Abstract
In this paper, the trajectory tracking control problem of a robot manipulator with cylindrical joints is considered by means of a nonlinear PD controller taking into account the delayed feedback structure. The conclusion about stability of a closed-loop system is obtained on the basis of the development of the direct Lyapunov method in the study of the stability property for a non-autonomous functional differential equation by constructing a Lyapunov functional with a semi-definite time derivative.
Highlights
Among the main control problems for robotic systems is the trajectory tracking of manipulators, mobile robots, mobile manipulators, unmanned aerial vehicles, and other systems
The aim of this paper is to study, in a nonlinear formulation, the trajectory tracking control problem of a serial robot manipulator with cylindrical joints with the determination of the admissible delay in the feedback structure
The direct Lyapunov method is developed in the direction of determining the properties of asymptotic stability, attraction of solutions of a nonautonomous functional differential equation with a righthand side which is periodic in a part of independent variables
Summary
Among the main control problems for robotic systems is the trajectory tracking of manipulators, mobile robots, mobile manipulators, unmanned aerial vehicles, and other systems. Certain difficulties lie in the need to compensate for centrifugal, Coriolis and gravitational forces In robotics, such a drawback can be avoided by using relay controllers [Khalil, 2001], [Spong et al, 2004], [Utkin et al, 2020]. The aim of this paper is to study, in a nonlinear formulation, the trajectory tracking control problem of a serial robot manipulator with cylindrical joints with the determination of the admissible delay in the feedback structure. The direct Lyapunov method is developed in the direction of determining the properties of asymptotic stability, attraction of solutions of a nonautonomous functional differential equation with a righthand side which is periodic in a part of independent variables
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