SYM — Program Package for Computer-aided Generation of Optimal Symbolic Models of Robot Manipulators

This contribution presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form. Since the computational efficiency of the generated symbolic models is extremely high, the real-time implementation of rather complicated mechanical equations become possible even on low-cost microcomputers.The program package SYM is concerned with serial-link manipulators with stiff or elastic joints. The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be modeled. The high-level program code for computing various kinematic and dynamic variables (elements of homogeneous transformation matrices, Jacobian matrices, driving torques, elements of dynamic model matrices etc.) is generated. The application of recursive symbolic relations yields high, but not the minimal numerical complexity. Thus, we also apply the second-step optimization of the generated symbolic code. This step is based on the extraction of the expressions which appear more that once in the output code.