A new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form

This paper presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form. 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 modelled. The output of the package is high-level computer program code for evaluation of various kinematic and dynamic variables: the homogeneous transformation matrix between the hand and base coordinate frame, Jacobian matrices, driving torques and the elements of dynamic model matrices. The dynamic model is based on the recursive Newton-Euler equations. The application of recursive symbolic relations yields nearly minimal numerical complexity. Further improvement of computational efficiency is achieved by introducing different computational rates for the terms depending on joint angles, velocities and accelerations. A comparative study of numerical complexity for several typical industrial robots is presented.

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