Comparativo entre métodos Jacobianos para solução da cinemática inversa de um manipulador baseado em quatérnios duais

Abstract

Inverse kinematics is an open problem in robotics, due to its high complexity and non-linearity. Comparative among the several methods of solution of this problematic is topic of tendency in the academic environment. There is also an evident academic interest in the application of modern tools for the solution of forward kinematics, such as the use of unit dual quaternions, to the detriment of classic homogeneous transformation matrices. In this work four Jacobian methods for the solution of inverse kinematics were compared, describing the structure of a manipulator with seven degrees of freedom through the dual quaternion algebra. The methods were implemented and analyzed in a simulation environment through Matlab software and performance metrics such as execution times, success rate, positional accuracy and error behavior over time for each method, evaluating 10,000 situations. The results were analyzed in the means of tables and comparative graphs, aiming to observe the performance of each algorithm in the various aspects (sic).