Dynamic Modeling of Flexible Manipulators without their Mass Matrices Inversion

Abstract

In recent scientific literature, much attention is paid to the optimal modeling of elastic dynamical systems. The relevance of these studies is dictated by the ever-increasing demand in the control theory of high-precision robotic manipulators and automatic mechanisms, which consists in the need for continuous adjustment of the movement of their executive bodies in real time, with account for the flexibility of the constituent links of these systems. The generalized Newton --- Euler method formulated in this regard served as a reliable platform for a subsequent progressive modification of dynamic analysis for a wide class of elastodynamic systems. The purpose of the study is to improve the existing computational algorithms to accelerate the computational process of dynamic analysis of flexible manipulators. In this regard, relying on symbolic-iterative calculus, we formulated and solved the mixed dynamic problem of the manipulators without inverting their mass matrices. Furthermore, we modified the Newton --- Raphson method, intended for a numerical integration of the Newton --- Euler equations of motion. Finally, we dynamically calculated the spatial five-elastic link manipulator by comparing the speed of computational processes carried out at constant accuracy of the problem modeling, and assessed the efficiency of the method of dynamic analysis of the manipulators. In this study, we introduce an advanced method of dynamic modeling of flexible manipulators without the well-known procedure of their mass matrices inversion