Analysis of positioning accuracy in case of design errors in the installation of mecanum wheels of the mobile platform

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. 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. 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.