donstuAdvanced Engineering Research (Rostov-on-Don)Advanced Engineering Research (Rostov-on-Don)2687-1653Don State Technical University10.23947/2687-1653-2023-23-4-356-364IQHEGMdonstu-2106Research ArticleMECHANICSМЕХАНИКАAnalysis of Positioning Accuracy in Case of Design Errors in the Installation of Mecanum Wheels of the Mobile PlatformАнализ точности позиционирования при конструкционных погрешностях в установке меканум-колёс мобильной платформыhttps://orcid.org/0009-0008-8029-3523ПанкратьеваГ. В.PankratevaG. V.

Галина Витальевна Панкратьева, кандидат физико-математических наук, доцент кафедры робототехники, мехатроники, динамики и прочности машин

111250, г. Москва, ул. Красноказарменная, 14

Galina V. Pankrateva, Cand.Sci. (Phys.-Math.), Associate Professor of the Department of Robotics, Mechatronics, Dynamics and Strength of Machines

14, Krasnokazarmennaya St., Moscow, 111250

gvpankr@gmail.comhttps://orcid.org/0009-0004-5238-4584МординА. Е.MordinA. E.

Антон Евгеньевич Мордин, студент кафедры робототехники, мехатроники, динамики и прочности машин 

111250, г. Москва, ул. Красноказарменная, 14

Anton E. Mordin, student of the Department of Robotics, Mechatronics, Dynamics and Strength of Machines

14, Krasnokazarmennaya St., Moscow, 111250

ToxaM_99@mail.ruhttps://orcid.org/0000-0002-9827-360XСайпулаевГ. Р.SaypulaevG. R.

Гасан Русланович Сайпулаев, аспирант и ассистент кафедры робототехники, мехатроники, динамики и прочности машин, ScopusID

111250, г. Москва, ул. Красноказарменная, 14

Gasan R. Saypulaev, postgraduate student, teaching assistant of the Department of Robotics, Mechatronics, Dynamics and Strength of Machines, ScopusID

14, Krasnokazarmennaya St., Moscow, 111250

saypulaevgr@mail.ruНациональный исследовательский университет «Московский энергетический институт»РоссияNational Research University “Moscow Power Engineering Institute”Russian Federation202327122023234356364Copyright © Pankrateva G.V., Mordin A.E., Saypulaev G.R., 20232023Панкратьева Г.В., Мордин А.Е., Сайпулаев Г.Р.Pankrateva G.V., Mordin A.E., Saypulaev G.R.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.vestnik-donstu.ru/jour/article/view/2106Introduction

Introduction. Mobile robots capable of omnidirectional movement are widely used in various fields of human activity. To provide high accuracy of positioning of omnidirectional platforms with mecanum wheels, it is required to develop their detailed mathematical models used in the construction of a motion control system. Due to the complicated design of the mecanum wheels, various errors may occur during the construction of omnidirectional platforms, including the error of installing such wheels on the platform. Its effect on the accuracy of the platform movement has not been studied before. This work aims at assessing the positioning errors that arise due to the presence of design errors in the installation of mecanum wheels, and analyzing the effect of these errors on the accuracy of program motion testing when using control at the kinematic level.

Materials and Methods

Materials and Methods. The analysis of positioning accuracy was based on mathematical modeling of the platform kinematics, taking into account structural errors in the installation of mecanum wheels. To describe the relationship between the angular speeds of rotation of the wheels and the speeds of the platform, the conditions of nonslip of the contact points on the support surface were used. Numerical calculations were carried out in the Wolfram Mathematica package.

Results

Results. A formula was obtained for estimating errors in platform pseudovelocities under program control formed at the kinematic level. The estimation of the errors of the platform speeds for simple movements was carried out. According to the calculation results, it has been shown that the speed errors are significant for robots with mecanum wheels operating autonomously.

Discussion and Conclusion. The calculation results demonstrated the significant impact of wheel installation errors on the positioning accuracy of the mecanum-platform, and confirmed the need to take into account these design errors when creating autonomous mecanum-platforms. The constructed model of the robot's kinematics makes it possible to predict errors in platform speeds that arise under program control, as well as deviations of the coordinates of the geometric center of the platform from the program motion. The proposed kinematic model can be used to improve the positioning accuracy through forming a platform motion control that compensates for the influence of wheel installation errors.

Введение

Введение. Мобильные роботы, способные осуществлять всенаправленное движение, широко применяются в различных областях человеческой деятельности. Для обеспечения высокой точности позиционирования всенаправленных платформ с меканум-колёсами требуется разработать их детальные математические модели, используемые при построении системы управления движением. Из-за непростой конструкции меканум-колёс при построении всенаправленных платформ могут возникать различные погрешности, включая погрешность установки таких колёс на платформу. Влияние ее на точность движения платформы ранее не исследовалось. Целью данной работы является оценка ошибок позиционирования, возникающих из-за наличия конструкционных погрешностей в установке меканум-колёс, и анализ влияния указанных погрешностей на точность отработки программного движения при использовании управления на кинематическом уровне.

Материалы и методы

Материалы и методы. Анализ точности позиционирования основан на математическом моделировании кинематики платформы с учетом конструкционных погрешностей в установке меканум-колёс. Для описания взаимосвязи между угловыми скоростями вращения колес и скоростями платформы используются условия непроскальзывания точек контакта по опорной поверхности. Численные расчеты проведены в математическом пакете Wolfram Mathematica.

Результаты исследования

Результаты исследования. Получена формула для оценки погрешностей псевдоскоростей платформы при программном управлении, формируемом на кинематическом уровне. Проведена оценка погрешностей скоростей платформы для простых движений. По результатам расчетов показано, что погрешности скоростей являются значительными для роботов с меканум-колёсами, функционирующих автономно.

Обсуждение и заключение

Обсуждение и заключение. Результаты расчетов продемонстрировали существенное влияние погрешностей установки колес на точность позиционирования меканум-платформы и подтвердили необходимость учитывать указанные конструкционные погрешности при создании автономных меканум-платформ. Построенная модель кинематики робота позволяет прогнозировать ошибки отработки скоростей платформы, возникающие при программном управлении, а также отклонения координат геометрического центра платформы от программного движения. Кинематическая модель может быть использована для повышения точности позиционирования за счет формирования управления движением платформы, компенсирующего влияние неточностей установки меканум-колёс.

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