Análise da eficiência computacional para solução do problema da cinemática inversa de robôs antropomórficos utilizando a teoria de bases de Gröbner.

Abstract

The Denavit-Hartenberg algorithm is a method used for decades to solve one of the classic problems in the kinematics of robotic manipulators, the inverse kinematic problem. When this method is used, there is a need for additional algorithms to solve the problem, such as the Paul method. The Gröbner Bases Theory for the solution of inverse kinematics, as a supplementary method to the Denavit-Hartenberg algorithm, will be presented in this work. To familiarize the reader with each method, the manipulator robots Stäubli TS20, a SCARA type robot, and Unimation PUMA 560, an anthropomorphic manipulator with six rotating joints, will be used as case studies applying the Paul method and the method proposed in this work, where the computational efficiency data will be used for comparison. The main goal of this work is to analyze the computational efficiency in solving the problem of the inverse kinematics of anthropomorphic manipulating robots using both methods. With each approach, the problem of inverse kinematics for the two serial robots will be solved. When comparing each method, this work will demonstrate that the method using Gröbner Bases Theory is more computationally efficient for the solution of the inverse kinematic problem of anthropomorphic robots.