Modelling of Dynamics of a Wheeled Mobile Robot with Mecanum Wheels with the use of Lagrange Equations of the Second Kind

Abstract

The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

Dynamics of omnidirectional unmanned rescue vehicle with mecanum wheels

“…where: E -total kinetic energy of the system, U -potential energy of the system [6,21]. It is assumed that the vehicle moves on a flat surface, so the relation (5) is simplified to the following form:…”

“…The problem of manoeuvrability can be solved using the so-called omnidirectional wheels (Fig. 1a), which consist of a hub and a specified number of rollers mounted on the hub circumference [3,4,5,6,7,8].…”

“…1a). Mecanum wheels are also often called, so-called Swedish wheels, due to the origin of their creator [3,5,6,9]. Only one publication [10] was found in the Web of Science database concerning omnidirectional platforms with six mecanum wheels.…”

“…Only one publication [10] was found in the Web of Science database concerning omnidirectional platforms with six mecanum wheels. Most publications about mecanum wheels concern platforms or wheeled mobile robots having four or three of these wheels [3,4,5,6,7,9,11,12,13,14,15,16,17,18].…”

Modeling of Two-Wheeled Self-Balancing Robot Driven by DC Gearmotors

“…Suppose that there is no slip between the wheels and the ground. The Lagrange's second order equations are used for modelling of a mechanical subsystem [4,9]. The no slip condition of movement is given by…”