Boris Adamov

This article is devoted to a study of the geometry and kinematics of the Mecanum wheels, also known as Ilon wheels or the Swedish wheels. The Mecanum wheels are one of the types of omnidirectional wheels. This property is provided by peripheral rollers whose axes are deviated from the wheel one by 45 degrees. A unified approach to studying the geometry and kinematics of the Mecanum wheels on a plane and on the internal or external surface of a sphere is proposed. Kinematic relations for velocities at the contact point of the wheel and the supporting surface, and angular velocities of the roller relative to the supporting surface are derived. They are necessary to describe the dynamics of the Mecanum systems taking into account forces and moments of contact friction in the presence of slipping. From the continuous contact condition, relations determining the geometry of the wheel rollers on a plane and on the internal or external surface of a sphere are obtained. The geometric relations for the Mecanum wheel rollers could help to adjust the existing shape of the Mecanum wheel rollers of spherical robots and ballbots to improve the conditions of contact between the rollers and the spherical surface. An analytical study of the roller geometry was carried out, and equations of their generatrices were derived. Under the no-slipping condition, expressions for rotational velocities of the wheel and the contacting roller are obtained. They are necessary for analyzing the motion of systems within the framework of nonholonomic models, solving problems of controlling Mecanum systems and improving its accuracy. Using the example of a spherical robot with an internal three-wheeled Mecanum platform, the influence of the rollers on the robot movement was studied at the kinematic level. It has been established that the accuracy of the robot movement is influenced not only by the geometric parameters of the wheels and the number of rollers, but also by the relationship between the components of the platform center velocity and its angular velocity. Results of the numerical simulation of the motion of the spherical robot show a decrease in control accuracy in the absence of feedback on the robot’s position due to effects associated with the finite number of rollers, their geometry and switching. These effects lead not only to high-frequency vibrations, but also to a “drift” of the robot trajectory relative to the reference trajectory. Further research on this topic involves the use of the motion separation methods and the statistical methods for kinematical and dynamical analysis of Mecanum systems.

The subject of this paper is a spherical robot with an internal platform with four classictype omniwheels. The motion of the spherical robot on a horizontal surface is considered and its kinematics is described. The aim of the research is to study the dynamics of the spherical robot with different levels of detailing of the contact friction model. Nonholonomic models of the dynamics of the robot with different levels of detailing of the contact friction model are constructed. The programmed control of the motion of the spherical robot using elementary maneuvers is proposed. A simulation of motion is carried out and the efficiency of the proposed control is confirmed. It is shown that, at low speeds of motion of the spherical robot, it is allowed to use a model obtained under the assumption of no slipping between the sphere and the floor. The influence of the contact friction model at high-speed motions of the spherical robot on its dynamics under programmed control is demonstrated. This influence leads to the need to develop more accurate models of the motion of a spherical robot and its contact interaction with the supporting surface in order to increase the accuracy of motion control based on these models.

The subject of this study is an omnidirectional mobile platform equipped with four Mecanum wheels. The movement of the system on a horizontal plane is considered. The aim of this research is to study the dynamics of the omnidirectional platform, taking into account the design of Mecanum wheels: the shape of the rollers and their finite number. The equations of motion of the onmidirectional mobile platform are derived taking into account the real design of the Mecanum wheels and their slippage. A comparative analysis of the results of numerical modeling for different models of contact friction forces is presented. It has been established that switching of contact rollers and displacement of contact points lead to the occurrence of high-frequency components of wheel rotation speeds, as well as an offset of their average values (in comparison with the modeling results without taking into account the design features of the chassis).

The object of the study is the mobile platform of the KUKA youBot robot equipped with four Mecanum wheels. The ideal conditions for the point contact of the wheels and the floor are considered. It is assumed that the rollers of each Mecanum wheel move without slipping and the center of the wheel, the center of the roller axis, and the point of contact of the roller with the floor are located on the same straight line. The dynamics of the system is described using Appel’s equations and taking into account the linear forces of viscous friction in the joints of the bodies. An algorithm for determination of the control forces is designed. Their structure is the same as that of the reactions of ideal constraints determined by the program motion of the point of the platform. The controlled dynamics of the system is studied using uniform circular motion of the platform point as an example: conditions for the existence and stability of steady rotations are found, conditions for the existence of stable-unstable stationary regimes and rotational motions of the platform are obtained. Within the framework of the theory of singular perturbations, an asymptotic analysis of the rotation of the platform is carried out.