Implementation of optimal energy displacements of the working tool of the two-link manipulator along the parabolic trajectory
Authors: Loveykin Vyacheslav , Mishchuk Dmitriy , Mishchuk Yeuvgen 
Published: December 2022

The intensive spread of automated and robotic systems in the construction industry poses a number of problematic and unsolved problems related to the efficiency and reliability of their use, namely: reducing dynamic loads in the structural elements of robots and manipulators, reducing energy costs to perform a given process by a robotic system. Particular attention is paid to the quality of control, in particular, in a limited working space when moving working bodies with hydraulically actuated manipulators, which are dominant in construction.
Problems: For welding of metal structures or when laying building elements using handling systems, the technology for performing such work involves the use of the tasks of moving special working bodies along parabolic trajectories. To implement the tasks set by manipulators, it is necessary to determine the control laws for the drive system. One of the ways to find the necessary functions for the control system is the use of optimization problems according to energy criteria and imposed geometric restrictions.
Purpose: to develop and investigate the modes of movement of the drive mechanism of a hydraulic manipulator with the implementation of an energy-intensive mode of operation of a mechanical system in a given space of movement of the working body along a hyperbolic trajectory.
Methodology: To achieve the goals of the study, it is proposed to use the optimization problem of minimizing energy consumption in the boom system of a two-link manipulator on a given parabolic trajectory of movement of its working body in a limited working space. In this paper, we consider the problem of conditional optimization, where the restrictions of the working space are imposed by the conditions of movement of the working body and the limiting restrictions on the movement of actuators. The objective optimization function is formed in the form of Lagrange equations from the components of energy consumption and the equation of a parabola that specifies the movement of the manipulator grip.
Results: To implement the optimal control of a two-link manipulator on a given parabolic trajectory, it is necessary to determine the extremals of the objective function functional in the form of the Lagrange equation for the components, which in this study were convolutions from the dependencies of energy consumption and the given equation for the trajectory of movement of the working body. The search for the minimum of the objective function is obtained in numerical form, based on which the form of the polynomial of the analytical dependence of the generalized coordinates on time is determined.
Conclusions: In further research, it is desirable to consider criteria that take into account various force loads, in particular, the root-mean-square value of the drive force and the intensity of its change over time, and it is also necessary to develop polynomial functions that can be used to express numerical solutions to optimization problems.