Conditions for the Applicability of the Lagrange Equations of the Second Kind to Mecanum-Wheeled Robots

Different approaches to describing the kinematics and dynamics of a mobile robot equipped with four Mecanum wheels are compared. Due to the no-slip rolling condition, the kinematic constraints imposed on the system are nonholonomic; therefore, the equations of nonholonomic mechanics must be used to model such a system. The necessary and sufficient conditions under which the dynamics of this system can be described using Lagrange equations of the second kind are derived. The solvability of the kinematic constraint equations using the pseudoinverse matrix is also analyzed.