Forward Kinematics Analysis of 6-DoF Articulated Robot using Screw Theory and Geometric Algebra

Abstract

This paper considers the problem of forward kinematics of serial robots in the geometric algebra framework. Unlike traditional techniques such as the Denavit-Hartenberg method, the approach of this work is to demonstrate the capacity of the geometric algebra (GA) to compute the forward kinematics. An important feature of this technique is the avoidance of the steps that are used in the traditional forward kinematics method, where it is well known that as the degrees of freedom (DoF) are increased, the traditional method is more tedious due to the large amount of D-H (Denavit-Hartenberg) parameters. In addition, using the traditional way is possible to have multiple results, although the analysis is still correct, could be a risk of confusion by different designers. Furthermore, the homogeneous matrices have diverse components that do not contain any relevant information (some 0s and 1s), where these components impact the computational cost of the algorithm. To avoid the mentioned issues, this work proposes an iterative method to compute the forward kinematics based on geometric algebra and screw theory, where the technique has been developed through SE(3). On the other hand, to illustrate the capability of the method, a numerical simulation of a 6-DoF robot has been computed using diverse positions.The present work is intuitive for new readers interested in the robotic field. With the new method, the users don’t need to have advanced knowledge of classical mechanics or vector algebra.