On the Control Problem of a Two-link Flat Manipulator with Nonseparate Multipoint Intermediate Conditions

Abstract

The article solves the problem of programmed control of the movement of a two-link flat manipulator on a fixed base with given initial, final conditions and unseparated values of the phase vector at intermediate points in time. Absolutely rigid links of the manipulator are interconnected by an ideal cylindrical hinge, and using the same hinge the first link is fixed to the base. Thus, the manipulator can perform movements only in the horizontal plane. The movements of the manipulator are described by a system of second-order Lagrange equations. The task of constructing programmed movement control of such a dynamic system is to construct laws of change in control moments that allow the manipulator to carry out programmed movement that transfers the system from a given initial state, ensuring satisfaction of the unseparated multipoint intermediate conditions, to the final state. Solutions of the considered problem are constructed using the methods of theory of control of finite-dimensnal systems with unseparated multipoint intermediate conditions. As an application of the proposed approach, functions of control and corresponding movement are constructed with given unseparated conditions on the coordinates of the phase vector at some two intermediate points in time. The corresponding graphs are constructed for the coordinates of the phase vector of the manipulator, confirming the theoretical results obtained.