On the Problem of Optimal Control of the Motion of Two-Link Planar Manipulator with Nonseparated Multipoint Intermediate Conditions

Abstract

The study focuses on the problem of optimal control of the motion of a two-link planar manipulator on a fixed base with given initial and final conditions, nonseparated conditions for the values of the phase vector at intermediate times, and with a quality criterion given over the entire time interval. It is assumed that absolutely rigid links of the manipulator are interconnected by an ideal cylindrical hinge, and the similar hinge is used to attach the first link to the base. The optimal rules of changing the control moments are constructed, which allow the manipulator to move from a given initial state to a final one, satisfying nonseparated multipoint intermediate conditions. An application of the proposed approach is exemplified by constructed control functions and the corresponding motion with given nonseparated conditions for the values of the phase vector coordinates at some two intermediate times.