novtexmechМехатроника, автоматизация, управлениеMekhatronika, Avtomatizatsiya, Upravlenie1684-64272619-1253Commercial Publisher «New Technologies»10.17587/mau.25.633-645novtexmech-1664Research ArticleРОБОТЫ, МЕХАТРОНИКА И РОБОТОТЕХНИЧЕСКИЕ СИСТЕМЫROBOT, MECHATRONICS AND ROBOTIC SYSTEMSИнтерполятор, обеспечивающий высокую точность поддержания скорости рабочего органа промышленного робота. Часть IAn Interpolator, Providing High Accuracy of Industrial Robot’s End-Effector Speed. Part IЛаричевД. В.LarichevD. V.

Студент

Москва

Moscow, 119454

dlaritchev@hotmail.comРомановМ. П.RomanovM. P.

Д-р техн. наук, зав. кафедрой

Москва

Moscow, 119454

m_romanov@mirea.ruРомановA. М.RomanovA. M.

Д-р техн. наук, проф.

Москва

Romanov Alexey M., Dr. habil., Professor

Moscow, 119454

romanov@mirea.ruМИРЭА — Российский технологический университетРоссияMIREA Russian Technological UniversityRussian Federation2024051220242512633645Copyright © Commercial Publisher «New Technologies», 20242024Commercial Publisher «New Technologies»Commercial Publisher «New Technologies»https://mech.novtex.ru/jour/about/submissions#copyrightNoticehttps://mech.novtex.ru/jour/article/view/1664

Интерполятор является одним из ключевых элементов систем контурного управления промышленными роботами, существенно влияющих на их точностные характеристики. В таких технологических задачах, как сварка, лазерная резка, нанесение покрытий и наплавка, помимо пространственной точности движения рабочего органа робота важную роль играет точность поддержания им скорости в процессе движения по сложным траекториям. Предлагается новое алгоритмическое обеспечение для решения задачи интерполяции при реализации контурного управления многоосевым промышленным роботом, основанное на применении В-сплайнов. Предложенные алгоритмы легко адаптируются для роботов с любой кинематикой, формируя на выходе как общую траекторию движения рабочего органа робота, так и уставки по току, скорости и положению для контуров управления каждого из его приводов. В рамках исследования на основе разработанных алгоритмических решений была создана программная реализация offUne-интерполятора, предназначенная для исполнения на базе контроллеров и приводов, произведенных компанией В&R Industrial Automation GmbH. В ходе натурных экспериментальных исследований, проведенных на манипуляционном роботе с кинематической схемой SCARA, было продемонстрировано, что разработанные алгоритмические решения превосходят штатный интерполятор промышленных систем управления роботами от компании В&R, улучшая результаты примерно в два раза с точки зрения пространственной точности и в четыре раза с точки зрения среднеквадратического отклонения скорости. Максимальное отклонение скорости инструмента от заданных значений при использовании разработанных алгоритмов за все время проведения экспериментов не превышало 2,4 мм/c, что сравнимо с результатами наиболее современных планарных решений на базе NURBS-кривых. При этом решения, предложенные в данной работе, в отличии от планарных аналогов подходят для многомерной интерполяции. В первой части работы рассматриваются алгоритмы, лежащие в основе разработнного многосевого интерполятора.

The interpolator is one of the critical components of contour control systems for industrial robots, which significantly affects their accuracy. In such technological tasks as welding, laser cutting, coating, and surfacing, in addition to the spatial accuracy of the robot’s end-effector, the accuracy of its velocity during motion along complex trajectories plays an important role. In this paper, we propose a new approach for solving the interpolation problem of a multi-axis industrial robot based on the В-splines. The proposed algorithms can be easily adapted for robots with any kinematics, generating the current, velocity, and position setpoints for the control loops of each of its actuators. А software implementation of the offline interpolator based on the proposed algorithms was developed and executed on В&R Industrial Automation GmbH industrial controllers. During the experimental studies performed on a manipulation robot with SCARA kinematic scheme, it was demonstrated that the developed algorithmic solutions outperform the standard interpolator of В&R industrial robot control systems, exceeding it up to 2 times in terms of spatial accuracy and up to 4 times in terms of root mean square velocity deviation. The maximum deviation of the tool’s velocity using the developed algorithms did not exceed 2.4 mm/s, comparable to the results of the most modern planar solutions based on NURBS curves. At the same time, unlike their planar analogs, the solutions proposed in this paper are suitable for multidimensional interpolation. In this part of the paper, we describe the algorithms of the developed multi-axis interpolator.

планирование траекторииманипуляторпромышленный роботинтеполяцияВ-сплайнкинематикаэлектроприводpath planningrobotic armindustrial robotinterpolationВ-splinekinematicsservodriveReferencesLi X. et al. А novel cartesian trajectory planning method by using triple NURBS curves for industrial robots // Robotics and Computer-Integrated Manufacturing. 2023. Vol. 83. P. 102576.Li X., Zhao H., He X., Ding H. А novel cartesian trajectory planning method by using triple NURBS curves for industrial robots, Robotics and Computer-Integrated Manufacturing, 2023, vol. 83, pp. 102576.Wang B. et al. Intelligent welding system technologies: State-of-the-art review and perspectives // Journal of Manufacturing Systems. 2020. Vol. 56. P. 373—391.Wang B., Hu S. J., Sun L., Freiheit T. Intelligent welding system technologies: State-of-the-art review and perspectives, Journal of Manufacturing Systems, 2020, vol. 56, pp. 373—391.Dolgui A., Pashkevich А. Manipulator motion planning for high-speed robotic laser cutting // International Journal of Production Research. 2009. Vol. 47, N. 20. P. 5691—5715.Dolgui A., Pashkevich А. Manipulator motion planning for high-speed robotic laser cutting, International Journal of Production Research, 2009, vol. 47, iss. 20, pp. 5691—5715.Gleeson D. et al. Generating optimized trajectories for robotic spray painting //IEEE Transactions on Automation Science and Engineering. 2022. Vol. 19, N. 3. P. 1380—1391.Gleeson D., Jakobsson S., Salman R., Ekstedt F., Sandgren N., Edelvik F., Carlson J. S., Lennartson В. Generating optimized trajectories for robotic spray painting, IEEE Transactions on Automation Science and Engineering, 2022, vol. 19, iss. 3, pp. 1380—1391.Yuan L. et al. Application of multidirectional robotic wire arc additive manufacturing process for the fabrication of complex metallic parts // IEEE Transactions on Industrial Informatics. 2019. Vol. 16, N. 1. P. 454-464.Yuan L., Ding D., Pan Z., Yu Z., Wu B.,van Duin S., Li H., Li W. Application of multidirectional robotic wire arc additive manufacturing process for the fabrication of complex metallic parts, IEEE Transactions on Industrial Informatics, 2019, vol. 16, iss. 1, pp. 454—464.Pires J. N., Loureiro A., B Imsjo G. Welding robots: technology, system issues and application. New York: Springer, 2006.Pires J. N., Loureiro A., B lmsjo G. Welding robots: technology, system issues and application, New York, Springer, 2006.Paul R., Luh J. Advanced industrial robot control systems // Ninth Conference on Production Research and Technology: (formerly NSF Grantees’ Conference). 1981. Vol. 1. P.65-74.Paul R., Luh J. Advanced industrial robot control systems, Ninth Conference on Production Research and Technology: (formerly NSF Grantees’ Conference), 1981, vol. 1, pp. 65—74.Koren Y. Robotics for engineers. New York: McGraw-НШ, 1985.Koren Y. Robotics for engineers, New York, McGraw-Hill, 1985.Fu K. S. et al. Robotics: control, sensing, vision, and intelligence. New York: McGraw-Hill, 1987. Vol. 1.Fu K. S., Gonzalez R. C., Lee C. G., Freeman H. Robotics: control, sensing, vision, and intelligence, New York, McGraw-Hill, 1987, vol. 1.Tamizi M. G., Yaghoubi M., Najjaran H. А review of recent trend in motion planning of industrial robots // International Journal of Intelligent Robotics and Applications. 2023. Vol. 7, No. 2. P. 253-274.Tamizi M. G., Yaghoubi M., Najjaran H. А review of recent trend in motion planning of industrial robots, International Journal of Intelligent Robotics and Applications, 2023, vol. 7, iss. 2, pp. 253—274.Голубов В. В., Манько С. В. Особенности и перспективы применения метода поисковых случайных деревьев для планирования перемещений автономных роботов // Russian Technological Journal. 2023. Vol. 11, No. 6. P. 16-27.Golubov V. V., Manko S. V. Features and perspectives of application of the rapidly exploring random tree method for motion planning of autonomous robotic manipulators, Russian Technological Journal, 2023, vol. 11, iss. 6, pp. 16—27.Wu P. et al. Optimal Time-Jerk Trajectory Planning for Delta Parallel Robot Based on Improved Butterfly Optimization Algorithm // Applied Sciences. 2022. Vol. 12, No. 16. P. 8145.Wu P., Wang Z., Jing H., Zhao P. Optimal Time—Jerk Trajectory Planning for Delta Parallel Robot Based on Improved Butterfly Optimization Algorithm, Applied Sciences, 2022, vol. 12, iss. 16, pp. 8145.Duan J. et al. Path planning based on NURBS for hyperredundant manipulator used in narrow space // Applied Sciences. 2022. Vol. 12, No. 3. P. 1314.Duan J., Wang B., Cui K., Dai Z. Path planning based on NURBS for hyper-redundant manipulator used in narrow space, Applied Sciences, 2022, vol. 12, iss. 3, pp. 1314.Liu X. et al. А High-Precision Planar NURBS Interpolation System Based on Segmentation Method for Industrial Robot // Applied Sciences. 2023. Vol. 13, No. 24. P. 13210.Liu X., Xu, Y., Cao J., Liu J., Zhao Y. А High-Precision Planar NURBS Interpolation System Based on Segmentation Method for Industrial Robot, Applied Sciences, 2023, vol. 13, iss. 24, pp. 13210.Shi B., Zeng Н. Time-optimal trajectory planning for industrial robot based on improved Hybrid-PSO // 2021 40th Chinese Control Conference (CCC). IEEE, 2021. P. 3888-3893Shi B., Zeng Н. Time-optimal trajectory planning for industrial robot based on improved Hybrid-PSO, 2021 40th Chinese Control Conference (CCC), IEEE, 2021, pp. 3888—3893.Dierckx P. An algorithm for smoothing, differentiation and integration of experimental data using spline functions // Journal of Computational and Applied Mathematics. 1975. Vol. 1, No. 3. P. 165-184.Dierckx P. An algorithm for smoothing, differentiation and integration of experimental data using spline functions, Journal of Computational and Applied Mathematics, 1975, vol. 1, iss. 3 , pp. 165—184.De Boor C. On calculating with В-splines // Journal of Approximation theory. 1972. Vol. 6, No. 1. P. 50-62.De Boor C. On calculating with В-splines, Journal of Approximation theory, 1972, vol. 6, iss. 1, pp. 50—62.De Boor C. А practical guide to splines. Vol. 27. New York: Springer-Verlag, 1978. P. 325.De Boor C. А practical guide to splines, New York, Springer-Verlag, 1978, vol. 27, pp. 325.Woltring H. J. А Fortran package for generalized, crossvalidatory spline smoothing and differentiation // Advances in Engineering Software (1978). 1986. Vol. 8, No. 2. P. 104-113.Woltring H. J. А Fortran package for generalized, crossvalidatory spline smoothing and differentiation, Advances in Engineering Software (1978), 1986, vol. 8, iss. 2, pp. 104—113.Hastie T. et al. The elements of statistical learning: data mining, inference, and prediction. Vol. 2. New York: Springer, 2009. P. 1-758.Hastie T., Tibshirani R., Friedman J. H., Friedman J. H. The elements of statistical learning: data mining, inference, and prediction, New York, Springer, 2009, vol. 2, pp. 1—758.Virtanen P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python // Nature methods. 2020. Vol. 17, No. 3. P. 261-272.Virtanen P., Gommers R., Oliphant T. E., Haberland M., Reddy T., Cournapeau D., Burovski E., Peterson P., Weckesser W., Bright J., van der Walt S. J., Brett M., Wilson J., Millman K. J., Mayorov N., Nelson A. R. J., Jones E., Kern R., Larson E, C. J. Carey, Polat I., Feng Y., Moore E. W., VanderPlas J., Laxalde D., Perktold J., Cimrman R., Henriksen I., Quintero E. A., Harris C. R., Archibald A. M., Ribeiro A. H., Pedregosa F., Paul van Mulbregt, SciPy 1.0 Contributors. SciPy 1.0: fundamental algorithms for scientific computing in Python, Nature methods, 2020, vol. 17, iss. 3, pp. 261—272.Fleisig R. V., Spence A. D. А constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining // Computer-Aided Design. 2001. Vol. 33, No. 1. P. 1-15.Fleisig R. V., Spence A. D. А constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining, Computer-Aided Design, 2001, vol. 33, iss. 1, pp. 1—15.Rysak P. Comparative analysis of code execution time by C and Python based on selected algorithms // Journal of Computer Sciences Institute. 2023. Vol. 26. P. 93-99.Rysak P. Comparative analysis of code execution time by C and Python based on selected algorithms, Journal of Computer Sciences Institute, 2023, vol. 26, pp. 93—99.Behnel S. et al. Cython: The best of both worlds // Computing in Science & Engineering. 2010. Vol. 13, No. 2. P. 31-39.Behnel S., Bradshaw R., Citro C., Dalcin L., Seljebotn D. S., Smith K. Cython: The best of both worlds, Computing in Science & Engineering, 2010, vol. 13, iss. 2, pp. 31—39.Smith K. W. Cython: А Guide for Python Programmers. Sebastopol: O’Reilly Media, Inc., 2015.Smith K. W. Cython: А Guide for Python Programmers. Sebastopol: O’Reilly Media, Inc., 2015.Nishino R., Loomis S. Н. C. CuPy: А numpy-compatible library for NVIDIA GPU calculations // 31st confernce on neural information processing systems. 2017. Vol. 151, No. 7.Nishino R., Loomis S. Н. C. CuPy: А numpy-compatible library for NVIDIA GPU calculations, 31st confernce on neural information processing systems, 2017, vol. 151, pp. 7.Farber R. CUDA application design and development. Amsterdam: Elsevier, 2011.Farber R. CUDA application design and development. Amsterdam: Elsevier, 2011.Romanov A. M., Gyrichidi N., Romanov M. P. А Novel Gripper with Integrated Rotary Unit and Force Control for Pick and Place Applications // Robotics. 2022. Vol. 11, No. 6. P. 155.Romanov A. M., Gyrichidi N., Romanov M. P. А Novel Gripper with Integrated Rotary Unit and Force Control for Pick and Place Applications, Robotics, 2022, vol. 11, iss. 6, pp. 155.

The authors declare that there are no conflicts of interest present.