On the Influence of the Wheels Deformability on the Differential Drive Robot Dynamics

The problem of determining the minimum number of wheel deformation parameters to adequately describe the vehicle dynamics is considered. The necessity to include some system parameter into consideration is proposed to determine via check of stabilization problem solvability (of a given unperturbed motion to nonasymptotic stability in all variables). In this paper, as a test case the problem of stabilization of rectilinear steady motion of the simplest and most studied model of differential drive robot is selected. Computational experiments made via PyStab software show that the formal realization of the controllability criterion for complete system does not always provide the practical solvability of stabilization problem. In this case the stabilizing control is determined by solution of linear-quadratic problem via N.N. Krasovskiy method for controllable linear subsystem. To learn about the stability of the full nonlinear system closed with found control, methods of analytical mechanics and nonlinear stability theory are involved. The study of the robot dynamics is performed by PyStab. This software is intended for automation of research of mechanical systems stability and stabilization problems. In the transition to the numerical consideration along with PyStab NSA software is used since calculation time and the structure of the nonlinear terms of equations of perturbed motion will depend on what stage of the calculations the substitution of numerical parameters of the system is performed.