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.
This paper proposes a method for implementing the program motion of a point of the platform. The structure of control forces repeats that of reactions of ideal constraints which are given by the program motion. Animations of the motion of the platform along a circle are presented below:
a) The case of stable steady rotation of the platform (the radius of the circle is larger than the critical one, conditions (4.8) are satisfied, see also the results of mathematical modeling in Fig. 4
b) The case of rotational motion (the radius of the circle is smaller than the critical one and conditions (4.8) are violated.