Analysis of Computational Efficiency applied to forward and Inverse Kinematics of Robotic Manipulators using Homogeneous Transformation Matrixes and Dual Quaternions

Abstract

The present work proposes a detailed study of the implementation of a mathematical tool called dual quaternions and a depth analysis of its evolution and potential application on the robotics field. In parallel to this view is presented a comparison between the traditional way of calculating rotation and translation in the kinematics of manipulator robots. Dual quaternions have been massively used in robotics because they are computationally more efficient in representing rotational information than the representation with homogeneous transformation matrices. Thus, this work aims to provide a detailed explanation through a step-by-step for the use of quaternion algebra, in a simplified way, were used examples to better understand the implementation. Although there is a lot of literature about the theoretical aspects of dual quaternions, in a few of them there are practical examples of how their use really works. This work gives a clear notion of the introduction to the dual quaternion theory, in addition to it,  this document also demonstrates its application to a 4-DOF serial robotic manipulator. In this dissertation it was possible to make a comparison between the direct and inverse kinematics calculated using the matrix algebra versus the quaternionic algebra, it was verified that the quaternions are computationally more efficient although they do not allocate smaller area of the program memory for the Atmel microcontroller Atmega 328/P. Simulations and experimental tests were performed to prove the results.