Analysis of the base motion model of industrial robots moving

ANALYSIS OF THE BASE MOTION MODEL OF INDUSTRIAL ROBOTS MOVING
R. Siddikov, D.K.Muhamediyeva, Мелизияев A.O., Мамасолиев A.A.


Abstract. Development of mathematical models and algorithms for optimal control of the functioning of industrial robots on a movable base to ensure the accuracy of the trajectory of movement and positioning is considered. An equation for the functioning of industrial robots on a movable base in the implementation of a complex spatial operation obtained and, on its basis, a mathematical model of optimal control is developed.
Keywords. Industrial robots, motion model, optimal control system, algorithm.


1. Introduction. Models of movement and control of industrial robots usually developed taking into account two components of the system: the base and the actuator of industrial robots. Accordingly, the control system of industrial robots also consists of two parts. For the base, the control will be direct (immediate), and for the actuator - feedback control. Analysis of studies shows that there are a number of shortcomings of actuators controlled by a feedback system [1-3]:
1. When the robot moves together with the part in existing models, the gravity of the part is taken into account only when calculating the last link - the gripping element, and when calculating the remaining intermediate links, this factor is not taken into account.

2. 
   The non-linearity of the impact of force factors formed during the movement of industrial robots on the connections is not taken into account; the movements of intermediate links are described by second-order differential equations, as analysis of the literature shows, with constant coefficients. According to practice, these differential equations should take into account the variability of the coefficients.
   

3. Primary motion error of industrial robots on a movable base is determined using the methods of the logical tree of possibilities and statistical testing. The Logical Possibility Tree is a short and simple method that provides the positional accuracy of the robot based on the distribution laws of discrete primary errors. However, this method has its drawbacks. In it, the model is not explicit and the decision is based on the knowledge and conclusions of the person who makes the decision. During the manipulation, not all parameters are taken into account, and the logical movements of the links are presented in a tree form. The logical feature tree is more in line with the links that move in sequence. It does not apply to links moving at the same time.
4. The main goal pursued from involving robots in the production process is to accurately and quickly perform all the operations of the process and timely provide the consumer with a quality product or semi-finished product. This is especially noticeable, for example, in machining processes in the mechanical engineering industry. When drawing up the equations of motion of the robot, external forces are taken into account, but internal forces are neglected. So, for example, when a robot moves with a part, it is necessary to take into account both external and internal forces.
Development of ways to control the objects under study, devoid of the above disadvantages, is one of the urgent problems in the field of research.