Comparison of Control Law Synthesis Methods for the Wheeled Robot Motion
Abstract
In modern control theory one of the most complex and actual issues is the control law synthesis for nonlinear systems. This is due to the fact that in most cases the mathematical model of the control object motion is described by a system of nonlinear differential equations and there are no universal approaches to the control law synthesis for such systems. As a rule, the choice of one or another control algorithm depends on many factors, including the type of system. This paper investigates the application of various methods for the control law synthesis of the wheeled robot motion. The aim of the control is to move the robot to a given position, i.e. solution of the positioning problem. As control algorithms, the feedback linearization method and the optimal damping method, which was first proposed by V.I. Zubov in the early 1960s, are considered. The feedback linearization method, after reducing the nonlinear system to a linear form, allows one to construct an optimal control by solving the LQR-optimization problem, while the optimal damping method allows one to obtain only an approximate solution of the optimal control problem, reducing it to a parametric optimization problem. However, the feedback linearization method has significant limitations in its use. The use of this method, in contrast to the method of optimal damping, is possible only for all-wheel systems. The selected approaches to the control law synthesis are compared. It is shown that the selected control algorithms ensure the achievement of the control aim and guarantee the global asymptotic stability of the equilibrium position of a closed-loop system. Examples of simulation modeling are given, demonstrating the correct functioning of a closed-loop control system.
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