IMPROVING EFFICIENCY OF SSCA KIDYM DYNAMICS PROGRAM MODULE BY USING AUTOMATICALLY GENERATED DLL-PROCEDURE AND BY OTHER MEANS

Abstract

The paper presents the results of research on the significant increase in the speed of solving the problems of the dynamics of discrete mechanical systems of an arbitrary form with arbitrary links by a special system of computer algebra (SSCA) KiDyM. In particular, an algorithm for determining the parameters of the additional rotation of the central coordinate systems (CS) of solid bodies in the presence of a non-diagonal inertia tensor to transform them into the main central SCs, in which Euler's equations have the simplest form, is implemented. The main central moments of inertia of the body are determined. A simpler description of SC transformations of robot links with open kinematic chains is proposed. It consists in a separate description of the positions of the SC of the links and the positions of the center of mass and the central SC in relation to the SC of the link. This approach leads to localized description of the kinematics of the mechanism and complete information about the inertial parameters of the link, such as mass, inertia tensor, position of the central SC. The possibility of errors in model descriptions is thereby reduced. On the example of the model of the lower limbs of an human like robot, the gain in the number of machine operations of this description is shown. The use of the software-generated DLL procedure for saving the mathematical model of the system is analyzed in detail. If necessary, it is loaded from an external medium (disk) into the computer's memory during numerical integration. For this purpose, a special procedure has been created in SSCA KiDyM, which transforms the internal representation of analytical expressions of the computer algebra system into program code in C++, calls the appropriate compiler, which creates and saves the DLL-procedure on the disk. In the numerical integration block, the system can load it and calculate the right-hand sides of the Cauchy form of the dynamic equations by the Runge-Kutta procedure. The time gain of this integration method compared to direct calculations of formula trees in PC memory for various tasks is shown. The time gain increases with the increase in the complexity of the mechanical system. A criterion for automatically switching such an algorithm depending on the amount of C++ code in the DLL procedure is proposed.