Optimization of trajectories of industrial manipulators by the method of moments

Abstract

Modern robotic systems are widely used in industry to perform tasks requiring high accuracy, speed, and reliability, and the existing optimal motion control of industrial manipulators faces several problems related to constraints on power consumption, computational resources of controllers, and dynamic characteristics of the system. In conditions where acceleration constraints and possible external disturbances must be considered, traditional methods of optimal control, such as dynamic programming and numerical solutions of boundary value problems, turn out to be computationally complex and not always applicable in real-time systems. The method of moments and its modifications allows us to construct a unified algorithm that ensures minimization of the cost functional while respecting the given constraints. The main advantage of the method of moments is its computational efficiency, which makes it the most effective tool for application in robotic systems. The scientific novelty of the study lies in the development of an iterative method that allows finding optimal control actions without the need to solve complex boundary value problems. The approach proposed by the authors allows us to adapt the control action depending on the changing conditions of the manipulator, for industrial processes where high control flexibility is required. The mathematical aspects of the method of moments, the algorithm of its adaptation to the tasks of trajectory control of industrial manipulators are analyzed, and the practical significance of this approach for robotic control systems is investigated. The results obtained prove that the method of moments is promising for optimizing the motion of manipulators under resource constraints and can be integrated into adaptive control systems for industrial robots.