# Research on the Dynamics of an Omnidirectional Platform Taking into Account Real Design of Mecanum Wheels (as Exemplified by KUKA youBot)

Received 14 August 2019; accepted 21 January 2020

2020, Vol. 16, no. 2, pp.  291-307

Author(s): Adamov B. I., Saypulaev G. R.

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).
Keywords: omniplatform, Mecanum platform, Mecanum wheel, youBot, omniwheel
Citation: Adamov B. I., Saypulaev G. R., Research on the Dynamics of an Omnidirectional Platform Taking into Account Real Design of Mecanum Wheels (as Exemplified by KUKA youBot), Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 2, pp.  291-307
DOI:10.20537/nd200205

## Supplement

The animations a) and b) visualize the results of a numerical simulation of the movement of the youBot mecanum platform. Translucent platforms move in accordance with the non-holonomic model 1a, and opaque ones, in accordance with model 2b (the real design of Mecanum wheels and contact Coulomb friction forces are taken into account). The control torques are chosen as functions of time $M_i=M_i (t), i=1,...4,$ according to the equations of the nonholonomic model 1a from the condition for implementing the following desired motions:

a) Translational motion in the circle.

b) Lateral motion around the circle.