A Dynamicly Consistent Model of Normal Reactions at Points of a Mobile Platform Contact with a Surface Taking Account of the Design of Mecanum Wheels and Multicomponent Friction

Abstract

The article investigates the influence of the dependence of normal reactions on motion parameters on the dynamics of a mobile platform by taking into account the design of mecanum wheels and multicomponent friction. To describe the dependence of normal reactions on motion parameters, the theorems on the change in momentum and angular momentum written for the mecanum platform are used. The influence of normal reactions on the dynamics of the mecanum platform is estimated from the results of numerical simulation. The mecanum platform dynamics model takes into account the design of the mecanum wheels and multicomponent friction. The multicomponent friction model proposed by V.F. Zhuravlev that takes into account sliding and spinning is considered. Estimates of the maximum deviations of the normal reactions of the supports, due to the dynamics of the mecanum platform, from the values of the normal reactions calculated for the mobile platform at rest (equal to 16.7% for KUKA youBot robot) are given. Inequalities that limit the maximum values of the control moments, under which the contacting rollers of the mecanum wheels do not come off from the supporting surface are obtained. Based on the simulation results, it is shown that the normal responses are changed by 5–6% of the normal response value calculated in the case of the mecanum platform at rest, which corresponds to the obtained estimates. These changes in normal reactions can lead to a decrease in the accuracy of the movement of the mecanum platform obtained with program control.