On a Method of the Mathematical Modeling of Wheel Deformation in the Problems of Controlling Wheeled Robots

The article discusses the problem of determining the minimum required number of tire deformation parameters to adequately describe the dynamics of a wheeled vehicle, since, as you know, the behavior of the model wheeled vehicle non-deformable wheel does not correspond to the real one. The need to include a particular parameter of the deformation in the consideration is proposed to be determined by testing the solvability of the stabilization problem for a given unperturbed motion to non-asymptotic stability with respect to all variables. In this work as a test problem was chosen to stabilize the rectilinear stationary motion of the simplest and most studied model of a two-wheeled mobile robot with a differential electric drive. A computational experiment using the PyStab software showed that the formal fulfillment of the criterion controllability for a complete system does not always ensure the practical solvability of the stabilization problem. In this situation, stabilizing control is determined by solving the linear-quadratic problem for a controlled linear subsystem by Krasovskii's method. The methods of analytical mechanics and nonlinear theory of stability are used, to obtain a conclusion about stability in a complete nonlinear system closed by this control. © 2020 IEEE.