncertain Environment.” in IEEE Trans. on indust. electronics, 2020, vol. 67/7, pp. 5586-5594.
• [28] M. Bottin, G. Rosati.“Trajectory Optimization of a Redundant Serial Robot Using Cartesian via Points and Kinematic Decoupling.” in Robotics, vol. 8/4, Art. N. 101, 2019.
• [29] N. Efimov. Quadratic forms and matrices. Fizmatlit, Moscow, 2012.
• [30] A. Lozhkin. Applied planemetry with singular transformations. IE UrO RAS, Ekaterinburg, 2009.
• [31] A. Lozhkin, A., N. Dyukina. Structurization of analytical geometry on the base of symmetries. LAP, Saarbruken, 2012.
• [32] F. Cao, J.L. Lisaniandothers. A theory of shape identification.Springer, Berlin Heidelberg, 2008.
• [33] P. Božek, A. Lozhkin, A. Gorbushin. "Geometrical Method for Increasing Precision of Machine Building Parts" In Proc. Procedia Engineering. vol. 149, 2016, pp 576-580
• [34] M. Beno, M. Zvoncan, M. Kovac, J. Peterka. “Circular interpolation and positioning accuracy deviation measurement on five axis machine tools with different structures.” Tehnicki vjesnik-technical gazette, vol20, pp. 479-484, Jun 2013.
• [35] J. Peterka, P. Pokorny, S. Vaclav. “CAM strategies and surface accuracy.” in Annals of DAAAM and Proc. of the Intern. DAAAM Symp. 2008. Annals of DAAAM for 2008 and 19th Intern. DAAAM Symposium, Intelligent Manufacturing and Automation: Focus on Next Generation of Intelligent Systems and Solutions, Trnava, 2008, pp.1061-1062.
• [36] M. Kovac, J. Peterka. “Selected 5-axis Strategies for Highspeed milling of Thin-walled Parts. ”Applied Mechanics and Materials. Vol. 467, pp. 466-469, Dec. 2013.
• [37] P.S. Aleksandrov. Lectures on analytical geometry, supplemented by the necessary information from the algebra. Ripol-classic, Moscow, 2002.
• [38] C.G. Gibson. Elementary geometry of differentiable curves: an undergraduate introduction. Cambridge, CUP, 2001.
• [39] A.A. Savelov. Plane curves. Systematics, properties, applications: reference manual. Editorial URSS, Moscow, 2010.
• [40] J. Hrbcek, P. Bozek and others. “Control system for the haptic paddle used in mobile robotics. ”IJARS, vol. 14, doi.org/10.1177/1729881417737039, 2017.
• [41] R. Pirnik, M. Hruboš and others. “Integration of inertial sensor data into control of the mobile platform. ”in Advances in Intelligent and Soft Computing, SDOT 2015, vol. 511, pp. 271-282.
• [42] E. Pivarciova, P. Božek and others. “Analysis of control and correction options of mobile robot trajectory by an inertial navigation system”. IJARS, vol. 15, pp. 1-15, 2018.
• [43] M. Nemeth, G. Michalconok and A. Peterkova. “The analysis of emerging failures of process control systems based on data mining.” in INES 2017 – IEEE 21st Int. Conf. on Intelligent Engineering Systems, Proceedings, 2017, pp. 55-59.
• [44] W. Puchala, W. Bialy, G. Bobkowski. “Possible Applications of Computer Maintenance Management Systems.” in Scientific Journals of the Maritime University of Szczecin – Zeszyty Naukowe Akademii Morskiej w Szczecinie. 2009, vol. 19, pp. 10-15.
• [45] P. Bozek. Robot path optimization for spot welding applications in automotive industry. Tehnički Vjesnik - Technical Gazette. Vol. 20, No. 5 , pp. 913-917, 2013.
• [46] A. Nemethova, D. Borkin and G. Michalconok. “Comparison of Methods for Time Series Data Analysis for Further Use of Machine Learning Algorithms.” in Proceed. of the Comput. Methods in Syst. and Soft. Springer, Cham, 2019, pp. 90-99.
• [47] R. Urban, M. Štroner, T. Křemen, J. Braunand, M. Möser, M. A novel approach to estimate systematic and random error of terrain derived from UAVs: a case study from a post-mining site Acta Montanistica Slovaca Volume 23 Issue 3 pp. 325-336, 2018.
• [48] M. Stroner, T. Kremen, J. Braun, R. Urban, P. Blistan, L. Kovanic. Comparison of 2.5D Volume Calculation Methods and Software Solutions Using Point Clouds Scanned Before and After Mining, Acta Montanistica Slovaca, Volume 24, Issue 4, 2019, pp. 296-306.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).