Symbolic calculation of the generalized inertia matrix of robots with a large number of joints

Abstract

The aim of this paper is to simplify numerical simulation of robots with a large number of joints. Many numerical methods based on different principles of mechanics are developed to obtain the equations that model the dynamic behavior of robots. In this paper, the efficiency of computer algebra application was compared with the most popular methods of forming the generalized inertia matrix of robots. To this end, the computer algebra system was used. Expressions for the generalized inertia matrix of the robots with a large number of joints have been derived, using the computer algebra technique with the following automatic program code generation. As shown in the paper, such an application could drastically reduce the number of floating point product operations, needed for efficient numerical simulation of robots.