Control of a Bilinear Model with Delay for a Single-Link Manipulator

Abstract

The problem of controlling a single-link technological manipulator on a mobile platform with time delays in the control system is considered. The delays appear, in particular, in the actuators of the manipulator. The mobile robot contains a wheeled group and a tracked group. The movement of the wheeled and tracked groups relative to each other allows reconfiguring the transport system to overcome obstacles. The manipulator is designed to perform technological operations, such as clearing rubble in emergency situations. A bilinear model for an onboard single-link manipulator is investigated. A mathematical model with a delay of the manipulator is constructed to find optimal control. The model of the manipulator control process is described by a nonlinear model. The control moment of the actuator is formed using regulators with an aftereffect from the beginning of the movement to the current moment. The task of optimal control of the manipulator is to determine the admissible control that minimizes the functional describing the deviation of the manipulator movement angle from the specified position and the proximity of its angular velocity to zero. The admissible control is a piecewise continuous function. A control minimizing the functional, depending on time and the measured trajectory is found. The functional and control correspond to the Bellman equation. The problem of synthesizing the optimal control of a single-link manipulator is reduced to finding a solution to a system of differential equations that satisfies the boundary conditions at the ends of the control interval.