On Some General Methods for Mathematical Modeling of the Dynamics of Manipulators with Parallel Kinematics

The level of development of technology for obtaining and processing measurement information, power electronics and actuators allows the use of the results of mathematical control theory with incomplete information in modern mechatronic systems. These results create the possibility of minimizing interference in the behavior of the object by minimizing the amount of measurement information and the number of actuators involved. A necessary condition for the realization of this possibility is the presence of an adequate nonlinear mathematical model of the control object. The development of methods for creating such models is hampered not so much by the technical complexity of the system under study, but by the fact that fundamentally new problems often arise in the study of a specific actually functioning device, which have never been encountered before in the relevant theory. Their solution requires research by theoretical specialists on the further development of the complex application of areas of analytical mechanics, nonlinear theory of stability, mathematical control theory with incomplete information, information technologies, etc., which were previously quite distant from each other. Rigorous justification of methods for obtaining such mathematical models, is based on complex sections of mathematics, mechanics and control theory, which have never been included in the curricula of standard engineering education. However, in our opinion, a significant expansion of the practical application of the latest results in engineering practice is possible due to such a presentation of algorithms for their qualified application, which does not require a complete understanding of all the abstract-theoretical foundations of their justification.